# Bridges in Mathematics Grade 5 Student Book Unit 2 Module 4 Answer Key

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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 2 Module 4

Bridges in Mathematics Grade 5 Student Book Unit 2 Module 4 Session 1 Answer Key

Fraction Equivalents

Question 1.
For each of the following pairs of fractions, draw in lines so they have the same number of pieces. Then write the equivalent fraction name beside both and write an equation under each to match the sketch. a.  Explanation:
Given,
$$\frac{1}{6}$$ = $$\frac{1}{2}$$
Rewrite the fractions by equalizing the denominators to find the equivalent fractions.
$$\frac{1 × 2}{6 × 2}$$ = $$\frac{1 × 6}{2 × 6}$$
$$\frac{2}{12}$$  = $$\frac{6}{12}$$

b.  Explanation:
Given,
$$\frac{3}{4}$$ = $$\frac{2}{5}$$
Rewrite the fractions by equalizing the denominators to find the equivalent fractions.
$$\frac{3 × 5}{4 × 5}$$ = $$\frac{2 × 4}{5 × 4}$$
$$\frac{15}{20}$$  = $$\frac{8}{20}$$

c.  Explanation:
Given,
$$\frac{2}{6}$$ = $$\frac{3}{8}$$
Rewrite the fractions by equalizing the denominators to find the equivalent fractions.
$$\frac{2 × 8}{6 × 8}$$ = $$\frac{3 × 6}{8 × 6}$$
$$\frac{16}{48}$$  = $$\frac{18}{48}$$

Question 2.
Teri and Jon each got a granola bar from their dad. Teri ate $$\frac{3}{5}$$ of hers. Jon ate $$\frac{2}{3}$$ of his. Who ate more? Exactly how much more? Use the rectangles below to help solve the problem. Show all of your work. ____ ate exactly ______ more than_____ Jon ate exactly $$\frac{1}{15}$$ more than Teri.

Explanation:
Given that,
Teri ate $$\frac{3}{5}$$ of hers.
Jon ate $$\frac{2}{3}$$ of his.
Rewrite the fractions by equalizing the denominators.
$$\frac{3 × 3}{5 × 3}$$  $$\frac{2 × 5}{3 × 5}$$
$$\frac{9}{15}$$  $$\frac{10}{15}$$
When denominators are same, we compare the numerators to know who ate more.
$$\frac{10-9}{15}$$ = $$\frac{1}{15}$$
Therefore, Jon ate more than Teri.

Question 3.
Ryan rode his bike $$\frac{5}{6}$$ of a mile. James rode his bike $$\frac{7}{8}$$ of a mile. Who rode farther? Exactly how much farther? Use the rectangles below to help solve the problem. Show all of your work. ____ rode exactly ____ more of a mile than _____ James rode exactly $$\frac{1}{24}$$ more of a mile than Ryan.

Explanation:
Given that,
Ryan rode his bike $$\frac{5}{6}$$ of a mile.
James rode his bike $$\frac{7}{8}$$ of a mile.
Rewrite the fractions by equalizing the denominators.
$$\frac{5 × 8}{6 × 8}$$  $$\frac{7 × 6}{8 × 6}$$
$$\frac{40}{48}$$  $$\frac{42}{48}$$
When denominators are same, we compare the numerators to know who ate more.
$$\frac{42-40}{48}$$ = $$\frac{2}{48}$$
Simplify, $$\frac{1}{24}$$
Therefore, James rode exactly $$\frac{1}{24}$$ more of a mile than Ryan.

Question 4.
Find the least common multiple (LCM) of each pair of numbers.
ex 6 and 8
6, 12, 18, 8, 16, 24 is the LCM of 6 and 8

a. 3 and 5
15 is the LCM of 3 and 5.

Explanation:
The least common multiple (LCM) of each pair of numbers.
3 and 5
3, 6, 9, 12, 15
5, 10, 15
15 is the LCM of 3 and 5.

b. 4 and 5
20 is the LCM of 4 and 5.

