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## Bridges in Mathematics Grade 5 Home Connections Answer Key Unit 2 Module 3

**Bridges in Mathematics Grade 5 Home Connections Unit 2 Module 3 Session 1 Answer Key**

**Using a Ratio Table**

Question 1.

Use a ratio table to multiply the numbers.

ex 23 × 26

a.

35 × 44

Answer:

By multiplying 35 by 2 we get 70.

35 × 2 = 70

By multiplying 35 by 4 we get 140.

35 × 4 = 140

By multiplying 35 by 40 we get 1400.

35 × 40 = 1400

By multiplying 35 by 44 we get 1540.

35 × 44 = 1540

b.

39 × 20

Answer:

By multiplying 39 by 2 we get 78.

39 × 2 = 78

By multiplying 39 by 20 we get 780.

39 × 20 = 780

c.

18 × 65

Answer:

65 × 1 = 65

By multiplying 65 by 1 we get 65.

65 × 2 = 130

By multiplying 65 by 2 we get 130.

65 × 20 = 1300

By multiplying 65 by 20 we get 1300.

65 × 18 = 1170

By multiplying 65 by 18 we get 1170.

d.

4 × 18

Answer:

1 × 18 = 18

By multiplying 1 by 18 we get 18.

2 × 18 = 36

By multiplying 2 by 18 we get 36.

10 × 18 = 180

By multiplying 10 by 18 we get 180.

4 × 18 = 72

By multiplying 4 by 18 we get 72.

e.

75 × 15

Answer:

By multiplying 15 by 1 we get 15.

15 × 1 = 15

By multiplying 15 by 100 we get 1500.

15 × 100 = 1500

By multiplying 15 by 50 we get 750.

15 × 50 = 750

By multiplying 15 by 25 we get 375.

15 × 25 = 375

By multiplying 15 by 75 we get 1125.

15 × 75 = 1125

Question 2.

True or False?

a. 98 × 34 = (100 × 34) – (2 × 34) _______

Answer:

98 × 34 = 3332

100 × 34 = 3400

2 × 34 = 68

3400 – 68 = 3332

3332 = 3332

98 × 34 = (100 × 34) – (2 × 34) is true

b. 46 × 28 = 23 × 56 ________

Answer:

46 × 28 = 1288

23 × 56 = 1288

1288 = 1288

46 × 28 = 23 × 56 is true.

Question 3.

Veronica has to multiply 398 × 18. She says she can multiply 400 × 18 and then take away one group of 18.

a. Do you agree with Veronica? Explain.

Answer: No, I do not agree with Veronica. She must take away 2 groups of 18 to get the right answer.

b. Write an expression that shows Veronica’s thinking.

Answer:

Veronica has to multiply 398 × 18. She says she can multiply 400 × 18 and then take away one group of 18.

(400 × 18) – (1 × 18)

7200 – 18 = 7182

c. What is 398 × 18? Show your work.

398

×18

7164

Question 4.

**CHALLENGE** The aquarium has 198 fish tanks with 15 fish in each. They also have 297 tanks with 12 crustaceans in each. Does the aquarium have more fish or more crustaceans? How many more? Make an estimate and explain your reasoning. Then determine the actual answer.

a. Estimate and reasoning: b Actual answer: (Show your work.)

Answer:

Given,

The aquarium has 198 fish tanks with 15 fish in each. They also have 297 tanks with 12 crustaceans in each.

Fish = 198 × 15 = 2970

Crustaceans = 297 × 12 = 3564

b. Actual answer: (Show your work.)

Answer: It has more Crustaceans than fishes.

c. Is your answer reasonable? (Think about your estimate.)

Answer: Yes

(200 × 15) – (2 × 15)

3000 – 30 = 2970

**Bridges in Mathematics Grade 5 Home Connections Unit 2 Module 3 Session 3 Answer Key**

**In the Library**

Question 1.

The librarian at our school asked the fourth and fifth graders to vote on their favorite kind of book. The circle graphs below show the results. Use the information to answer the questions below.

a. What fraction of the fourth graders said they liked nonfiction books best? How do you know?

Answer:

1 – \(\frac{1}{2}\) + \(\frac{1}{4}\)

1 – \(\frac{3}{4}\) = \(\frac{1}{4}\)

\(\frac{1}{4}\) fraction of the fourth graders said they liked nonfiction books best

b. If there are 96 fourth graders, how many like fantasy books best? Show your work.

