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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 5 Module 3

**Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Session 1 Answer Key**

**Picturing Fraction Multiplication**

Question 1.

Each of the pictures below shows the results of multiplying one fraction by another. Label each of the shaded regions with its dimensions and area. Then write a multiplication equation to match.

ex:

a.

Answer:

\(\frac{4}{5}\) x \(\frac{4}{5}\) = \(\frac{16}{25}\)

b.

Answer:

\(\frac{3}{4}\) x \(\frac{6}{8}\) = \(\frac{18}{32}\) = \(\frac{9}{16}\)

c.

Answer:

\(\frac{3}{5}\) x \(\frac{8}{10}\) = \(\frac{24}{50}\) = \(\frac{12}{25}\)

Question 2.

Pedro is using paper rectangles that are all the same size to make a collage. Each piece is \(\frac{3}{4}\) inch by \(\frac{1}{2}\) inch. What is the area of each piece? Use numbers, words, or pictures to solve the problem. Show your work.

Each piece had an area of ______________ square inch.

Answer:

Pedro is using paper rectangles that are all the same size to make a collage.

Each piece is \(\frac{3}{4}\) inch by \(\frac{1}{2}\) inch.

Area = \(\frac{3}{4}\) x \(\frac{1}{2}\)

Area = \(\frac{3}{8}\)

**Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Session 2 Answer Key**

**Modeling Fraction Multiplication**

Question 1.

Circle the picture that best represents each problem.

a. \(\frac{1}{2}\) × \(\frac{1}{2}\) = _______________

Answer:

\(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\)

b. \(\frac{2}{3}\) × \(\frac{1}{4}\) = _______________

Answer:

\(\frac{2}{3}\) × \(\frac{1}{4}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)

Question 2.

Use the squares to model each combination and find the products. You will need to divide the sides of each square in order to represent each fraction as a dimension.

a. \(\frac{4}{5}\) × \(\frac{5}{6}\) = _______________

Answer:

\(\frac{4}{5}\) × \(\frac{5}{6}\) = \(\frac{20}{30}\)

b. \(\frac{7}{8}\) × \(\frac{2}{5}\) = _______________

Answer:

\(\frac{7}{8}\) × \(\frac{2}{5}\) = \(\frac{14}{40}\) = \(\frac{7}{20}\)

c. \(\frac{1}{4}\) × \(\frac{2}{6}\) = _______________

Answer:

\(\frac{1}{4}\) × \(\frac{2}{6}\) = \(\frac{2}{24}\) = \(\frac{1}{12}\)

**Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Session 3 Answer Key**

**Reasoning About Multiplying with Fractions**

**Write =, >, or < to make each statement true.**

Question 1.

3 × 45 = B

a. B ________ 3

b. B ________ 45

Answer:

3 x 45 = B

3 x 45 = 135

B = 135

a. B **>** 3

b. B > 45

Question 2.

3 × 1 = C

a. C _________ 3

b. C _________ 1

Answer:

3 x 1 = C

3 x 1 = 3

C = 3

a. C = 3

b. C > 1

Question 3.

\(\frac{3}{4}\) × 1 = A

a. A ________ 1

b. A ________ \(\frac{3}{4}\)

Answer:

\(\frac{3}{4}\) × 1 = A

\(\frac{3}{4}\) × 1 = \(\frac{3}{4}\)

A = \(\frac{3}{4}\)

a. A < 1

b. A = \(\frac{3}{4}\)

Question 4.

\(\frac{1}{2}\) × \(\frac{1}{2}\) = P

a. P ________ \(\frac{3}{7}\)

b. P ________ \(\frac{4}{15}\)

c. P ________ 1

Answer:

\(\frac{1}{2}\) × \(\frac{1}{2}\) = P

\(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\)

P = \(\frac{1}{4}\)

a. P < \(\frac{3}{7}\)

b. P < \(\frac{4}{15}\)

c. P > 1

Question 5.

1\(\frac{7}{9}\) x \(\frac{5}{6}\) = Q

a. Q __________ 1\(\frac{7}{9}\)

b. Q __________ \(\frac{5}{6}\)

c. Q __________ 1

Answer:

1\(\frac{7}{9}\) x \(\frac{5}{6}\) = Q

1\(\frac{7}{9}\) x \(\frac{5}{6}\) = \(\frac{16}{9}\) x \(\frac{5}{6}\) = \(\frac{40}{27}\)

Q = \(\frac{40}{27}\)

a. Q > 1\(\frac{7}{9}\)

b. Q < \(\frac{5}{6}\)

c. Q > 1

Question 6.

