# 4.6 Add and subtract mixed numbers  (Page 4/4)

 Page 4 / 4

Subtract: $1\frac{3}{4}-6\frac{7}{8}.$

$-\frac{41}{8}$

Subtract: $10\frac{3}{7}-22\frac{4}{9}.$

$-\frac{757}{63}$

## Key concepts

• Add mixed numbers with a common denominator.
3. Simplify, if possible.
• Subtract mixed numbers with common denominators.
1. Rewrite the problem in vertical form.
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.
3. Subtract the fractions.
4. Subtract the whole numbers.
5. Simplify, if possible.
• Subtract mixed numbers with common denominators as improper fractions.
1. Rewrite the mixed numbers as improper fractions.
2. Subtract the numerators.
3. Write the answer as a mixed number, simplifying the fraction part, if possible.

## Practice makes perfect

In the following exercises, use a model to find the sum. Draw a picture to illustrate your model.

$1\frac{1}{5}+3\frac{1}{5}$

$2\frac{1}{3}+1\frac{1}{3}$

$3\frac{2}{3}$

$1\frac{3}{8}+1\frac{7}{8}$

$1\frac{5}{6}+1\frac{5}{6}$

$3\frac{2}{3}$

Add Mixed Numbers with a Common Denominator

$5\frac{1}{3}+6\frac{1}{3}$

$2\frac{4}{9}+5\frac{1}{9}$

$7\frac{5}{9}$

$4\frac{5}{8}+9\frac{3}{8}$

$7\frac{9}{10}+3\frac{1}{10}$

11

$3\frac{4}{5}+6\frac{4}{5}$

$9\frac{2}{3}+1\frac{2}{3}$

$11\frac{1}{3}$

$6\frac{9}{10}+8\frac{3}{10}$

$8\frac{4}{9}+2\frac{8}{9}$

$11\frac{1}{3}$

Model Subtraction of Mixed Numbers

In the following exercises, use a model to find the difference. Draw a picture to illustrate your model.

$1\frac{1}{6}-\frac{5}{6}$

$1\frac{1}{8}-\frac{5}{8}$

$\frac{1}{2}$

Subtract Mixed Numbers with a Common Denominator

In the following exercises, find the difference.

$2\frac{7}{8}-1\frac{3}{8}$

$2\frac{7}{12}-1\frac{5}{12}$

$1\frac{1}{6}$

$8\frac{17}{20}-4\frac{9}{20}$

$19\frac{13}{15}-13\frac{7}{15}$

$6\frac{2}{5}$

$8\frac{3}{7}-4\frac{4}{7}$

$5\frac{2}{9}-3\frac{4}{9}$

$1\frac{7}{9}$

$2\frac{5}{8}-1\frac{7}{8}$

$2\frac{5}{12}-1\frac{7}{12}$

$\frac{5}{6}$

Add and Subtract Mixed Numbers with Different Denominators

In the following exercises, write the sum or difference as a mixed number in simplified form.

$3\frac{1}{4}+6\frac{1}{3}$

$2\frac{1}{6}+5\frac{3}{4}$

$7\frac{11}{12}$

$1\frac{5}{8}+4\frac{1}{2}$

$7\frac{2}{3}+8\frac{1}{2}$

$16\frac{1}{6}$

$9\frac{7}{10}-2\frac{1}{3}$

$6\frac{4}{5}-1\frac{1}{4}$

$5\frac{11}{20}$

$2\frac{2}{3}-3\frac{1}{2}$

$2\frac{7}{8}-4\frac{1}{3}$

$-1\frac{11}{24}$

Mixed Practice

In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.

$2\frac{5}{8}·1\frac{3}{4}$

$1\frac{2}{3}·4\frac{1}{6}$

$6\frac{17}{18}$

$\frac{2}{7}+\frac{4}{7}$

$\frac{2}{9}+\frac{5}{9}$

$\frac{7}{9}$

$1\frac{5}{12}÷\frac{1}{12}$

$2\frac{3}{10}÷\frac{1}{10}$

23

$13\frac{5}{12}-9\frac{7}{12}$

$15\frac{5}{8}-6\frac{7}{8}$

$8\frac{3}{4}$

$\frac{5}{9}-\frac{4}{9}$

$\frac{11}{15}-\frac{7}{15}$

$\frac{4}{15}$

$4-\frac{3}{4}$

$6-\frac{2}{5}$

$5\frac{3}{5}$

$\frac{9}{20}÷\frac{3}{4}$

$\frac{7}{24}÷\frac{14}{3}$

$\frac{1}{16}$

$9\frac{6}{11}+7\frac{10}{11}$

$8\frac{5}{13}+4\frac{9}{13}$

$13\frac{1}{13}$

$3\frac{2}{5}+5\frac{3}{4}$

$2\frac{5}{6}+4\frac{1}{5}$

$7\frac{1}{30}$

$\frac{8}{15}·\frac{10}{19}$

$\frac{5}{12}·\frac{8}{9}$

$\frac{10}{27}$

$6\frac{7}{8}-2\frac{1}{3}$

$6\frac{5}{9}-4\frac{2}{5}$

$2\frac{7}{45}$

$5\frac{2}{9}-4\frac{4}{5}$

$4\frac{3}{8}-3\frac{2}{3}$

$\frac{17}{24}$

## Everyday math

Sewing Renata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs $2\frac{3}{8}$ yards of fabric for her husband’s shirt and $1\frac{1}{8}$ yards of fabric for her son’s shirt. How much fabric does she need to make both shirts?

Sewing Pauline has $3\frac{1}{4}$ yards of fabric to make a jacket. The jacket uses $2\frac{2}{3}$ yards. How much fabric will she have left after making the jacket?

$\frac{7}{12}\phantom{\rule{0.2em}{0ex}}\text{yards}$

Printing Nishant is printing invitations on his computer. The paper is $8\frac{1}{2}$ inches wide, and he sets the print area to have a $1\frac{1}{2}$ -inch border on each side. How wide is the print area on the sheet of paper?

Framing a picture Tessa bought a picture frame for her son’s graduation picture. The picture is $8$ inches wide. The picture frame is $2\frac{5}{8}$ inches wide on each side. How wide will the framed picture be?

$13\frac{1}{4}\phantom{\rule{0.2em}{0ex}}\text{inches}$

## Writing exercises

Draw a diagram and use it to explain how to add $1\frac{5}{8}+2\frac{7}{8}.$

Edgar will have to pay $\text{3.75}$ in tolls to drive to the city.

Explain how he can make change from a $\text{10}$ bill before he leaves so that he has the exact amount he needs.

How is Edgar’s situation similar to how you subtract $10-3\frac{3}{4}?$

Add $4\frac{5}{12}+3\frac{7}{8}$ twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

Subtract $3\frac{7}{8}-4\frac{5}{12}$ twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

After reviewing this checklist, what will you do to become confident for all objectives?

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