Explanation:
The least common multiple (LCM) of each pair of numbers.
4 and 5
4, 8, 12, 16, 20
5, 10, 15, 20
20 is the LCM of 4 and 5.

Question 5.
Circle the fraction you think is greater in each pair. Then find out for sure by rewriting the fractions so they have common denominators. (Hint: Use the information from problem 4 to help.) Finally, use the < or > sign to compare the two fractions.
ex > $$\frac{2}{6}$$
$$\frac{3 \times 3}{8 \times 3}$$ = $$\frac{9}{24}$$
$$\frac{2 \times 4}{6 \times 4}$$ = $$\frac{8}{24}$$

Which Is Bigger?

Question 1.
Compare the fractions using the comparison symbols <, >, and =. Show your work to prove how you know which fraction is greater.

a. $$\frac{1}{3}$$ ____ $$\frac{2}{5}$$
$$\frac{1}{3}$$ < $$\frac{2}{5}$$

Explanation:
Given,
$$\frac{1}{3}$$ ___ $$\frac{2}{5}$$
$$\frac{1 \times 5}{3 \times 5}$$ = $$\frac{5}{15}$$
$$\frac{2 \times 3}{5 \times 3}$$ = $$\frac{6}{15}$$
So, $$\frac{1}{3}$$ < $$\frac{2}{5}$$

b. $$\frac{3}{8}$$ ____ $$\frac{1}{3}$$
$$\frac{3}{8}$$ > $$\frac{1}{3}$$

Explanation:
Given,
$$\frac{3}{8}$$ ___ $$\frac{1}{3}$$
$$\frac{3 \times 3}{8 \times 3}$$ = $$\frac{9}{24}$$
$$\frac{1 \times 8}{3 \times 8}$$ = $$\frac{8}{24}$$
So, $$\frac{9}{24}$$ > $$\frac{8}{24}$$

c. $$\frac{3}{5}$$ ____ $$\frac{5}{9}$$
$$\frac{1}{3}$$ > $$\frac{2}{5}$$

Explanation:
Given,
$$\frac{3}{5}$$ ___ $$\frac{5}{9}$$
$$\frac{3 \times 9}{5 \times 9}$$ = $$\frac{27}{45}$$
$$\frac{5 \times 5}{9 \times 5}$$ = $$\frac{25}{45}$$
So, $$\frac{3}{5}$$ > $$\frac{5}{9}$$

d. $$\frac{5}{12}$$ ____ $$\frac{2}{5}$$
$$\frac{5}{12}$$ > $$\frac{2}{5}$$

Explanation:
Given,
$$\frac{5}{12}$$ ___ $$\frac{2}{5}$$
$$\frac{5 \times 5}{12 \times 5}$$ = $$\frac{25}{60}$$
$$\frac{2 \times 12}{5 \times 12}$$ = $$\frac{24}{60}$$
So, $$\frac{5}{12}$$ > $$\frac{2}{5}$$

Question 2.
Jeff and Eric were painting 2 walls in Jeff’s bedroom. The walls were exactly the same size. Jeff painted $$\frac{2}{3}$$ of the first wall. Eric painted $$\frac{4}{7}$$ of the other wall. Who painted more? How much more? Use numbers, labeled sketches, or words to solve the problem.
Jeff painted more than Eric.

Explanation:
Given that,
Jeff painted $$\frac{2}{3}$$ of the first wall.
$$\frac{2 \times 7}{3 \times 7}$$ = $$\frac{14}{21}$$
Eric painted $$\frac{4}{7}$$ of the other wall.
$$\frac{4 \times 3}{7 \times 3}$$ = $$\frac{12}{21}$$
So, $$\frac{2}{3}$$ > $$\frac{4}{7}$$