\(\frac{6}{17}\) × 7 = S

a. S _________ \(\frac{6}{17}\)

b. S _________ 7

c. S _________ 2

Answer:

\(\frac{6}{17}\) × 7 = S

\(\frac{6}{17}\) × 7 = \(\frac{42}{17}\)

S = \(\frac{42}{17}\)

a. S > \(\frac{6}{17}\)

b. S < 7

c. S > 2

Question 7.

Choose the pair of fractions that must have a product less than 1. Then compute the exact product.

2 × \(\frac{7}{8}\)

\(\frac{5}{8}\) × \(\frac{2}{3}\)

1\(\frac{1}{2}\) × 1\(\frac{1}{2}\)

3 × 2\(\frac{2}{3}\)

Answer: The pair of fractions that have a product less than 1 is \(\frac{5}{8}\) × \(\frac{2}{3}\) = \(\frac{5}{12}\)

2 × \(\frac{7}{8}\) = \(\frac{7}{4}\)

\(\frac{5}{8}\) × \(\frac{2}{3}\) = \(\frac{5}{12}\)

1\(\frac{1}{2}\) × 1\(\frac{1}{2}\) = \(\frac{3}{2}\) x \(\frac{3}{2}\) = \(\frac{9}{4}\)

3 × 2\(\frac{2}{3}\) = 3 x \(\frac{8}{3}\) = 3

**More Fraction Multiplication**

Question 1.

Fill in the chart to solve each of the problems below.

ex:

Multiplication Equation: \(\frac{2}{3}\) × \(\frac{2}{3}\) = \(\frac{4}{9}\)

Labeled Sketch:

a. Multiplication Equation: \(\frac{2}{3}\) × \(\frac{6}{7}\) =

Labeled Sketch:

Answer:

\(\frac{2}{3}\) × \(\frac{6}{7}\) = \(\frac{12}{21}\) = \(\frac{4}{7}\)

b. Multiplication Equation: \(\frac{1}{2}\) × \(\frac{4}{6}\) =

Labeled Sketch:

Answer:

\(\frac{1}{2}\) × \(\frac{4}{6}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)

c. Multiplication Equation: \(\frac{3}{4}\) × \(\frac{4}{8}\) =

Labeled Sketch:

Answer:

\(\frac{3}{4}\) × \(\frac{4}{8}\) = \(\frac{12}{32}\) = \(\frac{3}{8}\)

Question 2.

Solve each problem.

\(\frac{3}{4}\) × \(\frac{2}{4}\) = _______________

\(\frac{1}{4}\) × \(\frac{3}{6}\) = _______________

\(\frac{5}{6}\) × \(\frac{1}{2}\) = _______________

\(\frac{6}{7}\) × \(\frac{3}{5}\) = _______________

\(\frac{2}{3}\) × \(\frac{4}{5}\) = _______________

\(\frac{6}{8}\) × \(\frac{1}{2}\) = _______________

\(\frac{3}{4}\) × \(\frac{1}{3}\) = _______________

\(\frac{2}{7}\) × \(\frac{2}{4}\) = _______________

Answer:

\(\frac{3}{4}\) × \(\frac{2}{4}\) = \(\frac{6}{16}\) = \(\frac{3}{8}\)

\(\frac{1}{4}\) × \(\frac{3}{6}\) = \(\frac{3}{24}\) = \(\frac{1}{8}\)

\(\frac{5}{6}\) × \(\frac{1}{2}\) = \(\frac{5}{12}\)

\(\frac{6}{7}\) × \(\frac{3}{5}\) = \(\frac{18}{35}\)

\(\frac{2}{3}\) × \(\frac{4}{5}\) = \(\frac{8}{15}\)

\(\frac{6}{8}\) × \(\frac{1}{2}\) = \(\frac{6}{16}\)

\(\frac{3}{4}\) × \(\frac{1}{3}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

\(\frac{2}{7}\) × \(\frac{2}{4}\) = \(\frac{4}{28}\) = \(\frac{1}{7}\)

**Bridges in Mathematics Grade 5 Student Book Unit 5 Module 3 Session 4 Answer Key**

**Work Place Instructions 5B Tic-Frac-Toe**

Each pair of partners needs:

- 1 Tic-Frac-Toe Record Sheet
- 1 deck of Number Cards, with the 0s and wild cards removed
- 2 colored pencils, in different colors

1. Decide who will be the dealer. The dealer deals out four cards to each player.

2. Player 1 decides which space he wants to claim on the Tic-Frac-Toe Record Sheet. He arranges his four cards to make a fraction-times-a-fraction multiplication problem with a product that fits the description in the desired space.

