Adding and Subtracting Mixed Numbers Worksheets

How to Practice Operations with Mixed Numbers - Mixed numbers are the numbers that consist of a whole number and a fraction part. When performing operations on mixed numbers, we first convert them into an improper fraction and then perform any operation on them. Addition and Subtraction - The following steps are for performing addition and subtraction on a mixed number: First, convert all the mixed fractions of the given problem into improper fractions. Multiply the denominator with the whole number and add the product with the numerator. Multiply the numerator and the denominator of an improper fraction by a factor to get the lowest common denominator for each fraction. Add or subtract the fractions. Reduce the obtained fraction, if possible, and convert the improper fraction into a mixed number. Multiplication - The following steps are for performing multiplication on a mixed number: First, convert the given mixed number in the problem into improper fractions. Multiply the denominator with the whole number and add the product with the numerator. Next, multiply the numerators and the denominators. In case you can also reduce the numerators with denominators. Once you have multiplied, reduce the fraction, if possible. If the obtained fraction is improper, then convert them into a mixed number. Division - The following steps are for performing addition and subtraction on a mixed number: First, convert all the mixed fractions of the given problem into improper fractions. Multiply the denominator with the whole number and add the product with the numerator. Change the division into multiplication by taking the reciprocal of the divisor, for taking reciprocal; you will have to convert the numerator into denominator and the denominator into the numerator. Multiply the denominators and the numerators. In case you can also reduce or simplify the problem. Reduce the obtained fraction if possible. Convert the fraction into a mixed number if the achieved fraction is improper.

Basic Lesson

Demonstrates the addition, subtraction, and simplification of mixed numbers. Includes practice problems.

Intermediate Lesson

Shows students step by step how to add, subtract, and reduce mixed numbers.

Independent Practice 1

Students add and subtract a series of mixed numbers. The answers can be found below.

Independent Practice 2

18 problems that review all skills within the unit. The answer key is below.

Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

10 problems that test Adding and Subtracting Mixed Numbers skills. Scoring matrix.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

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Grade 7 - Expressions & Equations

Standard 7.EE.B.3 - Practice rounding mixed numbers to the nearest whole number.

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4.10: Add and Subtract Mixed Numbers (Part 1)

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Learning Objectives

  • Model addition of mixed numbers with a common denominator
  • Add mixed numbers with a common denominator
  • Model subtraction of mixed numbers
  • Subtract mixed numbers with a common denominator
  • Add and subtract mixed numbers with different denominators

be prepared!

Before you get started, take this readiness quiz.

  • Draw figure to model \(\dfrac{7}{3}\). If you missed this problem, review Example 4.1.6 .
  • Change \(\dfrac{11}{4}\) to a mixed number. If you missed this problem, review Example 4.1.9 .
  • Change \(3 \dfrac{1}{2}\) to an improper fraction. If you missed this problem, review Example 4.1.11 .

Model Addition of Mixed Numbers with a Common Denominator

So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.

If Ron has \(1\) dollar and \(1\) quarter, he has \(1 \dfrac{1}{4}\) dollars. If Don has \(2\) dollars and \(1\) quarter, he has \(2 \dfrac{1}{4}\) dollars. What if Ron and Don put their money together? They would have \(3\) dollars and \(2\) quarters. They add the dollars and add the quarters. This makes \(3 \dfrac{2}{4}\) dollars. Because two quarters is half a dollar, they would have \(3\) and a half dollars, or \(3 \dfrac{1}{2}\) dollars.

\[\begin{split} & 1 \dfrac{1}{4} \\ + & 2 \dfrac{1}{4} \\ \hline \\ & 3 \dfrac{2}{4} = 3 \dfrac{1}{2} \end{split} \nonumber \]

When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.

\[1 \dfrac{1}{4} + 2 \dfrac{1}{4} \nonumber \]

We can use fraction circles to model this same example:

Example \(\PageIndex{1}\): model

Model \(2 \dfrac{1}{3} + 1 \dfrac{2}{3}\) and give the sum.

We will use fraction circles, whole circles for the whole numbers and \(\dfrac{1}{3}\) pieces for the fractions.

This is the same as \(4\) wholes. So, \(2 \dfrac{1}{3} + 1 \dfrac{2}{3} = 4\).

Exercise \(\PageIndex{1}\)

Use a model to add the following. Draw a picture to illustrate your model. \(1 \dfrac{2}{5} + 3 \dfrac{3}{5}\)

Ex 4.6.1.png

Exercise \(\PageIndex{2}\)

Use a model to add the following. Draw a picture to illustrate your model. \(2 \dfrac{1}{6} + 2 \dfrac{5}{6}\)

Ex 4.6.2.png

Example \(\PageIndex{2}\): model

Model \(1 \dfrac{3}{5} + 2 \dfrac{3}{5}\) and give the sum as a mixed number.