Answer:

96 × \(\frac{1}{4}\) = 24

24 fourth graders like fantasy books best.

c. What fraction of the fifth graders said they like fantasy books best? How do you know?

Answer:

1 – \(\frac{3}{4}\) – \(\frac{1}{8}\)

\(\frac{1}{4}\) – \(\frac{1}{8}\)

LCD is 8

\(\frac{2}{8}\) – \(\frac{1}{8}\) = \(\frac{1}{8}\)

\(\frac{1}{8}\) fraction of the fifth graders said they like fantasy books best.

d. If there are 112 fifth graders, how many like nonfiction books best? Show your work.

Answer:

112 × \(\frac{1}{8}\) = 14

14 fifth graders like nonfiction books best.

e. What fraction of the fifth graders said they liked fiction books best? How do you know?

Answer:

\(\frac{3}{4}\) fraction of the fifth graders said they liked fiction books best.

Question 2.

Madeline walked 1\(\frac{1}{2}\) miles to her Aunt Jenny’s house yesterday morning. After visiting with Aunt Jenny, Madeline walked \(\frac{3}{4}\) of a mile to the park, where her mother picked her up. How many miles in all did she walk yesterday? Show all your work.

Answer:

Given,

Madeline walked 1\(\frac{1}{2}\) miles to her Aunt Jenny’s house yesterday morning. After visiting with Aunt Jenny, Madeline walked \(\frac{3}{4}\) of a mile to the park, where her mother picked her up.

1\(\frac{1}{2}\) + \(\frac{3}{4}\)

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

LCD is 4.

\(\frac{6}{4}\) + \(\frac{3}{4}\) = \(\frac{9}{4}\)

Question 3.

Sara and her mother bought some vegetables at the farmer’s market yesterday. They bought 2 \(\frac{3}{4}\) pounds of cabbage, \(\frac{1}{2}\) a pound of onions, and 1 \(\frac{3}{8}\) pounds of carrots. How many pounds of vegetables did they buy in all? Show all your work.

Answer:

Given,

Sara and her mother bought some vegetables at the farmer’s market yesterday. They bought 2 \(\frac{3}{4}\) pounds of cabbage, \(\frac{1}{2}\) a pound of onions, and 1 \(\frac{3}{8}\) pounds of carrots.

2 \(\frac{3}{4}\) + \(\frac{1}{2}\) + 1 \(\frac{3}{8}\)

\(\frac{11}{4}\) + \(\frac{1}{2}\) + \(\frac{11}{8}\)

LCD is 8

\(\frac{22}{8}\) + \(\frac{4}{8}\) + \(\frac{11}{8}\) = \(\frac{37}{8}\) = 4\(\frac{5}{8}\)

Question 4.

**CHALLENGE** Madison went to the mall with her big sister last weekend. Their mom dropped them on at 1:00 and said, “I’ll pick you up at 2:30. The girls spent \(\frac{5}{6}\) or an hour at the toy store, \(\frac{2}{3}\) of an hour at the pet store, and \(\frac{1}{2}\) an hour at the food court. When they got back to the bench to meet their mom, she was already there. She said, “Where have you been? I’ve been waiting _____ of an hour for you!” How long had their mom been waiting for them?

Answer:

Given,

Madison went to the mall with her big sister last weekend. Their mom dropped them on at 1:00 and said, “I’ll pick you up at 2:30.

2:30 – 1:00 = 1:30

The girls spent \(\frac{5}{6}\) or an hour at the toy store,

\(\frac{2}{3}\) of an hour at the pet store, and

\(\frac{1}{2}\) an hour at the food court.

\(\frac{5}{6}\) + \(\frac{2}{3}\) + \(\frac{1}{2}\)

LCD is 6

\(\frac{5}{6}\) + \(\frac{4}{6}\) + \(\frac{3}{6}\) = \(\frac{12}{6}\) = 2

2 – 1\(\frac{1}{2}\) = \(\frac{1}{2}\) hrs = 0.5 hr

**Bridges in Mathematics Grade 5 Home Connections Unit 2 Module 3 Session 5 Answer Key**

**Fraction Addition & Subtraction Story Problems**

Question 1.

Find the sum or the difference for each pair of numbers. Show all your work.

a.

