Section B: Practice Problems Fractions of Whole Numbers

Section Summary

Details

In this section, we explored the relationship between multiplication and division. We learned that 1 diagram can represent different multiplication and division expressions. For example, we can interpret this diagram with 4 different expressions:

3 diagrams of equal length. 4 equal parts. 1 part shaded. Total length, 1.

$\frac{3}{4}$ because each rectangle is divided into 4 equal parts and three of them are shaded.
$3 \times \frac{1}{4}$ because there are 3 parts shaded and each one is $\frac{1}{4}$ of the rectangle.
$3 \div 4$ because there are 3 rectangles and each one is divided into 4 equal parts.
$\frac{1}{4} \times 3$ because there are 3 rectangles and $\frac{1}{4}$ of each one is shaded.

We know that all of these expressions are equal because they all represent the same diagram. We can use any of these expressions to represent and solve this problem:

Mai ate $\frac{1}{4}$ of a 3 pound bag of blueberries. How many pounds of blueberries did Mai eat?

Problem 1 (Lesson 6)

Han cuts a 15-foot piece of rope into 4 equal parts. Decide whether each expression represents the length of each part of the rope in feet. Explain or show your reasoning.

$15 \div 4$
$4 \times 15$
$3 \frac{3}{4}$

Problem 2 (Lesson 7)

Find the value of each expression.

$\frac{1}{2} \times 6$
$\frac{1}{7} \times 6$
$\frac{1}{8} \times 11$
$\frac{1}{3} \times 34$

Problem 3 (Lesson 8)

Kiran ran $\frac{1}{5}$ the length of his road, which is 9 miles long.

How far did Kiran run?
Show or explain your thinking.

Problem 4 (Exploration)

Each square on the map represents 2,178 square feet. Make an estimate for the number of square feet shown on the map. Explain or show your reasoning.
Each square represents $\frac{1}{20}$ acre of actual land. How many square feet are in an acre? Explain or show your reasoning.

Problem 5 (Exploration)

A standard rectangular sheet of paper measures $8 \frac{1}{2}$ inches in width and 11 inches in length. How many square inches are there in a sheet of paper?

If you get stuck, consider using the grid.

Grid. 12 rows of 12 of the same size squares.