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Ratio word problems
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Use ratios to solve these word problems
Students can use simple ratios to solve these word problems ; the arithmetic is kept simple so as to focus on the understanding of the use of ratios.
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Ratio worksheets including relating visual quantities, ratio word problems, rate and ratio problems and finding equivalent ratios. These PDF worksheets are designed for 3rd through 6th grade students and include full answer keys.
Visual Ratio Worksheets
Equivalent Ratios Worksheets
Describing Rates and Ratios
Ratio Word Problem Worksheets
What Is A Ratio?
A ratio is the relationship or comparison between two numbers of the same unit. It is used to indicate how big or small a quantity is when compared to another. For ratios to have meaning you must know what is being compared and the units that are being used.
For example, there are 2 apples and 4 oranges in a fruit basket. We are comparing 2 pieces of apples to 4 pieces of oranges that is in the fruit basket. A general ratio may say “parts” for the units. In our example, the unit that we will use is “pieces” or simply just apples and oranges (2 pcs of apples, 4 pcs of oranges; or 2 apples, 4 oranges).
We write this ratio in three different ways:
- Using the : symbol
- As a fraction
- Using the word “to”
Please refer to the chart below…
No matter how a ratio is written, it is important that it be simplified down to the smallest whole numbers possible, just as with any fraction. When simplifying ratios, we use the highest common factor or HCF (otherwise known as the greatest common factor or GCF) of each of the numbers in the ratio. The term “simplest form” is the same as “lowest form” in ratio and fraction.
For the example above, the highest common factor or greatest common factor would be 2 as we can divide both 2 and 4 by 2.
Solving Ratio Problems
Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. A part-to-part ratio shows how one part relates to another part, and a part-to-whole ratio shows how one part relates to the whole. Ratios like these are much more common than you might think.
Let’s use the same example above: There are 2 apples and 4 oranges in a fruit basket.
Part-to-part ratio is shown as follows:
- The ratio of apples to oranges is 2:4.
- The ratio of oranges to apples is 4:2.
Whereas, the part-to-whole ratio that denotes the relationship between apples or oranges to all the fruits in the basket is as follows:
- The ratio of apples to all fruits is 2:6
- The ratio of oranges to all fruits is 4:6
Since there are 2 apples and the total number of fruits in the basket is 6 (2 apples + 4 oranges), the ratio of apples to the all the fruits is 2:6. We use the same method with oranges. There are 4 oranges and the total number of fruits in the basket is 6 (2 apples + 4 oranges), the ratio of oranges to the all the fruits is 4:6.
Now that we know how to solve and write simple ratios, let’s discuss equivalent ratios.
Equivalent Ratios
Equivalent ratios are equal in value to each other. They are similar to equivalent fractions. If the “antecedent” or the first term, and the “consequent” or the second term of a given ratio are multiplied or divided by the same number other than zero, it gives an equivalent ratio.
For example, when the antecedent and the consequent of the ratio 2:4 are multiplied by 2, we get, (2 × 2) : (4 × 2) or 4:8. Here, 2:4 and 4:8 are equivalent ratios.
Similarly, when both the terms of the ratio 2:4 are divided by 2, it gives 1:2, and 4:8 divided by 2, it gives 2:4. Here, 1:2 and 2:4 are equivalent ratios as well.
Take note that in equivalent ratios, if you multiply or divide both the numbers of the ratio by the same number, you get an equivalent ratio.
Another tip when working with equivalent ratio is to use its fraction form. This way, you can easily find equivalent ratios in higher terms, ratios in lower terms, and a missing term.
To find equivalent ratios in higher terms, multiply each term of the ratio by the same number. To find equivalent ratios in lower terms, divide each term of the ratio by the same number.
To find a missing term or an unknown value, follow these simple steps:
Step 1: Do the cross multiplication of known values
- Step 2: Divide the product by the unknown value.
- Step 3: Check your answer by doing the cross multiplication. If the results are equal, then your answer is correct.
Ratio Word Problems
Ratios are what we use to compare certain number values. People everywhere use ratios and they are often used in many real-world situations, which makes it a valuable skill to master. It helps us to simplify many of our interactions by putting numbers into perspective. Ratios are used in discounts, budgeting, and coupons at grocery stores. Understanding ratios would also enable student to understand interest on loans and how they are paid off. Let’s take a look at a few word problems, and practice working through them.