\(\frac{5}{14}\) + \(\frac{4}{5}\) =

Answer:

\(\frac{5}{14}\) + \(\frac{4}{5}\)

LCD of 14, 5 is 70

\(\frac{25}{70}\) + \(\frac{56}{70}\) = \(\frac{25+56}{70}\) = \(\frac{81}{70}\) = 1\(\frac{11}{70}\)

\(\frac{5}{14}\) + \(\frac{4}{5}\) = 1\(\frac{11}{70}\)

b.

\(\frac{7}{9}\) – \(\frac{4}{7}\) =

Answer:

\(\frac{7}{9}\) – \(\frac{4}{7}\)

LCD of 7, 9 is 63.

\(\frac{49}{63}\) – \(\frac{36}{63}\) = \(\frac{49-36}{63}\) = \(\frac{13}{63}\)

\(\frac{7}{9}\) – \(\frac{4}{7}\) = \(\frac{13}{63}\)

c.

1\(\frac{7}{15}\) + \(\frac{3}{9}\) =

Answer:

1\(\frac{7}{15}\) + \(\frac{3}{9}\)

1 + \(\frac{7}{15}\) + \(\frac{3}{9}\)

\(\frac{7}{15}\) + \(\frac{3}{9}\)

LCD of 9, 15 is 45

\(\frac{21}{45}\) + \(\frac{15}{45}\) = \(\frac{36}{45}\) = \(\frac{4}{5}\)

1 + \(\frac{4}{5}\) = 1\(\frac{4}{5}\)

d.

2\(\frac{1}{3}\) – 1\(\frac{3}{5}\) =

Answer:

2\(\frac{1}{3}\) – 1\(\frac{3}{5}\)

2 + \(\frac{1}{3}\) – 1 – \(\frac{3}{5}\)

2 – 1 = 1

\(\frac{1}{3}\) – \(\frac{3}{5}\)

LCD is 15

\(\frac{5}{15}\) – \(\frac{9}{15}\) = –\(\frac{4}{15}\)

1 – \(\frac{4}{15}\) = \(\frac{11}{15}\)

Question 2.

George and his dad made some snack mix for their camping trip. To make it, they used 2 cups of mini pretzels, \(\frac{3}{4}\) cup of peanuts, and \(\frac{2}{3}\) cup of chocolate chips. How many cups of snack mix did they have when they were finished? Show all your work.

Answer:

Given,

George and his dad made some snack mix for their camping trip.

To make it, they used 2 cups of mini pretzels, \(\frac{3}{4}\) cup of peanuts, and \(\frac{2}{3}\) cup of chocolate chips.

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

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

LCD is 12

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

2 + 1 \(\frac{5}{12}\) = 3 \(\frac{5}{12}\) cups of snack mix

Question 3.

Lisa drank \(\frac{7}{16}\) of a bottle of water during the soccer game. Julianne drank \(\frac{2}{3}\) of the water in a bottle that was the same size as Lisa’s. Who drank more water and by exactly how much? Show all of your work.

Answer:

Given,

Lisa drank \(\frac{7}{16}\) of a bottle of water during the soccer game.

Julianne drank \(\frac{2}{3}\) of the water in a bottle that was the same size as Lisa’s.

\(\frac{2}{3}\) – \(\frac{7}{16}\)

LCD is 48.

\(\frac{32}{48}\) – \(\frac{21}{48}\) = \(\frac{11}{48}\)

Question 4.

**CHALLENGE** Austin went to the science museum. He was there for 2 hours. He spent \(\frac{3}{5}\) of his time doing experiments. Then, he spent \(\frac{1}{3}\) of his time at the water station. Finally, he spent the rest of his time looking at skeletons. How long did Austin spend looking at skeletons? Show all your work, and express your answer as a number of minutes and as a fraction of an hour.

Answer:

Given,

Austin went to the science museum. He was there for 2 hours.

He spent \(\frac{3}{5}\) of his time doing experiments. Then, he spent \(\frac{1}{3}\) of his time at the water station.

1 – \(\frac{3}{5}\) – \(\frac{1}{3}\)

1 – \(\frac{9}{15}\) – \(\frac{5}{15}\) = \(\frac{1}{15}\)

2 hours = 120 minutes

120 × \(\frac{1}{15}\) = 8 minutes or 13/100 of an hour