what are the steps is problem solving involving division and other operations

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Here you will learn about division, including dividing into equal groups, long division, dividing decimals, and dividing fractions.

Students will first learn about division as part of operations and algebraic thinking in 3 rd grade.

What is division?

Division is the process of splitting a number into equal parts or a group of objects into smaller, equal groups. Division is one of the four basic operations (arithmetic operations) and it is the inverse or opposite of multiplication.

To write a division equation, you write the number being divided, the dividend , then a division sign, and then the number that the dividend is being divided by, which is called the divisor . The answer to a division equation is called the quotient .

For example,

Annie wants to split her 28 marbles into equal groups of 4. How many marbles will be in each group?

You would write this as

To solve, you need to divide 28 into 4 equal groups.

There are 7 in each group, so 28 \div 4=7

You can also solve division facts by writing the equation as an unknown factor problem.

For example, you can solve 28 \div 4 by finding the number that makes 28 when multiplied by 4.

• Long division

To divide larger numbers, you can use the standard algorithm for division, or long division.

Long division is a method of dividing a multi-digit number by another number by repeatedly subtracting multiples of the divisor from the dividend, determining the quotient digit by digit, and bringing down additional digits until the division is complete.

The quotient is shown at the top. There is no remainder, so

If a division problem ends in a remainder, the reminder can be written next to the quotient at the top. For example, if there was a remainder of 2, this could be written as R 2. Remainders can also be written as fractions or decimals.

Dividing fractions

To divide fractions, multiply the dividend (the first number in the equation) by the reciprocal of the divisor (second number in the equation). To find the reciprocal of a fraction, switch the numerator and denominator.

Note that a whole number written as a fraction would be the number over 1, so its reciprocal would be 1 over the number. Example: 5=\frac{5}{1} so its reciprocal is \frac{1}{5}.

To remember this process of dividing, think “Keep Change Flip.”

Dividing decimals

You can divide decimals using the standard algorithm, or long division. However, the divisor must be a whole number before you can start the long division process.

If the divisor is a decimal, you must multiply it by a power of 10 to shift the digits so there is no longer a decimal point. Whatever you multiply the divisor by, you must also multiply the dividend by.

a) 8.6 \div 2={?}

Since the divisor is a whole number, you can perform long division. Notice that the decimal point moves straight up to the same place in the quotient.

So, 8.6 \div 2=4.3

b) 24.66 \div 1.8={?}

In this example, the divisor, 1.8, is a decimal. Before you can begin the long division process, you will need to multiply 1.8 by a power of 10 so that it will be a whole number. Then you will need to multiply the dividend by that same power of 10.

To make 1.8 a whole number, you can multiply it by 10. Then you also multiply 24.66 by 10. So now, you would use long division to solve 246.6 \div 18.

Common Core State Standards

How does this relate to 3 rd grade through 6 th grade math?

• 3rd Grade – Operations and Algebraic Thinking (3.OA.A.2) Interpret whole-number quotients of whole numbers, e.g., interpret 56 \div 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 \div 8.
• 3rd Grade – Operations and Algebraic Thinking (3.OA.B.6) Understand division as an unknown-factor problem. For example, find 32 \div 8 by finding the number that makes 32 when multiplied by 8.
• 4th Grade – Number and Operations in Base Ten (4.NBT.B.6) Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• 5th Grade – Number and Operations in Base Ten (5.NBT.B.6) Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• 5th Grade – Number and Operations in Base Ten (5.NBT.B.7) Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
• 5th Grade – Number and Operations—Fractions (5.NF.B.7, 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (\cfrac{1}{3}) \div 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (\cfrac{1}{3}) \div 4 = \cfrac{1}{12} because (\cfrac{1}{12}) × 4 = \cfrac{1}{3}. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 \div (\cfrac{1}{5}), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 \div (\cfrac{1}{5}) = 20 because 20 \times (\cfrac{1}{5}) = 4 Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} lb of chocolate equally? How many \cfrac{1}{3} -cup servings are in 2 cups of raisins?
• 6th Grade – Number and Operations—Fractions (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (\cfrac{2}{3}) \div (\cfrac{3}{4}) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (\cfrac{2}{3}) \div (\cfrac{3}{4}) = \cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, (\cfrac{a}{b}) \div (\cfrac{c}{d}) = \cfrac{ad}{bc}.) How much chocolate will each person get if 3 people share \cfrac{1}{2} lb of chocolate equally? How many \cfrac{3}{4} -cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} mi and area \cfrac{1}{2} square mi?
• 6th Grade – Number and Operations—Fractions (6.NS.B.2) Fluently divide multi-digit numbers using the standard algorithm.
• 6th Grade – Number and Operations—Fractions (6.NS.B.3) Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