Bridges in Mathematics Grade 5 Student Book Unit 2 Module 4 Session 2 Answer Key

Using the Greatest Common Factor to Simplify Fractions

Question 1.
Simplify each of the fractions. Then fill in the rest of the table.  Explanation:
Given ,
$$\frac{8}{12}$$ = $$\frac{4}{6}$$
Divide the numerator and denominator with greatest common multiple factor.
Common multiple factors of 8 and 12 are:
8 = 1, 2, 4, 8
12 = 1, 2, 3, 4, 12
So, 4 is the greatest common multiple factor of 8 and 12.
$$\frac{8÷4}{12÷4}$$ = $$\frac{2}{3}$$
Divide the numerator and denominator with greatest common multiple factor.
Common multiple factors of 4 and 6 are:
4 = 1, 2, 4
6 = 1, 2, 3, 6
So, 4 is the greatest common multiple factor of 4 and 6.
$$\frac{4÷2}{6÷2}$$ = $$\frac{2}{3}$$
So, $$\frac{8}{12}$$ = $$\frac{4}{6}$$

Question 2.
Find the greatest common factor of each pair of numbers below.
ex
6 and 16
Factors of 6: 1, 2, 3, 6,
Factors of 16: 1, 2, 4, 8, 16
Greatest Common Factor: 2

a. 6 and 21
Factors of 6:
Factors of 21:
Greatest Common Factor:
6 and 21
Factors of 6: 1, 2, 3, 6,
Factors of 21: 1, 3, 7, 21
Greatest Common Factor: 3

Explanation:
We know that,
The greatest common factor is the greatest factor that divides both numbers.
To find the greatest common factor, first list the factors of each number.

b. 8 and 24
Factors of 8:
Factors of 24:
Greatest Common Factor:
8 and 24
Factors of 8: 1, 2, 4, 8,
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Greatest Common Factor: 8

Explanation:
We know that,
The greatest common factor is the greatest factor that divides both numbers.
To find the greatest common factor, first list the factors of each number.

c. 18 and 24
Factors of 18:
Factors of 24:
Greatest Common Factor:
18 and 24
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 12, 24
Greatest Common Factor: 6

Explanation:
We know that,
The greatest common factor is the greatest factor that divides both numbers.
To find the greatest common factor, first list the factors of each number.

Using the Greatest Common Factor to Simplify Fractions

Question 3.
ex $$\frac{6}{16}$$ $$\frac{6 \div 2}{16 \div 2}$$ = $$\frac{3}{8}$$ $$\frac{6}{16}$$ = $$\frac{3}{8}$$

a. $$\frac{6}{21}$$
$$\frac{2}{7}$$

Explanation:
Given, $$\frac{6}{21}$$
Simplify the fractions, $$\frac{6 \div 3}{21 \div 3}$$ = $$\frac{2}{7}$$
So, $$\frac{6}{21}$$ = $$\frac{2}{7}$$

b. $$\frac{8}{24}$$
$$\frac{1}{3}$$

Explanation:
Given, $$\frac{8}{24}$$
Simplify the fractions, $$\frac{8 \div 4}{24 \div 4}$$ = $$\frac{2}{6}$$ = $$\frac{1}{3}$$
So, $$\frac{8}{24}$$ = $$\frac{1}{3}$$

c. $$\frac{18}{24}$$
$$\frac{3}{4}$$

Explanation:
Given, $$\frac{18}{24}$$
Simplify the fractions, $$\frac{18 \div 6}{24 \div 6}$$ = $$\frac{3}{4}$$
So, $$\frac{18}{24}$$ = $$\frac{3}{4}$$

Question 4.
A fraction is in its simplest form when its numerator and denominator have no common factor other than 1. Look at the fractions below.

