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

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

**Fraction Problems**

Question 1.

Solve the following.

a. \(\frac{2}{5}\) of 60 = _____________

Answer:

\(\frac{2}{~~5~~}\) × ~~60~~

2 × 12 = 24

\(\frac{2}{5}\) of 60 = 24

b. \(\frac{2}{3}\) of 60 = ______________

Answer:

\(\frac{2}{3}\) of 60

\(\frac{2}{~~3~~}\) × ~~60~~

2 × 20 = 40

\(\frac{2}{3}\) of 60 = 40

c. \(\frac{3}{4}\) of 60 = _______________

Answer:

\(\frac{3}{4}\) of 60

\(\frac{3}{~~4~~}\) × ~~60~~

3 × 15 = 45

\(\frac{3}{4}\) of 60 = 45

Question 2.

Find the sum.

a. \(\frac{3}{4}\) + \(\frac{2}{3}\) = ______________

Answer:

\(\frac{3}{4}\) + \(\frac{2}{3}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then add the fractions.

LCD = 12

\(\frac{9}{12}\) + \(\frac{8}{12}\) = \(\frac{17}{12}\) = 1\(\frac{5}{12}\)

b. \(\frac{5}{6}\) + \(\frac{7}{9}\) = ______________

Answer:

\(\frac{5}{6}\) + \(\frac{7}{9}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then add the fractions.

LCD = 18.

\(\frac{15}{18}\) + \(\frac{14}{18}\) = \(\frac{29}{18}\) = 1 \(\frac{11}{18}\)

c. \(\frac{2}{7}\) + \(\frac{1}{4}\) = ______________

Answer:

\(\frac{2}{7}\) + \(\frac{1}{4}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then add the fractions.

LCD = 28

\(\frac{8}{28}\) + \(\frac{7}{28}\) = \(\frac{15}{28}\)

Question 3.

Find the difference.

a. \(\frac{1}{2}\) – \(\frac{2}{6}\) = ______________

Answer:

\(\frac{1}{2}\) – \(\frac{2}{6}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then subtract the fractions.

LCD = 6

\(\frac{3}{6}\) – \(\frac{2}{6}\) = \(\frac{1}{6}\)

b. \(\frac{5}{9}\) – \(\frac{1}{7}\) = ______________

Answer:

\(\frac{5}{9}\) – \(\frac{1}{7}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then subtract the fractions.

LCD = 63

\(\frac{35}{63}\) – \(\frac{9}{63}\) = \(\frac{26}{63}\)

c. \(\frac{8}{14}\) – \(\frac{2}{5}\) = ______________

Answer:

\(\frac{8}{14}\) – \(\frac{2}{5}\)

The denominator of both fractions is not the same. So find the lcm of the denominators and then subtract the fractions.

LCD = 70

\(\frac{40}{70}\) – \(\frac{28}{70}\) = \(\frac{12}{70}\) = \(\frac{6}{35}\)

Question 4.

Randy jogged in a park by his neighborhood every day after work. On Monday, he jogged 3\(\frac{2}{9}\) miles, and on Tuesday he jogged 3\(\frac{3}{8}\) miles.

a. On which day did Randy jog farther?

Answer:

Given,

Randy jogged in a park by his neighborhood every day after work.

On Monday, he jogged 3\(\frac{2}{9}\) miles, and on Tuesday he jogged 3\(\frac{3}{8}\) miles.

Randy jogged farther on Tuesday.

b. How much farther? Show your work.

Answer:

3\(\frac{2}{9}\) can be written in the decimal form as 3.22 mile.

3\(\frac{3}{8}\) can be written in the decimal form as 3.375 mile.

3.375 is greater than 3.22

3.375 – 3.22 = 0.155 mile

c. How far did Randy jog on the days combined? Show your work.

Answer:

3\(\frac{2}{9}\) can be written in the decimal form as 3.22 mile.

3\(\frac{3}{8}\) can be written in the decimal form as 3.375 mile.

3.22 + 3.375 = 6.595 mile

Question 5.

Carrie bought 3 watermelons for a school picnic. She used \(\frac{7}{8}\) of a watermelon for one class and 1\(\frac{1}{5}\) watermelons for another class. How much watermelon does Carrie have left for the last class? Show your work.

Answer:

Given,

Carrie bought 3 watermelons for a school picnic.

She used \(\frac{7}{8}\) of a watermelon for one class and 1\(\frac{1}{5}\) watermelons for another class.