Example 1: In a class, there are 12 boys and 16 girls. What is the ratio of boys to girls?
Alright, so let’s look at our problem, and see what it is asking us to find, and write out the information that we have been given.
So, there are 12 boys and 16 girls. Let’s write that down.
Now, the question is asking us to find the ratio of boys to girls. Well, we have 12 boys, and 16 girls, which gives us a ratio of 12:16. Note that when writing ratios, we write down what is mentioned first. In our example, “boys” is mentioned before “girls”.
The ratio of boys to girls is 12:16. Let’s look at another word problem.
Example 2: The ratio of girls to boys in a swimming club is 2:3. There are 18 girls. How many boys are there in the club?
Let’s start off the same way that we did our last problem. Read through the problem, write down what is given, and find out what is being asked.
We have all of our information given in the problem, but what are we looking for? It says that the ratio of girls to boys is 2:3 and that there are 18 girls. So, we need to find how many boys there are. How do we do that? We write the formula as follows:
To find a missing term or an unknown value, follow these steps I mentioned earlier:
Step 2: Divide the product by the unknown value.
Step 3: Check your answer by doing the cross multiplication.
The answer is correct because the results are equal. 2x27 equals to 54, and 3x18 also equals to 54.
Let’s try a word problem that involves rate and unit rate this time…
Rate is a ratio between two things that have different units of measure, while a Unit Rate describes the ratio of two different units for the quantity of one. We say that when the denominator in rate is 1, it is called Unit Rate .
Example 3: After working for 40 hours, Eric made $900 in gross pay. What is his pay rate per hour?
Again, read through the problem, write down what is given, and find out what is being asked.
To solve, we'll ignore the units ($ and hour) and focus just on the number part for a bit. Divide 900 by 40. You get 22.50. Eric’s pay rate is $22.50 per hour.
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Ratio Worksheets
Immerse yourself in practice with our printable ratio worksheets. Whether it is part-to-part ratios, part-to-whole ratios, identifying parts from the whole, or finding the whole from the parts, dividing quantities, generating equivalent ratios, or expressing the ratio in three different ways, that you are looking for, these pdfs have them all covered for your grade 5 through grade 8 learners. Instantly evaluate your ratio problems with the answer keys provided. Our free ratio worksheets are a must-have to get the ball rolling!
Part-to-Part Ratio | Level-1
Perk up with these part-to-part ratio worksheets and get children in grade 5 and grade 6 to count how many of one thing there is as compared to another and express it as a ratio.
- Download the set
Part-to-Part Ratio | Level-2
Fuel learning with these ratio pdfs where the two sets of objects are mixed up. Count the number of each kind and frame a ratio comparing the size of one number to the size of the other.
Part-to-Whole Ratio | Level-1
Comparing the number of butter cookies to the assorted cookies in a jar is an example of part-to-whole ratios. Measure the quantity of one item against the total and write the ratio.
Part-to-Whole Ratio | Level-2
Upscale with these printable part-to-whole ratio worksheets. Direct children to count the number of specified objects, add the three terms to find the whole and express them as a ratio.
Expressing Ratio in Three Ways | Pictures
Get acquainted with the different representations of a ratio. Count the two different sets of pictures and express the ratio by using "to", the colon symbol ":", and the fraction notation.
Representing Ratio in Three Ways | Standard
Doing away with pictures and presenting ratio in word format, these ratio worksheets are a sure-fire way to help learners transit easily as they read phrases and express the ratio in three ways.
Drawing Shapes to Represent the Ratio
Break away from the humdrum of regular printable ratio worksheets and get children to stay in the groove as they follow the instructions and sketch shapes to represent the ratio.
Coloring Objects to Represent the Ratio
Add a splash of color with these pdf worksheets where 5th grade, and 6th grade children are expected to color the specified number of objects as instructed and figure out the ratio.
Reducing Ratios to the Lowest Terms | Easy
Reducing is nothing but converting the ratio to its simplest form. Divide the antecedent and the consequent terms of the ratio, which are numbers within 50, by the GCF to reduce the ratio.
Reducing Ratios to the Lowest Terms | Moderate
Raise the bar for grade 6 and grade 7 learners with these reducing the ratios to the lowest terms worksheets where the number range gradually increases to 100.
Simplifying Ratios Involving Unit Conversion | Easy
Take your simplifying ratio skills to new heights with these pdfs. Using appropriate conversion formulas, make the units uniform and reduce the ratio to the simplest terms.
