Unit 4 End Study Guide

Explain or show how you could find  $5\div\frac{1}{3}$  by using the value of  $5\cdot3$  . If needed, use this diagram to support your reasoning.

•  $5\div\frac{1}{3}$  can be solved by multiplying by the denominator. 

• This problem can be solved by $5\times\frac{1}{3}$  .

• Each whole in 5 can be divided into 3 groups of  $\frac{1}{3}$  .

Find $12\div\frac{3}{5}$  . Only use a diagram if necessary. Show your reasoning.

•  $12\div\frac{5}{3}=\frac{2.4}{3}$  

•  $12\times\frac{5}{3}=\frac{15}{3}\ \frac{\div3}{\div3}=\frac{3}{1}=3$  

•  $12\times\frac{3}{5}=\frac{36}{5}$  

•  $\frac{12}{1}\times\frac{5}{3}=\frac{60}{3}=20$  

Find the value of $\frac{24}{25}\div\frac{4}{5}$ . Show your reasoning. 

•  $\frac{24}{25}\times\frac{5}{4}=\frac{120}{100}\ \frac{\div20}{\div20}=\frac{6}{5}$  

•  $\frac{25}{24}\times\frac{4}{5}=\frac{100}{120}\ \frac{\div20}{\div20}=\frac{5}{6}$  

•  $\frac{24}{25}\div\frac{5}{4}=\frac{4.8}{6.25}$  

•  $\frac{25}{24}\times\frac{5}{4}=\frac{125}{96}=1\ \frac{29}{96}$  

If $\frac{4}{3}$ liters of water are enough to water  $\frac{2}{5}$   of the plants in the house, how much water is necessary to water all the plants in the house? Make sure to write a multiplication and division equation. 

•  $?\cdot\frac{2}{5}=\frac{4}{5}$  or  $\frac{2}{5}\ \cdot\ ?=\frac{4}{5}$  

•  $\frac{4}{5}\div\frac{2}{3}=?$  or  $\frac{4}{5}\div?=\frac{2}{3}$  

• 3 $\frac{1}{3}$  Liters

•  $\frac{10}{3}$  Liters

A builder was building a fence, in the morning for  $\frac{2}{5}$   of an hour. In the afternoon, he worked for  $\frac{9}{10}$   of an hour. How many time as long as in the morning did he work in the afternoon?

Write a division equation to represent this situation, then answer the question.

•  $\frac{9}{10}\div\frac{2}{5}=?$  

•  $\frac{2}{5}\div\frac{9}{10}=?$  

• He worked 2 $\frac{1}{4}$  times as long in the morning as he did in the afternoon.

• He worked $\frac{9}{4}$  times as long in the morning as he did in the afternoon.

 Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 $\frac{3}{4}$  inches, and Frame B has a length of 7 $\frac{1}{2}$  inches.

Question: Without calculating, predict which frame has the shorter width. Explain your reasoning

• Frame A: When you have a bigger length, you need to multiply by a smaller width to get the same area.

• Frame B: When you have a bigger length, you need to multiply by a smaller width to get the same area.

• Frame A

• Frame B

 Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 $\frac{3}{4}$ inches, and Frame B has a length of 7 $\frac{1}{2}$  inches.

Question: Find the width of Frame B.

•  $45\div\frac{15}{2}=6\ inches$  

•  $45\div\frac{3}{4}=60\ inches$  

•  $\frac{3}{4}\div\frac{1}{2}=1\ \frac{1}{2}\ inches$  

•  $\frac{1}{2}\div\frac{3}{4}=\frac{1}{3}inches$  

How many cubes with an edge length of $\frac{1}{3}$ inch are needed to build a cube with an edge length of 1 inch? 

• 27 cubes

• 6 cubes

• 3 cubes

• Not enough information given

What is the volume, in cubic inches, of one cube with an edge length of $\frac{1}{3}$ inch? 

•  $\frac{1}{27}in^3$  

•  $27\ inches^2$  

•  $\frac{1}{27}inches^2$  

•  $27\ inches^3$  

A storage box has a volume of 56 cubic inches, and the base of the box is 4 inches by 4 inches.

Question: What is the height of the box?

• $3\ \frac{1}{2}\ inch$

• $\frac{7}{2}inch$

• $\frac{2}{7}inch$

• $4\ \frac{1}{2}inch$