[FREE] Multiplication and Division Worksheet (Grade 4, 5 and 7)

Use this quiz to check your grade 4, 5 and 7 students’ understanding of multiplication and division. 10+ questions with answers covering a range of 4th, 5th and 7th grade multiplication and division topics to identify areas of strength and support!

How to divide

In order to divide objects into equal groups:

• Identify the total number of objects.
• Determine the number of groups.
• Divide the objects into equal groups.

In order to divide using long division:

Set up the problem.

Divide, multiply and subtract.

Repeat step \bf{2} until the remainder is \bf{0}, or smaller than the divisor and finish to find the quotient.

In order to divide decimals:

If the divisor is a whole number, go to step \bf{3}. If not, decide the power of ten that will make the divisor a whole number.

Multiply both the divisor and the dividend by the same power of \bf{10} .

If the dividend is a decimal number, line up the decimal point of the dividend with the decimal point of the quotient. You may need to include zeros as place holders.

• Perform long division.

In order to divide fractions:

Take the reciprocal (flip) of the divisor (second fraction).

Change the division sign to a multiplication sign.

Multiply the fractions together.

If possible, simplify or convert to a mixed number.

Division examples

Example 1: divide objects into equal groups.

Marcus has 45 pieces of candy. He wants to divide his candy equally between himself and his 8 friends. How many pieces of candy will each person get?

Marcus has a total of 45 pieces of candy.

2 Determine the number of groups.

Marcus is going to divide his candy between himself and 8 friends, so the candy will be divided into 9 equal groups.

3 Divide the objects into equal groups.

45 \div 9=5 in each group

So each person gets 5 pieces of candy.

Example 2: long division (no remainder)

Solve 3211 \div 13 using long division.

When using long division, the numbers are set up under a symbol that is commonly referred to as a “bus stop” or a “house.”

The divisor goes outside of the “house” on the left, and the dividend goes inside the “house.” The quotient will go on top.

The remainder is zero, so the long division process is done.

That means 3,211 \div 13=247.

Example 3: long division (with remainder)

Solve 857 \div 5 using long division. Write the remainder as a fraction.

There is a remainder of 2. The directions state to write the remainder as a fraction. To do this, you write the remainder as the numerator and the divisor as the denominator.

So the quotient is 171 \cfrac{2}{5}.

Example 4: dividing decimals (whole number divisor)

Solve 71.4 \div 12 using long division.

In this division equation, the divisor, 12, is a whole number, so you can skip to step 3.

Do long division.

Notice that when getting a remainder when dividing decimals, you add a zero to the end of the dividend to bring down, then continue dividing.

Example 5: dividing decimals (decimal divisor)

Solve 5.13 \div 1.35 using long division.

The divisor, 1.35, is a decimal, so you need to multiply it by a power of 10 to make it a whole number.

To make 1.35 a whole number, you can multiply it by 10^2 or 100. You will also need to multiply the dividend by the same number.

So the new division equation will be 513 \div 135.

Since the dividend and divisor are now whole numbers, there is no decimal point in the dividend to bring up to the quotient. There will only be a decimal point in the quotient if there is a remainder.

So, 5.13 \div 1.35=3.8

Example 6: whole number divided by a fraction

Solve 6 \div \cfrac{2}{3}

Note that a whole number written as a fraction is the number as the numerator and 1 as the denominator. So the number 6 as a fraction is \cfrac{6}{1}.

\cfrac{6}{1} \times \cfrac{3}{2}=\cfrac{18}{2}

Example 7: fraction divided by a whole number

Solve \cfrac{4}{5} \div 3 .

The fraction is in its simplest form, so the quotient is \cfrac{4}{15}.