Simplifying Ratios Involving Unit Conversion | Moderate
Bring uniformity in the units before reducing the ratio to lowest terms as you make headway with these printable simplifying ratio worksheets involving numbers within 100.
Finding the Parts from the Whole
Add up the terms of the ratio. Divide the whole quantity by the sum of the parts to find the unit rate. Multiply each term with the unit rate to find the two parts. Not as complicated as it sounds!
Finding the Whole from Parts
The ratio of two numbers and the quantity of one part is provided. Scale up the other term by multiplying it and figure out the other quantity, add the two quantities to find the whole.
Dividing Quantities into 3-Part Ratios
Add the three terms to find the total number of parts the quantity should be divided into. Multiply each term in the ratio with the unit rate and share the quantity in the given ratio.
Writing the Equivalent Ratios
Scale up each ratio by multiplying the antecedent and the consequent terms by the same number and write an equivalent ratio and complete the table with the missing equivalent ratios.
Finding Unknown Quantities from Equivalent Ratios
Instruct 7th grade and 8th grade learners to simplify ratios and check for equivalence, work out the unknown quantity in an equivalent equation, and solve word problems too.
Ratio Word Problems
Go beyond books and practice the real-time application of ratio concepts as you solve word problems involving part-to-part ratios, part-to-whole ratios, and much more.
(27 Worksheets)
Proportion Worksheets
Comprehend the distinction between ratio and proportion with this batch of proportion worksheets offering exercises like finding proportions, identifying them from graphs, and more!
(120 Worksheets)
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RATIO WORKSHEETS
Welcome to our collection of ratio worksheets designed to help students practice and master the concept of ratios. Ratios are fundamental in mathematics and are used to compare quantities in different situations. Whether you’re introducing ratios for the first time or reinforcing previously learned concepts, these worksheets offer a variety of exercises suitable for different levels of proficiency. From basic ratio problems to more complex scenarios, students will find ample opportunities to sharpen their skills and deepen their understanding of ratios.
Our worksheets are designed to gradually increase in difficulty, allowing students to build upon their skills and knowledge as they progress through the exercises.
Ratio Worksheets
Parts of a ratio.
Write the parts of ratio using the given pictures.
Parts of a Ratio #1
Parts of a ratio #2, parts of a ratio #3, finding ratio.
Find the ratio and answer the given word problems.
Finding Ratio #1
Finding ratio #2, finding ratio #3, ratio in three ways.
Write the ratio in three different ways.
Ratio in Three Ways #1
Ratio in three ways #2, ratio in three ways #3, color & draw.
Color the pictures for the given ratio. Draw the pictures for the given ratio.
Color & Draw #1
Color & draw #2, color & draw #3, shaded/unshaded region.
Find the ratio for the shaded and unshaded regions.
Shaded/Unshaded Region #1
Shaded/unshaded region #2, shaded/unshaded region #3, simplifying ratio.
Simplify the ratio and color the way from start to finish.
Simplifying Ratio #1
Simplifying ratio #2, simplifying ratio #3, equivalent ratio.
These worksheets describe the equivalent ratio for easy understanding.
Equivalent Ratio #1
Equivalent ratio #2, equivalent ratio #3, ratio: money.
Here money concepts included, to find the ratio of shares.
Ratio: Money #1
Ratio: money #2, ratio: money #3, using customary units.
These ratio worksheets have problems with the customary units.
Using Customary Units #1
Using customary units #2, using metric units.
These ratio worksheets have problems with the metric units.
Using Metric Units #1
Using metric units #2, using metric units #3, ratio word problems.
Our worksheets help students understand how ratios are used in everyday situations, making learning more relatable and engaging.
Ratio Word Problems #1
Ratio word problems #2, ratio word problems #3, get posts by email.
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Ratio Worksheets
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Ratio and Proportion Worksheet
Welcome to our Ratio and Proportion worksheet page. Here you will find our range of 6th Grade worksheets which will help your child learn about ratios and proportions in a practical context.
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Ratio and Proportion Worksheets
Our ratio and proportion worksheets have all been designed to use pictures and practical contexts to support understanding.
The sheets have been put in order of difficulty, with the easiest first.
Each problem sheet comes complete with an answer sheet.
There are two sections to our worksheets:
- the first section involves using the image to work out the ratios and proportions involved.
