Section A: Practice Problems Fraction Multiplication

Section Summary

Details

In this unit, we learned to multiply fractions. First we learned to multiply unit fractions. For example, we learned that $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$ .

Square, length and width, 1. Partitioned into 5 rows of 3 of the same size rectangles. 2 rectangles shaded. — A

In diagram A, we can see that $\frac{2}{5}$ of $\frac{1}{3}$ of a square is the same size as $\frac{2}{15}$ of the whole square. Next, we learned how to multiply any fraction by a fraction.

Square, length and width, 1. Partitioned into 6 rows of 7 of the same size rectangles. 20 rectangles shaded. — B

In diagram B, we can see that $\frac{4}{6} \times \frac{5}{7} = \frac{20}{42}$ . We can multiply the numerators, $4 \times 5$ to find the numerator in the product. We can multiply the denominators, $6 \times 7$ , to find the denominator in the product. We can represent this relationship with the equation: $\frac{(4 \times 5)}{(6 \times 7)} = \frac{20}{42}$ . Diagram B shows $4 \times 5$ or 20 pieces with $6 \times 7$ or 42 pieces in the whole square.

Problem 1 (Pre-Unit)

There are 63 students in the cafeteria. There are 9 students at each table.

At how many tables are the students seated?
Write a division equation to represent your answer.

Problem 2 (Pre-Unit)

What is the area of this figure? Explain your reasoning.

Problem 3 (Pre-Unit)

Select all expressions that are equivalent to $\frac{12}{5}$ .

$6 \times \frac{2}{5}$
$5 \times \frac{1}{12}$
$12 \times \frac{1}{5}$
$8 \times \frac{4}{5}$
$4 \times \frac{3}{5}$

Problem 4 (Pre-Unit)

Jada has 8 pennies. Each one weighs $\frac{5}{2}$ grams. How much do Jada’s pennies weigh altogether? Explain your reasoning.

Problem 5 (Lesson 1)

Shade $\frac{1}{2}$ of $\frac{1}{5}$ of the square.
Explain where you see $\frac{1}{2}$ of $\frac{1}{5}$ in your drawing.

Problem 6 (Lesson 2)

Write an expression for how much of the square is shaded.
Find the value of your expression.

Problem 7 (Lesson 3)

Write an equation representing the shaded part of the diagram.
Explain how the diagram shows each part of your equation.

Problem 8 (Lesson 4)

Write an expression for the shaded region of the square.
Explain how your expression matches the shaded region.

Problem 9 (Lesson 5)

Write an expression for the area of the shaded region.
Explain how the diagram shows your expression.

Problem 10 (Lesson 6)

Write a multiplication expression for the area of the shaded region. Explain your reasoning.
What is the area of the shaded region in square units?

Problem 11 (Lesson 7)

Find the value that makes each equation true.

$\frac{7}{10} \times \frac{3}{5} =$
$\frac{2}{5} \times$ $= \frac{8}{45}$
$\times \frac{4}{9} = \frac{28}{45}$

Problem 12 (Lesson 8)

This flag of Sweden is $3 \frac{1}{5}$ inches wide and 2 inches tall. The rectangle in the upper right is $\frac{9}{5}$ inches wide and $\frac{4}{5}$ inch tall.

What is the area of the whole flag?
What is the area of the rectangle in the upper right?

Problem 13 (Exploration)

On this American flag the width of the blue rectangle is $\frac{2}{5}$ the width of the flag. What fraction of the area of the flag is the blue rectangle? Explain or show your reasoning.

Problem 14 (Exploration)

Jada folded a square piece of paper in half many times, sometimes horizontally and sometimes vertically. She shaded the folded piece of paper and then unfolded it. Here is a picture.

Diagram, square. Length and width, 1. Rectangular portion shaded with length, about 1 eighth, width, about 1 sixteenth.

What fraction of the paper did Jada shade? Explain how you know.