Example 8: fraction divided by a fraction

Solve \cfrac{3}{4} \div \cfrac{1}{2}

Teaching tips for division

• Review divisibility rules to assist students with long division. Divisibility rules help with long division by allowing students to more quickly identify potential divisors, reducing the number of attempts needed to find the correct one. For example, “A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. “
• Teach students different strategies for solving division problems, such as repeated subtraction, equal groups, or using multiplication facts. Encourage them to choose the strategy that works best for them.
• Offer plenty of opportunities for students to practice division through hands-on activities and games, not just worksheets.
• Knowing multiplication tables can help students divide, so provide practice for fluency as needed.

Easy mistakes to make

• Forgetting place value Students may forget to align digits correctly when performing long division, leading to errors in the quotient.
• Forgetting to check for remainders Students may forget to check for remainders or may incorrectly interpret them.

Related multiplication and division lessons

• Multiplication and division
• Multiplicative comparison
• Multiplying multi digit numbers
• Dividing multi digit numbers
• Multiplying and dividing integers
• Negative times negative (coming soon)
• Negative numbers
• Multiplying and dividing rational numbers (coming soon)

Practice division questions

1. Johnny has 30 marbles. He divided them evenly between 6 jars. How many marbles are in each jar? Which model represents this problem?

In this word problem, you have a total of 30 objects being divided into 6 groups, so you need to solve 30 \div 6.

The model that shows 6 groups with 5 circles in each group is correct.

2. Solve 1728 \div 27 .

You can find the quotient using long division.

3. Solve 893 \div 12. Write the remainder as a fraction.

First, use long division to solve. When doing so, you get a remainder of 5. To include the remainder in the quotient as a fraction, you write the remainder as the numerator and the divisor as the denominator.

Therefore, 893 \div 12=74 \cfrac{5}{12}

4. Solve 196.2 \div 9 .

This division problem has a decimal, which is the dividend. The divisor is a whole number, however, so you can jump right into the long division process to solve. The decimal point will be placed in the quotient in the same place as the dividend.

5. Solve 136.92 \div 8.4

Since the divisor is a decimal, first you need to multiply it by a power of 10 to make it a whole number. Since there is one decimal place, you can multiply it by 10 to make it a whole number. Then, you need to multiply the dividend by the same number before beginning the long division process.

6. Solve 9 \div \cfrac{1}{3} .

To solve, take the reciprocal of the divisor and then change to multiplication.

7. Solve \cfrac{3}{8} \div 6. Simplify your answer.

\cfrac{3}{48} can be simplified to \cfrac{1}{16}.

Since the directions specify that the answer must be simplified, the correct answer is \cfrac{1}{16}.

8. Solve \cfrac{5}{6} \div \cfrac{2}{3}. Simplify your answer.

\cfrac{15}{12} can be simplified to \cfrac{5}{4} then simplified again to 1 \cfrac{1}{4} \, .

Since the directions specify that the answer must be simplified, the correct answer is 1 \cfrac{1}{4}.

Division FAQs

Division is a mathematical operation that involves splitting a quantity into equal parts or groups, or determining how many times one number (the divisor) is contained within another number (the dividend). The result of division is called the quotient.

Division by zero is “undefined.” This means that it is not possible to divide any number by zero and get a meaningful result.

The division operation is represented by a horizontal line with a dot above and below it called an obelus (\div). It can also be represented by a forward slash (/).

The next lessons are

• Types of numbers
• Rounding numbers
• Factors and multiples

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Division Word Problems (2-step word problems)

Here are some examples of division word problems that can be solved in two steps. We will illustrate how block diagrams or tape diagrams can be used to help you to visualize the division word problems in terms of the information given and the data that needs to be found. We also learn how to solve multiplication and division word problems by identifying key terms.

Related Pages 1-Step Division Word Problems Multiplication and Division Word Problems More Word Problems More Singapore Math Lessons

Block diagrams are used in Singapore Math and tape diagrams are used in the Common Core Math.

We use division or multiplication when the problem involves equal parts of a whole. Sometimes, the problem involves comparison and it becomes a 2-step problem. The following diagram shows how to use equal parts of a whole and comparison. Scroll down the page for examples and solutions.