- the second section involves coloring in the objects to show the required ratio, and working out the proportion of one object to the whole set.
Using these sheets will help your child to:
- learn about how ratio works;
- write and use ratios in their lowest terms;
- understand what proportion is and learn to show proportion in simplest form.
Want to test yourself to see how well you have understood this skill?.
- Try our NEW quick quiz at the bottom of this page.
Quicklinks to ...
- How do Ratio and Proportion Work?
Find the Ratio and Proportion Worksheets
Ratio and proportion color in worksheets.
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Ratio and Proportion Online Quiz
How do ratio and proportion work, how to work out ratios and proportions.
When we look at ratios, we are usually looking at the relationship of one object compared to another.
When we are looking at proportions, we are looking at one object compared to the whole set of objects.
Proportions are usually written as fractions.
Let's have a look at the example below:
There are 3 orange fish and 2 blue fish, so the ratio of orange fish to blue fish is 3:2.
There are 3 orange fish out of 5 fish, so the proportion of orange fish is 3 ⁄ 5 .
There are 2 blue fish out of 5 fish, so the proportion of blue fish is 2 ⁄ 5 .
What does lowest term ratio mean?
Just like fractions, ratios can be simplified.
We can simplify ratios by finding common factors of the numbers involved and dividing them all by the common factors.
The ratios are in lowest terms (or simplest form) when there are no more common factors except 1.
Look at the example below:
The ratio of yellow snails to red snails is 2 to 4 or 2 : 4.
Because these two numbers have a common factor of 2, they can both be divided by 2 to give a simpler ratio.
So 2 : 4 = 1 : 2
There are now no common factors apart from 1, so we cannot simplify the ratio further.
So the ratio of yellow snails to red snails in lowest terms is 1 : 2.
This means that there 1 yellow snail for every 2 red snails.
How can we simply the proportion?
The proportion is usually written as a fraction.
We can simplify the proportion by writing the fraction in simplest form.
Look at the snail example again:
There are 2 yellow snails and 4 red snails, so 2 out of 6 snails are yellow and 4 out of 6 snails are red.
The proportion of yellow snails is 2 ⁄ 6 . This can be simplified to 1 ⁄ 3 .
The proportion of red snails is 4 ⁄ 6 . This can be simplified to 2 ⁄ 3 .
Sheets 1 to 3 involve finding simple ratios and proportions with no need to convert to lowest terms. They are great as an introduction to ratio and proportion.
Sheets 4 and 5 involve recording ratios and proportions in lowest terms.
Sheet 6 involves recording ratios and proportions in lowest terms to 3 different objects. It is the hardest sheet.
- Ratio and Proportion Sheet 1
- PDF version
- Ratio and Proportion Sheet 2
- Ratio and Proportion Sheet 3
- Ratio and Proportion Sheet 4
- Ratio and Proportion Sheet 5
- Ratio and Proportion Sheet 6
These sheets involve coloring the objects according to the given ratios and working out the proportions.
Sheet 1 involves coloring in objects and recording numbers of objects where the ratios match the total number of objects.
Sheet 2 is similar to Sheet 1, but the number of objects is sometimes a multiple of the ratios.
Sheet 3 involves coloring 3 different objects and working out each of the 3 proportions according to the given ratios.
- Ratio and Proportion Color In Sheet 1
- Ratio and Proportion Color In Sheet 2
- Ratio and Proportion Color In Sheet 3
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
More Ratio & Unit Rate Worksheets
We have a selection of other ratio worksheets, which involve only ratio questions.
We also have a collection of ratio word problem worksheets.
- Ratio Part to Part Worksheets
- Unit Rate Problems 6th Grade
5th Grade Percentage Worksheets
Take a look at our percentage worksheets for finding the percentage of a number or money amount.
We have a range of percentage sheets from quite a basic level to much harder.
- Percentage of Numbers Worksheets
- Money Percentage Worksheets
- Percentage Word Problems
Related Fraction Worksheets
- Fractions Decimals Percents Worksheets
- Simplifying Fractions Worksheets
- Free Printable Fraction Riddles (harder)
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| → → Proportions Options include using whole numbers only, numbers with a certain range, or numbers with a certain number of decimal digits. Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file. You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program. Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options: Use these quick links to create some common types of proportion worksheets. Below, with the actual generator, you can generate worksheets to your exact specifications.
