Section B: Practice Problems Add and Subtract Fractions with Unlike Denominators

Section Summary

Details

In this section we learned to add and subtract fractions. When the denominators are the same, such as $\frac{7}{10} + \frac{4}{10}$ , we can just add the tenths and see that there are 11 of them so $\frac{7}{10} + \frac{4}{10} = \frac{11}{10}$ . When the denominators are not the same, such as $\frac{1}{6} + \frac{3}{8}$ , we look for a common denominator so that we can add parts of the same size. One way to find a common denominator is to use the product of the two denominators, $6 \times 8$ , because that’s always a multiple of both denominators. Using 48 as a denominator we find $\frac{1}{6} + \frac{3}{8} = \frac{1 \times 8}{6 \times 8} + \frac{3 \times 6}{8 \times 6}$ . This means $\frac{1}{6} + \frac{3}{8} = \frac{26}{48}$ . For the expression $\frac{1}{6} + \frac{3}{8}$ we can also use a smaller common denominator. Since $24$ is a multiple of 6 and 8 we can also rewrite $\frac{1}{6} + \frac{3}{8}$ as $\frac{4}{24} + \frac{9}{24}$ which is $\frac{13}{24}$ .

Problem 1 (Lesson 8)

Find the value of each sum. Explain or show your reasoning.

$\frac{5}{6} + \frac{2}{6}$
$\frac{5}{6} + \frac{2}{3}$
How were the calculations the same? How were they different?

Problem 2 (Lesson 9)

Explain why the expressions $\frac{2}{3} - \frac{7}{12}$ and $\frac{8}{12} - \frac{7}{12}$ are equivalent.
How is the expression $\frac{8}{12} - \frac{7}{12}$ helpful to find the value of $\frac{2}{3} - \frac{7}{12}$ ?

Problem 3 (Lesson 10)

Find the value of each expression. Explain or show your reasoning.

$\frac{1}{4} + \frac{1}{5}$
$\frac{10}{9} - \frac{3}{4}$

Problem 4 (Lesson 11)

Find the value of $2 \frac{3}{4} - \frac{1}{3}$ . Explain or show your reasoning.
Find the value of $3 \frac{2}{7} - \frac{4}{5}$ . Explain or show your reasoning.

Problem 5 (Lesson 12)

Jada picked $4 \frac{2}{3}$ cups of blackberries. Andre picked $3 \frac{5}{8}$ cups of blackberries.

How many cups of blackberries did Jada and Andre pick together? Explain or show your reasoning.
How many more cups of blackberries did Jada pick than Andre? Explain or show your reasoning.

Problem 6 (Lesson 13)

Find the value of each expression. Explain or show your reasoning.

$\frac{7}{8} + \frac{4}{13}$
$\frac{7}{8} - \frac{3}{20}$

Problem 7 (Lesson 14)

Here are the lengths of some pieces of ribbon measured in inches:

$3 \frac{1}{4}$
$4 \frac{1}{8}$
$3 \frac{6}{8}$
$3 \frac{1}{8}$
$2 \frac{5}{8}$
$3 \frac{2}{4}$
$3 \frac{1}{4}$
$3 \frac{7}{8}$
$4 \frac{1}{8}$
$3 \frac{1}{2}$
$2 \frac{7}{8}$
$4 \frac{1}{8}$
$3 \frac{3}{4}$
$3 \frac{2}{8}$

Complete the line plot with the ribbon lengths.
What is the sum of the lengths of the ribbons that measure more than 4 inches? Explain or show your reasoning.

Problem 8 (Lesson 15)

Han is making a line plot of the seedlings his class grew. This is what he has done so far.

Dot plot titled Growing Plants from 0 to 3 by 1’s.

Use this information to complete the line plot. Explain or show your reasoning.

There are 15 seedlings altogether.
The tallest seedling is $2 \frac{1}{8}$ taller than the shortest seedling.
There are 3 seedlings of the shortest height.

Problem 9 (Exploration)

Put the numbers 2, 3, 4, and 5 in the four boxes so that the expression is as close to 1 as possible. $\frac{}{} + \frac{}{}$
Put the numbers 2, 3, 4, and 5 in the four boxes so that the expression is as close to 1 as possible. $\frac{}{} - \frac{}{}$

Problem 10 (Exploration)

Make a line plot of seedling heights so that each of these statements is true.

There are 12 measurements.
The largest measurement is $2 \frac{3}{8}$ inches more than the smallest measurement.
The sum of the measurements is $18 \frac{3}{8}$ inches.

Explain how you made the line plot.