• Circle the fractions that can be simplified.
• Put a line under the fractions that are already in simplest form.

$$\frac{3}{6}$$ $$\frac{5}{8}$$ $$\frac{4}{10}$$ $$\frac{12}{15}$$ $$\frac{2}{7}$$ $$\frac{8}{14}$$ $$\frac{3}{13}$$ Explanation:
For each problem, show all your work using numbers, words, or labeled sketches.
Convert an improper fraction to a mixed number if needed and be sure to write your answer in simplest form.
In the above shown figure circled the fractions that can be simplified.
$$\frac{3}{6}$$  $$\frac{4}{10}$$ $$\frac{12}{15}$$  $$\frac{8}{14}$$
in the above figure a line under the fractions that are already in simplest form.
$$\frac{5}{8}$$ $$\frac{2}{7}$$ $$\frac{3}{13}$$

Question 5.
Carlos and Jade are eating mini pizzas for lunch. Jade eats $$\frac{3}{4}$$ of her mini pizza. Carlos eats $$\frac{8}{12}$$ of his mini pizza. How much pizza do they eat together?
1$$\frac{10}{24}$$ of pizza.

Explanation:
Given that,
Jade eats $$\frac{3}{4}$$ of her mini pizza.
Carlos eats $$\frac{8}{12}$$ of his mini pizza.
Rewrite the fractions by equalizing the denominators.
$$\frac{3×12}{4×12}$$ = $$\frac{36}{48}$$ = 1
$$\frac{8×4}{12×4}$$ = $$\frac{32}{48}$$
So, $$\frac{36+32}{48}$$ = $$\frac{68}{48}$$ = $$\frac{34}{24}$$
Simplify, 1$$\frac{10}{24}$$

Question 6.
Adam and Sophie are also eating mini pizzas for lunch. Adam ate $$\frac{5}{8}$$ of his pizza. Sophie ate $$\frac{2}{3}$$ of her pizza.
a. Who ate more?
Sophie ate more.

Explanation:
Given that,
Adam ate $$\frac{5}{8}$$ of his pizza.
Sophie ate $$\frac{2}{3}$$ of her pizza.
Rewrite the fractions by equalizing the denominators.
$$\frac{5×3}{8×3}$$ = $$\frac{15}{24}$$
$$\frac{2×8}{3×8}$$ = $$\frac{16}{24}$$
By comparing both, Sophie ate more.

b. How much more?
Sophie ate $$\frac{1}{24}$$ more.

Explanation:
Given that,
Adam ate $$\frac{5}{8}$$ of his pizza.
Sophie ate $$\frac{2}{3}$$ of her pizza.
Rewrite the fractions by equalizing the denominators.
$$\frac{5×3}{8×3}$$ = $$\frac{15}{24}$$
$$\frac{2×8}{3×8}$$ = $$\frac{16}{24}$$
By comparing both, $$\frac{16}{24}$$ – $$\frac{15}{24}$$
Therefore, Sophie ate $$\frac{1}{24}$$ more.

Simplifying Fractions

Question 1.
List the factors of each number below.
a. 12: ____________
1, 2, 3, 4, 6, 12

Explanation:
A factor is a number that divides another number, leaving no remainder.
When we multiply two whole numbers gives us a product,
then the numbers we are multiplying are factors of the product because they are divisible by the product.
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
4 x 3 = 12
6 x 2 = 12
12 x 1 = 12

b. 15: _________
1, 3, 5, 15

Explanation:
A factor is a number that divides another number, leaving no remainder.
When we multiply two whole numbers gives us a product,
then the numbers we are multiplying are factors of the product because they are divisible by the product.
1 x 15 = 15
3 x 5 = 15
5 x 3 = 15
15 x 1 = 15

c. 18: ____________
1, 2, 3, 6, 9, 18

Explanation:
A factor is a number that divides another number, leaving no remainder.
When we multiply two whole numbers gives us a product,
then the numbers we are multiplying are factors of the product because they are divisible by the product.
1 x 18 = 18
2 x 9 = 18
3 x 6 = 18
6 x 3 = 18
9 x 2 = 18
18 x 1 = 18

Question 2.
Find the simplest form of each fraction below. The factors from item 1 might help.