 Real World Algebra by Edward ZaccaroAlgebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty. GCSE Tutoring Programme "Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring." In order to access this I need to be confident with: This topic is relevant for:  Ratio Problem SolvingHere we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems. There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. What is ratio problem solving?Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem. A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,
As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer. The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution. Let’s look at a couple of methods we can use when given certain pieces of information.  When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation. For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets. Charlie and David share 40 sweets, how many sweets do they each get? We use the ratio to divide 40 sweets into 8 equal parts. Then we multiply each part of the ratio by 5. 3 x 5:5 x 5 = 15:25 This means that Charlie will get 15 sweets and David will get 25 sweets.
Step-by-step guide: Dividing ratios (coming soon)
Ratios and fractions (proportion problems)We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.
Simplifying and equivalent ratios
Equivalent ratios
Units and conversions ratio questionsUnits and conversions are usually equivalent ratio problems (see above).
Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life. Top tip: if you are converting units, always write the units in your ratio. Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages . Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios. How to do ratio problem solvingIn order to solve problems including ratios: Identify key information within the question. Know what you are trying to calculate. Use prior knowledge to structure a solution. Explain how to do ratio problem solving Ratio problem solving worksheetGet your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions. Related lessons on ratioRatio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Ratio problem solving examplesExample 1: part:part ratio. Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch? Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ? Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P). We could write this as  Where the letter above each part of the ratio links to the question. We know that 465 students have school dinner. 2 Know what you are trying to calculate. From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.  We need to find the value of p. 3 Use prior knowledge to structure a solution. We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other. So the value of p is equal to 7 \times 93=651. There are 651 students that have a packed lunch. Example 2: unit conversionsThe table below shows the currency conversions on one day.  Use the table above to convert £520 (GBP) to Euros € (EUR).  Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR). The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state  We know that we have £520. We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.  To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520. 1.17 \times 520=608.4 So £520 = €608.40. Example 3: writing a ratio 1:nLiquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n. Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n. Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000. 2l = 2000ml So we can also express the ratio as 500:2000 which will help us in later steps. We want to simplify the ratio 500:2000 into the form 1:n. We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).  So the ratio of plant food to water in the form 1:n is 1:4. Example 4: forming and solving an equationThree siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total? Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ? We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have  We also know that Luke receives £8. We want to calculate the total amount of pocket money for the three siblings. We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4. Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.  The total amount of pocket money is therefore 4+7+8=£19. Example 5: simplifying ratiosBelow is a bar chart showing the results for the colours of counters in a bag.  Express this data as a ratio in its simplest form. From the bar chart, we can read the frequencies to create the ratio.  We need to simplify this ratio. To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2. \begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned} HCF (12,16,10) = 2 Dividing all the parts of the ratio by 2 , we get  Our solution is 6:8:5 . Example 6: combining two ratiosGlass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda. Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda . We know the two ratios  We are trying to find the ratio of all 3 components: silica, lime and soda. Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.  We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.  Example 7: using bar modellingIndia and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity? India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity? We know that the initial ratio is 5:2 and that India has three more parts than Beau. We want to find the original quantity. Drawing a bar model of this problem, we have  Where India has 5 equal shares, and Beau has 2 equal shares. Each share is the same value and so if we can find out this value, we can then find the total quantity. From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.  We can find the value of one share by working out 75 \div 3=25g.  We can fill in each share to be 25g.  Adding up each share, we get India = 5 \times 25=125g Beau = 2 \times 25=50g The total amount of popcorn was 125+50=175g. Common misconceptions
Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.
For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.
Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ). 
For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.