\(\frac{7}{8}\) + 1\(\frac{1}{5}\)

\(\frac{7}{8}\) + 1 + \(\frac{1}{5}\)

\(\frac{7}{8}\) + \(\frac{1}{5}\)

LCD is 40

\(\frac{35}{40}\) + \(\frac{8}{40}\) = \(\frac{43}{40}\) = 1 \(\frac{3}{40}\)

1 + 1 + \(\frac{3}{40}\) = 2\(\frac{3}{40}\)

3 – 2\(\frac{3}{40}\) = \(\frac{37}{40}\)

**Bridges in Mathematics Grade 5 Student Book Unit 3 Module 1 Session 2 Answer Key**

**Work Place Instructions 3A Beat the Calculator: Fractions**

Each pair of players needs:

- 1 set of Beat the Calculator: Fractions Cards
- 2 pencils
- scratch paper
- 1 calculator

1. Shuffle the cards, lay them face down, and decide who will use the calculator first.

2. The player with the calculator turns over a card so both players can see it.

3. The player with the calculator enters the problem shown on the card.

• Fractions are entered as division expressions.

• Mixed numbers must be entered with a + between the whole number and the fraction part of the expression.

(Example: 2\(\frac{1}{2}\) – \(\frac{3}{4}\) will be entered as 2 + 1 ÷ 2 – 3 ÷ 4.)

4. At the same time, the other player uses the most efficient strategy she can think of for the numbers in the expression. (It’s OK to work mentally or use a piece of scratch paper to do the figuring.)

5. The player who gets the correct answer first keeps the card.

6. Players compare answers and share strategies for evaluating the expression.

The calculator will give a decimal answer. To see if that decimal is equivalent to the fraction answer, clear the calculator and enter the fraction as a division problem. The calculator will show the decimal equivalent to that fraction.

7. Players switch roles and draw another card to solve.

8. The player with the most cards at the end wins.

**Game Variations**

A. Players make up their own problems and write them on cards, mix the cards up, and then choose from those problems.

B. Instead of racing the calculator, players race each other.

C. Players play cooperatively by drawing a card and discussing their preferred mental strategy.

D. Players spread the cards face down on the table. Each player chooses a different card at the same time and then players race to see who gets the correct answer first.

Answer:

**Fraction & Decimal Equivalents**

Question 1.

Match each fraction on the left with its decimal equivalent on the right. (Hint: Think about money. Remember that a penny is \(\frac{1}{100}\) of a dollar and a dime is \(\frac{1}{10}\) of a dollar.)

Answer:

Question 2.

Susan said, “I multiplied 100 by 47, and then I removed one group of 47.” Write an expression to represent how Susan solved 99 × 47. Then evaluate the expression.

Answer:

99 × 47 = (100 – 1) × 47 = (100 × 47) – 47

4700 – 47 = 4653

Question 3.

Match each expression with the correct rectangular prism below. The numbers in parentheses represent the dimensions of the prism’s base.

Answer:

a. (4 × 6) × 5

24 × 5 = 120

b. (4 × 5) × 6

20 × 6 = 120

c. (6 × 5) × 4

30 × 4 = 120

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

**Place Value Patterns**

Predict the product and record your prediction. Then enter the problem in a calculator and write the results.

Question 1.

Take a moment to study the chart above. What patterns or interesting results do you notice? Record your observations.

Answer:

Question 2.

Circle the correct word in each sentence below.

a. When a number is multiplied by 10, the result is (larger, smaller) than the number.

Answer: When a number is multiplied by 10, the result is larger than the number.

b. When a number is divided by 10, the result is (larger, smaller) than the number.

Answer: When a number is divided by 10, the result is larger than the number.

**Adding & Subtracting Decimals**

The Ramirez kids earn money each week for the chores they complete around the house. They made a bar graph showing how much they each earned in the first two weeks of the year. Use the graph to answer the questions below. Show all your work.

Question 1.

Look at the information for Sarah’s earnings.

a. How much did Sarah earn in Week 1?

Answer: From the above bar graph, we can say that Sarah earn $1.2 in Week 1.

b. How much did Sarah earn in Week 2?

Answer: From the above bar graph, we can say that Sarah earn $3.6 in Week 2.

c. How much more did Sarah earn in Week 2 than in Week 1?

Answer:

$3.6 – $1.2 = $2.4

Thus Sarah earn $2.4 in Week 2 than in Week 1.

Question 2.

How much more did Johnny earn in Week 2 than in Week 1?

Answer:

From the above bar graph, we can say that Johnny earn $1.4 in Week 1.

From the above bar graph, we can say that Johnny earn $8.6 in Week 2.

$8.6 – $1.4 = $7.2

Johnny earn $7.2 in Week 2 than in Week 1

Question 3.

How much more did Richard earn in Week 2 than in Week 1?