We will use fraction circles, whole circles for the whole numbers and \(\dfrac{1}{5}\) pieces for the fractions.

Adding the whole circles and fifth pieces, we got a sum of \(3 \dfrac{6}{5}\). We can see that \(\dfrac{6}{5}\) is equivalent to \(1 \dfrac{1}{5}\), so we add that to the \(3\) to get \(4 \dfrac{1}{5}\).

Exercise \(\PageIndex{3}\)

Model, and give the sum as a mixed number. Draw a picture to illustrate your model. \(2 \dfrac{5}{6} + 1 \dfrac{5}{6}\)

\(4\dfrac{2}{3}\)

Ex 4.6.3.png

Exercise \(\PageIndex{4}\)

Model, and give the sum as a mixed number. Draw a picture to illustrate your model. \(1 \dfrac{5}{8} + 1 \dfrac{7}{8}\)

\(3\dfrac{1}{2}\)

Ex 4.6.4.png

Add Mixed Numbers

Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.

HOW TO: ADD MIXED NUMBERS WITH A COMMON DENOMINATOR

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Step 3. Simplify, if possible.

Example \(\PageIndex{3}\): add

Add: \(3 \dfrac{4}{9} + 2 \dfrac{2}{9}\).

Exercise \(\PageIndex{5}\)

Find the sum: \(4 \dfrac{4}{7} + 1 \dfrac{2}{7}\).

\(5\dfrac{6}{7}\)

Exercise \(\PageIndex{6}\)

Find the sum: \(2 \dfrac{3}{11} + 5 \dfrac{6}{11}\).

\(7\dfrac{9}{11}\)

In Example \(\PageIndex{3}\), the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.

Example \(\PageIndex{4}\): add

Find the sum: \(9 \dfrac{5}{9} + 5 \dfrac{7}{9}\).

Exercise \(\PageIndex{7}\)

Find the sum: \(8 \dfrac{7}{8} + 7 \dfrac{5}{8}\).

\(16\dfrac{1}{2}\)

Exercise \(\PageIndex{8}\)

Find the sum: \(6 \dfrac{7}{9} + 8 \dfrac{5}{9}\).

\(15\dfrac{1}{3}\)

An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.

Example \(\PageIndex{5}\): add

Add by converting the mixed numbers to improper fractions: \(3 \dfrac{7}{8} + 4 \dfrac{3}{8}\).

Since the problem was given in mixed number form, we will write the sum as a mixed number.

Exercise \(\PageIndex{9}\)

Find the sum by converting the mixed numbers to improper fractions: \(5 \dfrac{5}{9} + 3 \dfrac{7}{9}\)

\(9\dfrac{1}{3}\)

Exercise \(\PageIndex{10}\)

Find the sum by converting the mixed numbers to improper fractions: \(3 \dfrac{7}{10} + 2 \dfrac{9}{10}\)

\(6\dfrac{3}{5}\)

Table \(\PageIndex{1}\) compares the two methods of addition, using the expression \(3 \dfrac{2}{5} + 6 \dfrac{4}{5}\) as an example. Which way do you prefer?

Model Subtraction of Mixed Numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process. Start with one whole.

A shaded circle is shown. Below it is a 1. There are arrows pointing to a shaded circle divided into 2 equal parts. Below it is 2 over 2. Next to this are two circles, each divided into 2 equal parts. The top circle has the right half shaded and the bottom circle has the left half shaded.

Figure \(\PageIndex{1}\)

Algebraically, you would write:

On the left, it says 1 minus 1 half. There is an arrow pointing to 2 over 2 minus 1 over 2. There is another arrow pointing to 2 over 2 minus 1 over 2 equals 1 over 2.

Example \(\PageIndex{6}\): subtract

Use a model to subtract: \(1 − \dfrac{1}{3}\).

There is a table with five rows and three columns. The first column is not labeled. The second column is labeled “Model.” The third column is labeled “Math Notation.” In the first column, the first row says, “Rewrite vertically. Start with one whole.” The next row says, “Since one-third has denominator 3, cut the whole into 3 pieces. The 1 whole becomes 3 thirds.” The next row says, “Take away one-third.” The last row says, “There are two-thirds left.” In the “Model” column, there is a picture of a shaded circle. Below that is a picture of a shaded circle divided into 3 equal pieces. Below that is a picture of a circle divided into 3 equal pieces with 2 pieces shaded. In the “Math Notation” column, the first row shows 1 minus 1 third. The next row says 3 thirds minus 1 third. The last row says 3 thirds minus 1 third is 2 thirds.