The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal. Practice ratio problem solving questions1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?  8-3=5 computer games sold for every 3 board games. 2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K? 3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n. 4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle. 5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form. 6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month. Ratio problem solving GCSE questions1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules. Write this in the form 1gram:n where n represents the number of water molecules in standard form. 2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece. Calculate the length of the plank of wood. 5-3=2 \ parts = 36cm so 1 \ part = 18cm 3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K. (b) Sally is 16 years younger than Kim. Calculate the sum of their ages. Learning checklistYou have now learned how to:
The next lessons are
Still stuck?Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.  Find out more about our GCSE maths tuition programme. Privacy Overview Ratio Practice QuestionsClick here for questions, click here for answers, gcse revision cards.  5-a-day Workbooks Primary Study Cards Privacy Policy Terms and Conditions Corbettmaths © 2012 – 2024 Ratio WorksheetsRatio worksheets help students practice concepts like part-to-part, part-to-whole ratios, dividing quantities, reducing ratios, generating equivalent ratios, and more. These worksheets encourage students to practice more questions and solidify their understanding of the topic. Benefits of Ratio WorksheetsA ratio worksheet is beneficial when it comes to practicing the concept of ratio. These worksheets have questions in various formats which keep the learning process engaging and interesting. Ratio worksheets deal with the logical and reasoning aspect of mathematics and help students in real-life scenarios as well. The stepwise approach of these worksheets makes students solve a variety of questions with ease. These math worksheets also come with visuals which can help students to get a better understanding and easily navigate through these worksheets in an engaging manner. The stepwise approach of these worksheets helps students understand concepts better and solidify their understanding of the topic. Download Ratio Worksheet PDFsThese ratio worksheets can be downloaded for free in PDF format. Regular practice of these worksheets can help students score well in their exams.
☛ Check Grade wise Ratio Worksheets
 Simplifying Ratios Pixel Picture ( Editable Word | PDF | Answers ) Simplifying Ratios Odd One Out ( Editable Word | PDF | Answers ) Equivalent Ratios Match-Up ( Editable Word | PDF | Answers ) Working with Ratio Practice Strips ( Editable Word | PDF | Answers ) Dividing in a Ratio Practice Strips ( Editable Word | PDF | Answers ) Dividing in a Ratio Fill in the Blanks ( Editable Word | PDF | Answers ) Dividing in a Ratio Crack the Code ( Editable Word | PDF | Answers ) Combining Ratios Practice Strips ( Editable Word | PDF | Answers ) Sharing and Combining Ratios Practice Strips ( Editable Word | PDF | Answers ) Solving Ratio Problems Practice Strips ( Editable Word | PDF | Answers ) Solving Ratio Problems Practice Grid ( Editable Word | PDF | Answers ) Harder Ratio Problems Practice Strips ( Editable Word | PDF | Answers ) Fractions and Ratio Worded Problems Practice Strips ( Editable Word | PDF | Answers ) Unitary Method Practice Strips ( Editable Word | PDF | Answers ) Unitary Method Match-Up ( Editable Word | PDF | Answers ) Best Buys Practice Strips ( Editable Word | PDF | Answers ) *NEW* Best Buys Fill in the Blanks ( Editable Word | PDF | Answers ) Currency Conversions Practice Strips ( Editable Word | PDF | Answers ) Proportion Worded Problems Practice Strips ( Editable Word | PDF | Answers ) Proportion Worded Problems Practice Grid ( Editable Word | PDF | Answers ) Mixed Ratio and Proportion Revision Practice Grid ( Editable Word | PDF | Answers ) |
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These ratio worksheets will generate 16 Ratio and Rate problems per worksheet. These Ratio Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Ratios and Rates Word Problems Worksheets. These Ratio Worksheets will produce eight ratio and rates word problems for the students to solve.
K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. Become a member to access additional content and skip ads. Ratio word problems. Students can use simple ratios to solve these word problems; the arithmetic is kept simple so as to focus on the understanding of the use of ratios.
Find here an unlimited supply of worksheets with simple word problems involving ratios, meant for 6th-8th grade math. In level 1, the problems ask for a specific ratio (such as, "Noah drew 9 hearts, 6 stars, and 12 circles. What is the ratio of circles to hearts?"). In level 2, the problems are the same but the ratios are supposed to be simplified.
Ratio Word Problem Worksheets. We are delighted to share this set of extensively well-researched ratio word problem worksheets which will help students in grade 5 through grade 8 to grasp the basics of ratio calculations. These printable worksheets include simple theme-based ratio word problems, finding the ratio between two quantities, word ...
Here you will find a range of problem solving worksheets about ratio. The sheets involve using and applying knowledge to ratios to solve problems. The sheets have been put in order of difficulty, with the easiest first. They are aimed at students in 6th grade. Each problem sheet comes complete with an answer sheet.
Ratio worksheets including relating visual quantities, ratio word problems, rate and ratio problems and finding equivalent ratios. These PDF worksheets are designed for 3rd through 6th grade students and include full answer keys. ... Solving Ratio Problems. Ratios can be classified into two types. One is part to part ratio and the other is part ...
Download the set. Dividing Quantities into 3-Part Ratios. Add the three terms to find the total number of parts the quantity should be divided into. Multiply each term in the ratio with the unit rate and share the quantity in the given ratio. Download the set. Writing the Equivalent Ratios.
