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  $\frac{1}{3}$  .

Tags

CCSS.5.NF.B.7B

CCSS.5.NF.B.7C

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. 

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

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

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

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

Tags

CCSS.7.NS.A.2B

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

Tags

CCSS.6.NS.A.1

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.

Tags

CCSS.6.NS.A.1

 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

Tags

CCSS.5.NF.B.5B

 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.

•  $45\div\frac{15}{2}=6\ inches$  

•  $45\div\frac{3}{4}=60\ inches$  

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

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

Tags

CCSS.7.EE.B.3

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

Tags

CCSS.6.G.A.2

CCSS.5.MD.C.5B

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

•  $\frac{1}{27}in^3$  

•  $27\ inches^2$  

•  $\frac{1}{27}inches^2$  

•  $27\ inches^3$  

Tags

CCSS.6.G.A.2

CCSS.5.MD.C.5B

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?

• $3\ \frac{1}{2}\ inch$

• $\frac{7}{2}inch$

• $\frac{2}{7}inch$

• $4\ \frac{1}{2}inch$

Tags

CCSS.6.G.A.2

CCSS.5.MD.C.5B