Answer:

From the above bar graph, we can say that Richard earn $4.6 in Week 1.

From the above bar graph, we can say that Richard earn $10 in Week 2.

$10 – $4.6 = $5.4

Richard earn $5.4 in Week 2 than in Week 1

Question 4.

How much more did Mr. and Mrs. Ramirez pay their children in Week 2 than in Week 1?

Answer:

**Bridges in Mathematics Grade 5 Student Book Unit 3 Module 1 Session 4 Answer Key**

**What’s the Share?**

**Write and solve an equation to represent each of the problems below.**

Question 1.

Ten friends went out for a special dinner. If each person paid $24, what was the total cost of the dinner?

Answer:

Given,

Ten friends went out for a special dinner.

Each person paid $24

24 × 10 = $240

The total cost of the dinner is $240.

Question 2.

After dinner, the friends went out for ice cream. If each of the 10 friends paid $2.40, what was the total cost of the ice cream?

Answer:

Given,

After dinner, the friends went out for ice cream.

Each of the 10 friends paid $2.40

2.40 × 10 = $24

Thus the total cost of the ice cream is $24.

Question 3.

Another group of 10 friends bought tickets to a concert, but it was canceled before they could attend. If each of the 10 friends received a refund of $26 for the cost of the tickets, what was the total refund amount?

Answer:

Given,

Another group of 10 friends bought tickets to a concert, but it was canceled before they could attend.

Each of the 10 friends received a refund of $26 for the cost of the tickets

26 × 10 = $260

The total refund amount is $260.

Question 4.

The group also received a refund for parking. If each of the ten friends received a $2.60 refund for parking, what was the total parking refund?

Answer:

Given,

The group also received a refund for parking.

Each of the ten friends received a $2.60 refund for parking

2.60 × 10 = $26

The total parking refund is $26.

Question 5.

Jenny had a box with the dimensions (5 × 7) × 2 and it was filled with baseballs. Each ball took up a 1 × 1 × 1 space. How many baseballs were in Jenny’s box?

Answer:

Given,

Jenny had a box with the dimensions (5 × 7) × 2 and it was filled with baseballs.

Volume of the box = 5 × 7 × 2 = 70

Each ball took up a 1 × 1 × 1 space.

Volume of the ball = 1 × 1 × 1 = 1

N = 70/1

N = 70

Thus 70 baseballs in the Jenny’s box.

Question 6.

Richard also had a box full of baseballs. The dimensions of his box were 4 × (4 × 5). Each ball took up a 1 × 1 × 1 space. How many baseballs were in Richard’s box?

Answer:

Given,

Richard also had a box full of baseballs. The dimensions of his box were 4 × (4 × 5).

V = 4 × (4 × 5) = 4 × 20 = 80

Each ball took up a 1 × 1 × 1 space.

V = 1 × 1 × 1 = 1

N = 80/1 = 80

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

**Decimal Color & Order**

Question 1.

In each box below, color in the grids to show the number. Then write the number the way you’d read it over the phone to someone. The first one is done for you.

ex:

a.

Answer:

b.

Answer:

c.

Answer:

d.

Answer:

e.

Answer:

Question 2.

List the numbers from the boxes above, including the example, on these lines. Write them in order from least to greatest.

__________ < __________ < __________ < __________ < __________ < __________

Answer:

0.12 < 0.21 < 1.02 < 1.12 < 1.2 < 2

Question 3.

Jana says that 0.16 is greater than 0.4 because 16 is greater than 4. Do you agree with her? Use numbers, words, or labeled sketches to explain your answer.

Answer:

Given,

Jana says that 0.16 is greater than 0.4 because 16 is greater than 4.

Yes

0.16 is greater than 0.40

16 is greater than 4.

Yes, I agree with Jana.

Question 4.

**CHALLENGE** Use the digits 2, 4, and 6 to create six different decimal numbers and write them in the boxes below. When you’re finished, write the numbers in order from least to greatest.

__________ < __________ < __________ < __________ < __________ < __________

Answer:

2.46, 2.64, 4.62, 4.26, 6.42, 6.24

2.46 < 2.64 < 4.26 < 4.62 < 6.24 < 6.42

**More Decimal Color & Order**

Question 1.

In each box below, color in the grids to show the number. Then write the number the way you’d read it over the phone to someone. The first one is done for you.

ex:

a.

Answer:

b.

Answer:

c.

Answer:

d.

Answer:

e.

Answer:

Question 2.

List the numbers from the boxes above, including the example, on these lines. Write them in order from least to greatest.

__________ < __________ < __________ < __________ < __________ < __________

Answer:

0.18 < 0.81 < 1.08 < 1.18 < 1.8 < 1.81