a. $$\frac{12}{15}$$ =
$$\frac{4}{5}$$

Explanation:
Given, $$\frac{12}{15}$$
The common multiple factors of 12 and 15 are 3.
$$\frac{12 \div 3}{15 \div 3}$$ = $$\frac{4}{5}$$

b. $$\frac{4}{18}$$ =
$$\frac{2}{9}$$

Explanation:
Given, $$\frac{4}{18}$$
The common multiple factors of 4 and 18 are 2.
$$\frac{4 \div 2}{18 \div 2}$$ = $$\frac{2}{9}$$

c. $$\frac{15}{18}$$ =
$$\frac{5}{6}$$

Explanation:
Given, $$\frac{15}{18}$$
The common multiple factors of 15 and 18 are 3.
$$\frac{15 \div 3}{18 \div 3}$$ = $$\frac{5}{6}$$

d. $$\frac{18}{12}$$ =
$$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

Explanation:
Given, $$\frac{18}{12}$$
The common multiple factors of 18 and 12 are 6.
$$\frac{18 \div 6}{12 \div 6}$$ = $$\frac{3}{2}$$

Question 3.
Find the simplest form of each fraction. Show your work.

a. $$\frac{21}{28}$$ =
$$\frac{3}{4}$$

Explanation:
Given, $$\frac{21}{28}$$
The common multiple factors of 21 and 28 are 7.
$$\frac{21 \div 7}{28 \div 7}$$ = $$\frac{3}{4}$$

b. $$\frac{36}{45}$$ =
$$\frac{4}{5}$$

Explanation:
Given, $$\frac{36}{45}$$
The common multiple factors of 36 and 45 are 9.
$$\frac{36 \div 9}{45 \div 9}$$ = $$\frac{4}{5}$$

c. $$\frac{27}{18}$$ =
$$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

Explanation:
Given, $$\frac{27}{18}$$
The common multiple factors of 27 and 18 are 9.
$$\frac{27 \div 9}{18 \div 9}$$ = $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

Question 4.
Suzie says that $$\frac{7}{35}$$ is a fraction in simplest form. Do you agree or disagree? Explain.
Yes, Agree.

Explanation:
Given that,
Suzie says that $$\frac{7}{35}$$ is a fraction in simplest form.
The common factor of 7 and 35 are 7.
7 x 1 = 7
7 x 5 = 35

Question 5.
Alex says that all unit fractions are in simplest form. Do you agree or disagree? Explain. (A unit fraction has 1 as its numerator, like $$\frac{1}{3}$$ or $$\frac{1}{12}$$.)
Yes, all unit fractions proper fractions .

Explanation:
As we know that,
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer .

Question 6.
Find $$\frac{12}{15}$$ + $$\frac{2}{3}$$. Show your work.
1$$\frac{7}{15}$$

Explanation:
Given, $$\frac{12}{15}$$ + $$\frac{2}{3}$$
When the fractions are unlike, take the LCM of the denominators.
$$\frac{(12×1) + (2×5)}{15}$$ = $$\frac{12+10}{15}$$ = $$\frac{22}{15}$$
Reduce to the simplest form, 1$$\frac{7}{15}$$

Bridges in Mathematics Grade 5 Student Book Unit 2 Module 4 Session 3 Answer Key

Problem Solving with the LCM & GCF

Question 1.
Julia bought $$\frac{3}{5}$$ of a yard of red ribbon and $$\frac{10}{15}$$ of a yard of purple ribbon.

a. Which piece of ribbon was longer?
Purple ribbon.

Explanation:
Given that,
Julia bought $$\frac{3}{5}$$ of a yard of red ribbon.
$$\frac{10}{15}$$ of a yard of purple ribbon.
Take the LCM of the denominators.
LCM of 5 and 15 is 5.
$$\frac{3}{5}$$ = $$\frac{3 × 3}{5 × 3}$$ = $$\frac{9}{15}$$
By compare both the fractions, purple ribbon is $$\frac{1}{15}$$ yard longer.

b. Exactly what fraction of a yard longer was it?
Given that,
Julia bought $$\frac{3}{5}$$ of a yard of red ribbon.
$$\frac{10}{15}$$ of a yard of purple ribbon.
The LCM of 5 and 15 = 5
$$\frac{3}{5}$$ = $$\frac{3 × 3}{15}$$ = $$\frac{9}{15}$$
By compare both the fractions,
$$\frac{10}{15}$$ – $$\frac{9}{15}$$ = $$\frac{1}{15}$$
So, purple ribbon is $$\frac{1}{15}$$ yard longer.