Example: Marcus had 700 marbles. He gave away 175 marbles and put the remaining marbles equally into 5 bags. How many marbles were there in each bag?

Solution: Step 1: Find how many marbles he had left.

700 – 175 = 525 He had 525 marbles left.

Step 2: Find the number of marbles in each box.

525 ÷ 5 = 105 There were 105 marbles in each box.

Example: Rosalind made 364 donuts. She put 8 donuts into each box. a) How many boxes of donuts were there? How many donuts were left over? b) If she sold each box for $3, how much money would she receive?

Solution: Step 1: Find the number of boxes of donuts.

364 ÷ 8 = 45 remainder 4 There were 45 boxes of donuts. 4 donuts were left over.

Step 2: Find how much money she would receive.

45 × 3 = 135 She would receive $135.

How to solve a 2-step division word problem using multiple tape diagrams?

Example: Ben is making math manipulatives to sell. He needs to make at least $450. Each manipulative costs $18 to make. He is selling them for $30 each. What is the minimum number he can sell to reach his goal?

How to use tape diagrams to solve fractional division problems? Basic algorithms and checks are also demonstrated.

Example: When someone donated 14 gallons of paint to Rosendale Elementary School, the fifth grade decided to use it to paint murals. They split the gallons equally among the four classes. a) How much paint did each class have to paint their mural? b) How much pain will three classes use? Show your thinking using words, numbers, or pictures. c) If 4 students share a 30 square foot wall equally, how many square feet of the wall will be painted by each student?

How to solve division word problems using the Algebra method and the Singapore Math method?

Example: Jeremy bought 8 identical pens and 5 identical notebooks. The cost of 8 pens is the same as the cost of 5 notebooks. Each notebook costs 30 cents more than each pen. How much did Jeremy spend altogether?

How to solve a multiplication and division 2-step problem? Using the comparison model, this video teaches how to approach a given 2-step problem on multiplication and division, and shows the detailed steps of how to solve it.

Example: Billy bought 5 bags of balls. Each bag contained 40 balls. He packed the balls into packets of 8 balls each. How many packets did he get?

How to solve a subtraction and division 2-step problem? Using the comparison model, this video teaches how to approach a given 2-step problem on subtraction and division, and shows the detailed steps of how to solve it.

Example: A boy collects a total of 316 stamps, stickers and coins. He collects 4 times as many stamps as stickers. There are 46 coins. How many stickers are there?

How to solve a division and fraction word problem visually?

Example: Mimi’s market sold 24 heads of lettuce one morning. That afternoon 2/7 of the remaining heads of lettuce were sold. The number of heads left was now 1/2 of the number the market had at the beginning of the day. How many heads of lettuce were there at the beginning of the day?

How to solve a part whole division word problems using bar models? Tips for Bar Modeling Division Problems

• Show units by dividing one long unit bar into its parts.
• If the question asks for the value of one of the parts of a unit bar, write your question mark right inside that section of the unit bar.
• 28 playing cards are arranged equally in 4 rows. How many playing cards are there in each row?
• If 18 cookies are arranged equally in 6 piles. How many cookies are there in each pile?
• A woman divided her lottery winnings of $92,000 into 8 equal parts. She gave 4 portions to her husband, 1 portion to her daughter, and divided the rest equally among three charities. How much more money did the husband receive than the daughter?
• Tralise has a library that she does not want to keep because she prefers digital books, so she divided to give her books away. She divided her collection of 1200 books into 10 equal parts. She gave 3 portions to her sister, 4 portions to her best friend, and the rest equally to three nieces. How many books did her best friend receive?
• Oscar had 3 times as many cookies as Zoe. After Oscar ate 50 cookies, he had half as many cookies as Zoe. How many cookies did Oscar have left?

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Course: 6th grade   >   Unit 7

• One-step division equations
• One-step multiplication equations

One-step multiplication & division equations

• One-step multiplication & division equations: fractions & decimals
• One-step multiplication equations: fractional coefficients

Multiplication and division are inverse operations

If we start with 7, multiply by 3, then divide by 3, we get back to 7:

7 ⋅ 3 ÷ 3 = 7 ‍  

If we start with 8, divide by 4, then multiply by 4, we get back to 8:

8 ÷ 4 ⋅ 4 = 8 ‍  

Solving a multiplication equation using inverse operations

6 t = 54 6 t 6 = 54 6                     Divide each side by six. t = 9                     Simplify. ‍  

Let's check our work.