Ratio Problems Worksheet Solve.If the problem asks for a ratio, give it in simplified form. 1 a. A jar pinto beans and black beans in a ratio of 1 : 1, and 300 of the beans are pinto beans. How many beans in total are there in the jar? 2 a. Jayden and Caden share a reward of $140 in a ratio of 2 : 5. What fraction of the total reward does ...
From basic ratio problems to more complex scenarios, students will find ample opportunities to sharpen their skills and deepen their understanding of ratios. Our worksheets are designed to gradually increase in difficulty, allowing students to build upon their skills and knowledge as they progress through the exercises.
3 of the counters are red. 8. The other counters are yellow and white in the ratio 1:4. Work out how many counters of each colour there are. Question 10: The sizes of the interior angles of a pentagon are in the ratio 1:2:5:5:7 Calculate the size of the largest. Question 11: Jack is 10 years old.
The knowledge of ratio and translating the real word problems into mathematics is a must-have skill in order to get fluent in arithmetic and hence these worksheets aim at focussing at enough practice on ratios. Download Ratio Word Problems Worksheet PDFs. These math worksheets should be practiced regularly and are free to download in PDF formats.
Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to solve word problems that involve two and three way ratios. These worksheets explain how to solve two and three way ratio word problems. Sample problems are solved and practice problems are provided.
1 worksheet with 15 Ratio Problem Solving questions targeting the skills and knowledge needed in 6th Grade and 7th Grade. Practice with 10 skills based questions; then develop those skills further with 5 applied questions. Includes answer key with relevant common core state standards. Aligned to Ratio and Proportional Relationships, 6.RP.A.3, 7 ...
6rp1 × Description: "This worksheet is designed to enhance children's understanding of ratios in a fun and engaging way. Featuring 10 unique math problems, it uses real-life examples to teach the concept of proportional relationships. Ideal for distance learning, it can be easily customized, providing flexible formats such as flashcards.
Each problem sheet comes complete with an answer sheet. There are two sections to our worksheets: the first section involves using the image to work out the ratios and proportions involved. the second section involves coloring in the objects to show the required ratio, and working out the proportion of one object to the whole set.
Proportion Worksheets. Create proportion worksheets to solve proportions or word problems (e.g. speed/distance or cost/amount problems) — available both as PDF and html files. These are most useful when students are first learning proportions in 6th, 7th, and 8th grade. Options include using whole numbers only, numbers with a certain range ...
Proportion Word Problems. 3) One cantaloupe costs $2. How many cantaloupes can you buy for $6? 5) Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall? 7) Jasmine bought 32 kiwi fruit for $16. How many kiwi can Lisa buy if she has $4? 9) One bunch of seedlees black ...
By solving the problems in 6th grade ratio worksheets, children can increase their speed and accuracy. Questions are structured in a way to improve a student's logical and analytical abilities. These 6th grade math worksheets are provided with answer keys with step-by-step solutions to help students in case they get stuck while solving a question.
The Corbettmaths Textbook Exercise on Ratio: Problem Solving. ... Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. ... Ratio: Problem Solving Textbook Exercise. Click here for Questions. Textbook Exercise. Previous: Ratio: Difference Between Textbook Exercise. Next: Reflections Textbook ...
Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE . Related lessons on ratio. Ratio problem solving is part of our series of lessons to support revision on ratio. You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use ...
Click here for Answers. Practice Questions. Previous: Percentages of an Amount (Non Calculator) Practice Questions. Next: Rotations Practice Questions. The Corbettmaths Practice Questions on Ratio.
Ratio Worksheets - Worksheets aid in improving the problem-solving skills of students in turn guiding the kids to learn and understand the patterns as well as the logic of math faster. Access the best math worksheets at Cuemath for free. Grade. KG. 1st. 2nd. 3rd. 4th. 5th. 6th. 7th. 8th. Algebra 1. Algebra 2.
RATIO AND PROPORTION | Dr Austin Maths. Simplifying Ratios Pixel Picture (Editable Word | PDF | Answers ) Simplifying Ratios Odd One Out (Editable Word | PDF | Answers) Equivalent Ratios Match-Up (Editable Word | PDF | Answers) Working with Ratio Practice Strips (Editable Word | PDF | Answers) Dividing in a Ratio Practice Strips (Editable Word ...