Learn on PengienVision, Mathematics, Grade 5Chapter 7: Use Equivalent Fractions to Add and Subtract Fractions

Lesson 11: Add and Subtract Mixed Numbers

In this Grade 5 lesson from enVision Mathematics Chapter 7, students learn how to add and subtract mixed numbers by finding common denominators and regrouping when necessary. The lesson builds on equivalent fractions to solve multi-step real-world problems, such as calculating remaining lengths of fabric or wrapping paper. Students also practice order-of-operations with mixed number expressions using parentheses.

Section 1

Adding and Subtracting Mixed Numbers with Unlike Denominators

Property

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD.
Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Examples

Add $3\frac{1}{3} + 4\frac{1}{2}$ . The LCD of 3 and 2 is 6. The problem becomes $3\frac{2}{6} + 4\frac{4}{6}$ . Add the wholes $3+4=7$ and fractions $\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1$ . The sum is $7+1=8$ .

Subtract $8\frac{1}{4} - 3\frac{5}{6}$ . The LCD of 4 and 6 is 12. This is $8\frac{3}{12} - 3\frac{10}{12}$ . Borrow 1 from 8 to get $7\frac{15}{12}$ . Now, $7\frac{15}{12} - 3\frac{10}{12} = 4\frac{5}{12}$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Adding and Subtracting Mixed Numbers with Unlike Denominators

Property

Examples

Add $3\frac{1}{3} + 4\frac{1}{2}$ . The LCD of 3 and 2 is 6. The problem becomes $3\frac{2}{6} + 4\frac{4}{6}$ . Add the wholes $3+4=7$ and fractions $\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1$ . The sum is $7+1=8$ .

Subtract $8\frac{1}{4} - 3\frac{5}{6}$ . The LCD of 4 and 6 is 12. This is $8\frac{3}{12} - 3\frac{10}{12}$ . Borrow 1 from 8 to get $7\frac{15}{12}$ . Now, $7\frac{15}{12} - 3\frac{10}{12} = 4\frac{5}{12}$ .

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Adding and Subtracting Mixed Numbers with Unlike Denominators

Property

Examples

Add $3\frac{1}{3} + 4\frac{1}{2}$ . The LCD of 3 and 2 is 6. The problem becomes $3\frac{2}{6} + 4\frac{4}{6}$ . Add the wholes $3+4=7$ and fractions $\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1$ . The sum is $7+1=8$ .

Subtract $8\frac{1}{4} - 3\frac{5}{6}$ . The LCD of 4 and 6 is 12. This is $8\frac{3}{12} - 3\frac{10}{12}$ . Borrow 1 from 8 to get $7\frac{15}{12}$ . Now, $7\frac{15}{12} - 3\frac{10}{12} = 4\frac{5}{12}$ .