Solving a division equation using inverse operations.

x 5 = 7 x 5 ⋅ 5 = 7 ⋅ 5                     Multiply each side by five. x = 35                     Simplify. ‍  

Summary of how to solve multiplication and division equations

Let's try solving equations.

• (Choice A)   Multiply each side by 8 ‍   . A Multiply each side by 8 ‍   .
• (Choice B)   Divide each side by 8 ‍   . B Divide each side by 8 ‍   .
• (Choice C)   Multiply each side by 72 ‍   . C Multiply each side by 72 ‍   .
• (Choice D)   Divide each side by 72 ‍   . D Divide each side by 72 ‍   .
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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4 Operations: Mixed word problems

Add / subtract / multiply / divide.

Students use the 4 basic operations (addition, subtraction, multiplication and division) to solve these word problems. Some questions will have more than one step. Mixing word problems encourages students to read and think about the questions rather than recognizing a pattern to the solutions.

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Lesson Plan: Word Problems: Multiplication and Division Mathematics • Third Year of Primary School

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers using multiplication facts up to 10 × 10.

Students will be able to

• identify whether a word problem can be solved by using multiplication or division,
• write equations to represent word problems,
• solve one- and two-step word problems involving multiplication and division,
• use multiplication or division to check the answer to a word problem.

Prerequisites

Students should already be familiar with

• multiplication facts up to 1 0 × 1 0 ,
• addition and subtraction of two-digit numbers,
• using bar models to model word problems,
• the fact that multiplication and division are inverse operations.

Students will not cover

• using fractions or decimals,
• solving problems with more than two steps.

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How to Solve Word Problems Involving the Division of Fractions

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• 00:04 How to solve word…
• 01:43 How to solve word…

Lisa has a bachelor's degree from Cal State Fullerton and a master's degree from the University of Kentucky, both in mathematics. She's taught College Algebra, Contemporary Mathematics, and a Mathematics for Elementary School Teachers sequence. She has also led workshops in mathematics courses ranging from Intermediate Algebra to Calculus III.

Bri Mallery holds a Bachelor of Science Degree in Applied Mathematics with an Emphasis in Computer Science from Chapman University, as well as a Master of Science Degree in Secondary Education. Bri has 9 years of teaching experience and has taught Pre-Algebra, Algebra 1, Geometry, and Algebra 2.

Step 1: Identify the fractions that will be divided, namely {eq}\frac{A}{B}, \ \frac{C}{D} {/eq} .

Step 2: Identify whether we are solving for "how many groups" or "how many units in one group" to be able to set up the equation {eq}\frac{A}{B}\div\frac{C}{D}= E, {/eq} where E is what we are solving for.

Step 3: Solve our equation by either multiplying by the reciprocal {eq}\big(\frac{A}{B}\times\frac{D}{C}=E\big) {/eq} or rewriting our equation as a multiplication problem and solving by cross-multiplication {eq}\big(\frac{A}{B}=\frac{C\times E}{D}\big) {/eq}

Step 4: Interpret our answer in the context of the problem.

How to Solve Word Problems Involving the Division of Fractions: Vocabulary

Fraction Division: When we want to divide two fractions {eq}\frac{A}{B}, \ \frac{C}{D} {/eq}, we form the equation {eq}\frac{A}{B}\div\frac{C}{D}= E, {/eq} where E is what we are solving for. There are multiple perspectives for which we can understand how to divide fractions:

• How Many Groups? Say {eq}\frac{A}{B} {/eq} represents the number of units to be put into equal groups, and {eq}\frac{C}{D} {/eq} represents the number of units in 1 group. If we perform {eq}\frac{A}{B}\div\frac{C}{D}= E, {/eq} E represents how many groups we have to begin with. This equation is equivalent to solving {eq}\frac{A}{B}=\frac{C\times E}{D}. {/eq}
• How Many Units In One Group? Say {eq}\frac{A}{B} {/eq} represents the number of units to be put into equal groups, and {eq}\frac{C}{D} {/eq} represents the number of groups. If we perform {eq}\frac{A}{B}\div\frac{C}{D}= E, {/eq} E represents how many units are in one group. This equation is, again, equivalent to solving {eq}\frac{A}{B}=\frac{C\times E}{D}. {/eq}