Exercise \(\PageIndex{11}\)

Use a model to subtract: \(1 − \dfrac{1}{4}\).

\(\dfrac{3}{4}\)

Exercise \(\PageIndex{12}\)

Use a model to subtract: \(1 − \dfrac{1}{5}\).

\(\dfrac{4}{5}\)

What if we start with more than one whole? Let’s find out.

Example\(\PageIndex{7}\): subtract

Use a model to subtract: \(2 − \dfrac{3}{4}\).

There is a table with four rows and three columns. The first column is not labeled. The second column is labeled “Model.” The third column is labeled “Math Notation.” In the first column, the first row says, “Rewrite vertically. Start with two wholes.” The next row says, “Since three-fourths has denominator 4, cut one of the wholes into 4 pieces. You have one whole and 4 fourths.” The next row says, “Take away three-fourths.” The last row says, “There is 1 and 1 fourth left.” In the “Model” column, there is a picture of two shaded circles. Below that is a picture of two shaded circles. One of the circles is divided into 4 equal pieces. Below that is a picture of one full shaded circle and a circle divided into 4 equal pieces with 1 piece shaded. In the “Math Notation” column, the first row shows 2 minus 3 fourths. The next row says 1 and 4 fourths minus 3 fourths. The last row says 1 and 4 fourths minus 3 fourths equals 1 and 1 fourth.

Exercise \(\PageIndex{13}\)

Use a model to subtract: \(2 − \dfrac{1}{5}\).

\(\dfrac{9}{5}\)

Exercise \(\PageIndex{14}\)

Use a model to subtract: \(2 − \dfrac{1}{3}\).

\(\dfrac{5}{3}\)

In the next example, we’ll subtract more than one whole.

Example \(\PageIndex{8}\): subtract

Use a model to subtract: \(2 − 1 \dfrac{2}{5}\).

There is a table with five rows and three columns. The first column is not labeled. The second column is labeled “Model.” The third column is labeled “Math Notation.” In the first column, the first row says, “Rewrite vertically. Start with two wholes.” The next row says, “Since two-fifths has denominator 5, cut one of the wholes into 5 pieces. You have one whole and 5 fifths.” The next row says, “Take away 1 and two-fifths.” The last row says, “There is 3 fifths left.” In the “Model” column, there is a picture of two shaded circles. Below that is a picture of two shaded circles. One of the circles is divided into 5 equal pieces. Below that is a picture of one full unshaded circle and a circle divided into 5 equal pieces with 3 pieces shaded. In the “Math Notation” column, the first row shows 2 minus 1 and 2 fifths. The next row says 1 and 5 fifths minus 1 and 2 fifths. The last row says 1 and 5 fifths minus 1 and 2 fifths equals 3 fifths.

Exercise \(\PageIndex{15}\)

Use a model to subtract: \(2 − 1 \dfrac{1}{3}\).

\(\dfrac{2}{3}\)

Exercise \(\PageIndex{16}\)

Use a model to subtract: \(2 − 1 \dfrac{1}{4}\).

What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a \(\$1\) bill and one quarter. What could you do? You could change the dollar bill into \(4\) quarters. The value of \(4\) quarters is the same as one dollar bill, but the \(4\) quarters are more useful for the parking meter. Now, instead of having a \(\$1\) bill and one quarter, you have \(5\) quarters and can put \(3\) quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

Example \(\PageIndex{9}\): subtract

Use a model to subtract: \(1 \dfrac{1}{4} − \dfrac{3}{4}\)

Exercise \(\PageIndex{17}\)

Use a model to subtract. Draw a picture to illustrate your model. \(1 \dfrac{1}{3} − \dfrac{2}{3}\)

Ex 4.6.17.png

Exercise \(\PageIndex{18}\)

Use a model to subtract. Draw a picture to illustrate your model. \(1 \dfrac{1}{5} − \dfrac{4}{5}\)

Ex 4.6.18.png

Contributors and Attributions

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/[email protected] ."

renaming mixed numbers to subtract

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  1. PDF Step 1 Step 2

    Name Homework & Practice 7-10 Subtract Mixed Numbers In 1-9, find each difference. 1. 43 2. 3. 5 = 4 ˜ 15 - 21 3 = 2 ˜ 15 Write equivalent fractions with a common denominator. You can use fraction strips. Find the difference 24 6 - 1 3 6. Subtract the fractions. Then subtract the whole numbers. 4 6-3 6 = 1 6 2 - 1 = 1 So, 22 3 - 1 1 2 = 1 1 ...