Question 2.
Anthony goes running three times a week. This week, he ran $$\frac{3}{5}$$ of a mile on Monday, $$\frac{2}{3}$$ of a mile on Wednesday, and $$\frac{3}{4}$$ of a mile on Friday. How far did Anthony run this week?
2 $$\frac{1}{60}$$ miles.

Explanation:
Anthony ran $$\frac{3}{5}$$ of a mile on Monday,
$$\frac{2}{3}$$ of a mile on Wednesday,
$$\frac{3}{4}$$ of a mile on Friday.
Total miles did Anthony run this week,
$$\frac{3}{5}$$ + $$\frac{2}{3}$$ + $$\frac{3}{4}$$
LCM of 5, 3 and 4 = 60
$$\frac{(3 × 12) + (2 × 20) + (3 × 15)}{60}$$ = $$\frac{36 + 40 + 45}{60}$$
= $$\frac{121}{60}$$ = 2 $$\frac{1}{60}$$ miles.

Question 3.
On Monday, Leah spent $$\frac{5}{6}$$ of an hour working on her homework, on Tuesday, she spent $$\frac{3}{4}$$ of an hour on her homework, and on Wednesday she finished her homework in $$\frac{5}{8}$$ of an hour.

a. On which day did Leah spent the least amount of time on her homework? Prove it.
Leah spent the least amount of time on her homework on Wednesday.

Explanation:
Given that,
On Monday, Leah spent $$\frac{5}{6}$$ of an hour working on her homework.
On Tuesday, she spent $$\frac{3}{4}$$ of an hour on her homework.
On Wednesday she finished her homework in $$\frac{5}{8}$$ of an hour.
Take LCM of 6, 4, 8 = 24
$$\frac{(5 × 4)}{24}$$; $$\frac{(3 × 6)}{24}$$; $$\frac{(5 × 3)}{24}$$
= $$\frac{20}{24}$$; $$\frac{18}{24}$$; $$\frac{15}{24}$$
BY comparing all the fractions, Leah spent the least amount of time on her homework on Wednesday.

b. How much time did Leah spend doing homework on Monday, Tuesday, and Wednesday in all?
2 $$\frac{5}{24}$$ hours.

Explanation:
Given that,
On Monday, Leah spent $$\frac{5}{6}$$ of an hour working on her homework.
On Tuesday, she spent $$\frac{3}{4}$$ of an hour on her homework.
On Wednesday she finished her homework in $$\frac{5}{8}$$ of an hour.
Take LCM of 6, 4, 8 = 24
$$\frac{(5 × 4) + (3 × 6) + (5 × 3)}{24}$$ = $$\frac{20 + 18 + 15}{24}$$
= $$\frac{53}{24}$$ = 2 $$\frac{5}{24}$$ hours.

Question 4.
On Monday, Kevin spent $$\frac{4}{5}$$ of an hour working on his homework, on Tuesday he spent $$\frac{2}{3}$$ of an hour on his homework, and on Wednesday he finished his homework in $$\frac{7}{10}$$ of an hour. How long did Kevin spend doing homework on Monday, Tuesday, and Wednesday in all?
2 $$\frac{5}{30}$$ hours.

Explanation:
Given that,
On Monday, Kevin spent $$\frac{4}{5}$$ of an hour working on his homework.
On Tuesday he spent $$\frac{2}{3}$$ of an hour on his homework.
On Wednesday he finished his homework in $$\frac{7}{10}$$ of an hour.
Total hours did Kevin spend doing homework on Monday, Tuesday, and Wednesday in all,
Take LCM of 5, 3, 10 = 30
$$\frac{(4 × 6) + (2 × 10) + (7 × 3)}{30}$$ = $$\frac{24 + 20 + 21}{30}$$
= $$\frac{65}{30}$$ = 2 $$\frac{5}{30}$$ hours.