Two cards are numerators and the other two cards are denominators. For example, with the cards 2, 5, 5, and 8, a player could make \(\frac{2}{5}\) × \(\frac{5}{8}\). Since \(\frac{2}{5}\) × \(\frac{5}{8}\) = \(\frac{1}{4}\), Player 1 can fill any space where the product is less than 1, p < 1. By rearranging the cards to make \(\frac{8}{2}\) × \(\frac{5}{5}\) = 4 instead, Player 1 can fill in any space where the product is greater than 1, p > 1.

3. Player 1 writes the equation in the blank in the desired space with a colored pencil.

4. Player 2 arranges her four cards and uses the other colored pencil to write her equation in a space that describes her product.

5. Players continue, using four new cards on each turn and filling spaces until one player has claimed four spaces in a horizontal, vertical, or diagonal row, and wins the game.

Game Variations

A. Change some of the spaces to read p > 2 for products greater than 2 but less than 3, and p > 3 for products greater than 3.

B. Include the wild cards in the deck. A wild card can be any numeral 1-9.

Answer: Tried the game by changing some of the spaces to read p > 2 for products greater than 2 but less than 3, and p > 3 for products greater than 3. Also, included a wild card of number 7.

**Tic-Frac-Toe Moves**

In Tic-Frac-Toe, you draw four number cards and arrange them to make two fractions, then multiply them to get a product greater than 1 or a product less than 1.

Question 1.

Bill has the cards 6, 4, 2, and 5.

a. How could he arrange his cards to make two fractions with a product greater than 1?

Answer:

Bill has the cards 6, 4, 2, and 5.

Bill can arrange his cards has \(\frac{4}{2}\) × \(\frac{6}{5}\).

b. What would his product be? Write and solve an equation to show.

Answer:

Since \(\frac{4}{2}\) × \(\frac{6}{5}\)= \(\frac{12}{5}\) = 2\(\frac{2}{5}\) which is greater than 1.

c. How could he arrange his cards to make a product less than 1?

Answer:

Bill has the cards 6, 4, 2, and 5.

Bill can arrange his cards has \(\frac{6}{4}\) × \(\frac{2}{5}\).

d. What would his product be? Write and solve an equation to show.

Answer:

Since \(\frac{6}{4}\) × \(\frac{2}{5}\)= \(\frac{3}{5}\) which is less than 1.

Question 2.

Jeremiah has the cards 3, 9, 4, and 1.

a. How could he arrange his cards to make two fractions with a product greater than 1?

Answer:

Jeremiah has the cards 3, 9, 4, and 1

Jeremiah can arrange his cards has \(\frac{9}{3}\) × \(\frac{4}{1}\).

b. What would his product be? Write and solve an equation to show.

Answer:

Since \(\frac{9}{3}\) × \(\frac{4}{1}\)= \(\frac{12}{1}\) = 12 which is greater than 1.

c. How could he arrange his cards to make a product less than 1?

Answer:

Jeremiah has the cards 3, 9, 4, and 1

Jeremiah can arrange his cards has \(\frac{3}{9}\) × \(\frac{1}{4}\).

d. What would his product be? Write and solve an equation to show.

Answer:

Since \(\frac{3}{9}\) × \(\frac{1}{4}\)= \(\frac{1}{12}\) which is less than 1.

Question 3.

Find the products.

\(\frac{4}{7}\) × \(\frac{1}{3}\) = ________________

\(\frac{5}{6}\) × \(\frac{3}{5}\) = ________________

\(\frac{4}{3}\) × \(\frac{3}{4}\) = ________________

\(\frac{3}{7}\) × \(\frac{7}{5}\) = ________________

Answer:

\(\frac{4}{7}\) × \(\frac{1}{3}\) = \(\frac{4}{21}\)

\(\frac{5}{6}\) × \(\frac{3}{5}\) = \(\frac{15}{30}\) = \(\frac{1}{2}\)

\(\frac{4}{3}\) × \(\frac{3}{4}\) = \(\frac{12}{12}\) = 1

\(\frac{3}{7}\) × \(\frac{7}{5}\) = \(\frac{21}{35}\) = \(\frac{3}{5}\)