  2. PDF Lesson 7.7 Name Add and Subtract Mixed Numbers Numbers and Operations

    Subtract the fractional parts of the mixed. Then cross out 2 3 _ 6 to model the subtraction. numbers. Then subtract the whole-number parts of the. mixed numbers. 3 4 __ 6. The difference is _. So, there are _ quesadillas left. Share and Sh. Write the sum as a mixed number with the fractional part less than 1.

  3. Fractions Worksheets

    The answer worksheet will show the progression on how to solve the problems. First find the common denominator and adjust the fractions. The next step is to regroup if needed. Then subtract the numerators and whole numbers. Then check to see if we need to simplify or reduce the mixed number. This fraction worksheet will generate 10 or 15 mixed ...

  4. Add and subtract mixed numbers (with regrouping) (practice)

    Add and subtract mixed numbers (with regrouping) Google Classroom. Subtract. 5 2 5 − 3 4 5 =. Loading... Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

  5. Adding and Subtracting Mixed Numbers Worksheets

    Division - The following steps are for performing addition and subtraction on a mixed number: First, convert all the mixed fractions of the given problem into improper fractions. Multiply the denominator with the whole number and add the product with the numerator. Change the division into multiplication by taking the reciprocal of the divisor ...

  6. PDF Fractions- Add and Subtract w/Mixed Numbers

    examples of adding and subtracting mixed numbers. Encourage adding color to the posters, arrows, and other helpful text to assist viewers in learning how to add/subtract mixed numbers. 5. Once completed, the students may share their posters with the class. 6. Distribute Practice page. Check and review the students' responses. 7.

  7. 4.7: Add and Subtract Mixed Numbers

    Step 1. Rewrite the problem in vertical form. Step 2. Compare the two fractions. If the top fraction is larger than the bottom fraction, go to Step 3. If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction. Step 3. Subtract the fractions. Step 4.

  8. PDF NS7-13 Adding and Subtracting Mixed Numbers

    Answers: a) 7 3/5, b) 5 5/8, c) 3 6/7, d) 8 7/10, Bonus: 10 7/8 Adding mixed numbers by converting to improper fractions. Remind students that they can change any mixed number to an improper fraction, then have them change 1 1/6 and 2 1/6 to improper fractions (7/6 and 13/6). Write on the board: 1 1 7 13 1 2 6 66 6 20 6 + = + =

  9. IXL

    20. hr. min. sec. SmartScore. out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)!

  10. Fractions

    Select the correct answer. Your score. Correct — Incorrect —. In order to become skilled in mathematics you need to practice! Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again.

  11. Add and Subtract Mixed Numbers

    Grade 7 - Expressions & Equations. Standard 7.EE.B.3 - Practice rounding mixed numbers to the nearest whole number. Included Skills: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.

  12. 4.10: Add and Subtract Mixed Numbers (Part 1)

    This page titled 4.10: Add and Subtract Mixed Numbers (Part 1) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax. To add mixed numbers with a common denominator, first rewrite the problem in vertical form. Then, add the whole numbers and the fractions together. Finally, simplify the sum if possible.

  13. Lesson 7-10 Subtract Mixed Numbers Envision 2020

    About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...

  14. Add and subtract mixed numbers with unlike denominators (no regrouping

    Subtracting mixed numbers: 7 6/9 - 3 2/5. Video 2 minutes 21 seconds 2:21. Adding mixed numbers: 19 3/18 + 18 2/3. Report a problem. Loading... Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ...

  15. Add & Subtract Mixed Numbers

    This lesson shows you a couple of methods to add and subtract mixed numbers with common denominators. You should get very comfortable after watching this.

  16. Subtracting mixed numbers word problem

    Subtracting Mixed Numbers Word ProblemPractice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-...

  17. Adding and Subtracting Mixed Numbers Worksheet

    Students practice adding and subtraction mixed number in the 14 question worksheet. There are 7 addition and 7 subtraction problems and includes and answer key. Great for a class review or homework activity. Extra licenses are $0.75. The activity in included in the ULTIMATE FRACTIONS BUNDLE. Save $$$ by and get over 90 fraction games and ...

  18. Mixed Numbers Calculator

    Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).

  19. Adding And Subtracting Mixed Numbers Using Models Worksheet ...

    Apple's Class. 5.0. (6) $3.00. PDF. Use these rigorous but fun, mixed numbers worksheets to review and practice the concept of addition and subtraction of fractions greater than one. These handouts present mixed numbers using models such as pizzas. No prep necessary. Just print and go.

  20. Renaming mixed numbers to subtract

    Identify the least common denominator 2. Generate equivalent fractions with the common denominator 3. Rename the fractions to subtract 4. Subtract the fractions Each step will be on a different task card. At the final step, students will earn a map piece to glue onto their map. This activity was desig.

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  22. Sec. 7-9: Use Models to Subtract Mixed Numbers

    Subtracting Mixed Numbers

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