Question 5.
CHALLENGE Who spent more time doing homework over Monday, Tuesday, and Wednesday, Leah or Kevin? How much more? How much time did the two of them combined spend doing homework? Express your answers as fractions or mixed numbers, and in hours and minutes as well.
4$$\frac{45}{120}$$ hours.

Explanation:
with reference to the information given in Question 3 and 4,
Leah spent 2 $$\frac{5}{24}$$ hours and Kevin spent 2 $$\frac{5}{30}$$ hours.
First convert mixed fractions into improper fractions.
2 $$\frac{5}{24}$$ hours = $$\frac{53}{24}$$ hours.
2 $$\frac{5}{30}$$ hours = $$\frac{65}{30}$$ hours.
LCM of 24 and 30 = 120
$$\frac{(53 × 5) + (65 × 4)}{120}$$ = $$\frac{265 + 260}{120}$$
= $$\frac{525}{120}$$ = 4$$\frac{45}{120}$$ hours.

Evan’s Turtle

Question 1.
One side of the aquarium’s base is $$\frac{3}{4}$$ of a yard long. The other side is $$\frac{5}{7}$$ of a yard long. What is the perimeter of the base of the aquarium?
Perimeter = $$\frac{15}{21}$$ yards.

Explanation:
Given that,
One side of the aquarium’s base is $$\frac{3}{4}$$ of a yard long.
The other side is $$\frac{5}{7}$$ of a yard long.
Perimeter = Length x width
P = $$\frac{3}{4}$$ x $$\frac{5}{7}$$
P = $$\frac{3 × 5}{4 × 7}$$
P = $$\frac{15}{21}$$

Question 2.
Evan found two sticks for his turtle’s aquarium. One stick was $$\frac{3}{4}$$ of a foot long and the other was $$\frac{10}{12}$$ of a foot long. Which stick was longer? What fraction of a foot longer?
The other stick is $$\frac{1}{12}$$ of a foot longer.

Explanation:
Given that,
One stick was $$\frac{3}{4}$$ of a foot long.
The other was $$\frac{10}{12}$$ of a foot long.
Fraction of the foot longer,
Rewrite the fractions with common denominators.
$$\frac{3}{4}$$ = $$\frac{3×3}{4×3}$$ = $$\frac{9}{12}$$
By compare both the fractions, the other stick is $$\frac{1}{12}$$ of a foot longer.

Question 3.
On Friday, Evan’s turtle swam for $$\frac{4}{10}$$ of an hour. Then, he slept for $$\frac{3}{8}$$ of an hour.

a Did Evan’s turtle swim or sleep longer? How much longer?
Evan’s turtle swim $$\frac{18}{80}$$ hours longer.

Explanation:
Given that,
Evan’s turtle swam for $$\frac{4}{10}$$ of an hour.
Then, he slept for $$\frac{3}{8}$$ of an hour.
Rewrite the fractions with common denominators.
$$\frac{4}{10}$$ = $$\frac{4×8}{10×8}$$ = $$\frac{48}{80}$$
$$\frac{3}{8}$$ = $$\frac{3×10}{8×10}$$ = $$\frac{30}{80}$$
By compare both the fractions, Evan’s turtle swim $$\frac{18}{80}$$ hours longer.

b. How long did Evan’s turtle swim and sleep?
$$\frac{78}{80}$$ hours.
Evan’s turtle swam for $$\frac{4}{10}$$ of an hour.
Then, he slept for $$\frac{3}{8}$$ of an hour.
$$\frac{4}{10}$$ = $$\frac{4×8}{10×8}$$ = $$\frac{48}{80}$$
$$\frac{3}{8}$$ = $$\frac{3×10}{8×10}$$ = $$\frac{30}{80}$$
$$\frac{48+30}{80}$$ = $$\frac{78}{80}$$