There are also multiple techniques to solve these problems:

• Multiply by reciprocal: When performing division of fractions, this is the same as multiplication of our original fraction with the reciprocal of our second fraction. That is, {eq}\frac{A}{B}\div\frac{C}{D}= E, {/eq} can be rewritten as {eq}\frac{A}{B}\times\frac{D}{C}=\frac{A\times D}{B\times C}= E. {/eq}
• Cross-Multiplication: If we rewrite our division problem to be of the form {eq}\frac{A}{B}=\frac{C\times E}{D}, {/eq} we can multiply across the diagonal entries (top left with bottom right and top right with bottom left) to turn this into {eq}A\times D=B\times (C\times E). {/eq}

We will now demonstrate two examples in detail.

How to Solve Word Problems Involving the Division of Fractions: Example 1

Talia has a ribbon that is {eq}\frac57 {/eq} feet in length. For a project, she needs ribbon pieces that are {eq}\frac{1}{14} {/eq}feet long. How many pieces can she cut from her ribbon for this project?

Step 1: Identify the fractions that will be divided.

Our two fractions, in this case, are the {eq}\frac57 {/eq} feet of ribbon and the {eq}\frac{1}{14} {/eq} feet of ribbon.

Step 2: Identify whether we are solving for "how many groups" or "how many units in one group" 'to be able to set up the equation.

Note that our two units are the length of our ribbon and the pieces of our ribbon. The {eq}\frac57 {/eq} represents the amount of ribbon that needs to be separated into pieces (i.e., "the number of units to be put in equal groups" ), and the {eq}\frac{1}{14} {/eq} represents the size that each piece of ribbon should be (i.e., "how many units are in one group" ). We are solving for how many pieces of ribbon we will create in total (i.e., "how many groups" ), so we set up our equation as {eq}\frac{5}{7}\div\frac{1}{14}= E, {/eq} where E is what we are solving for.

Step 3: Solve our equation.

We can solve this either by cross-multiplication or multiplying by the reciprocal. For this problem, let's try the first method:

{eq}\begin{align} \frac{5}{7}&=\frac{1\times E}{14}\\ 5\times14&=7\times E\\ \frac{70}{7}&=E\\ E&=10 \end{align} {/eq}

In the context of this problem, we can create 10 pieces that are {eq}\frac{1}{14} {/eq} feet long from a {eq}\frac57 {/eq} foot piece of ribbon.

How to Solve Word Problems Involving the Division of Fractions: Example 2

Michael drinks {eq}\frac23 {/eq} cup of his milkshake, which is {eq}\frac45 {/eq} of a serving. How many cups would be in one serving of his milkshake?

Step 1: Identify the fractions that will be divided

Our two fractions in this case are the {eq}\frac23 {/eq} cup of milkshake and the {eq}\frac45 {/eq} of a serving.

Step 2: Identify whether we are solving for "how many groups" or "how many units in one group"' to be able to set up the equation.

Note that our two units are the length of cups of milkshake and the servings of our milkshake. The {eq}\frac23 {/eq} represents the amount of milkshake that has been consumed so far (i.e., "the number of units to be put in equal groups" ), and the {eq}\frac45 {/eq} represents the number of servings that the milkshake is worth (i.e., "how many groups" ). We are solving for how much milkshake is going to be in one serving (i.e., "how many units in one group" ), so we set up our equation as {eq}\frac23\div\frac45= E, {/eq} where E is what we are solving for.

We can solve this either by cross-multiplication or multiplying by the reciprocal. For this problem, let's try the second method:

{eq}\begin{align} \frac23\times\frac54&=E\\ \frac{2\times5}{3\times4}&=E\\ \frac{10}{12}&=E\\ E&=\frac56 \end{align} {/eq}

In the context of this problem, one serving of milkshake is worth {eq}\mathbf{\frac56} {/eq} of a cup .

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