## Math Expressions Common Core Grade 4 Unit 7 Lesson 13 Answer Key Focus on Mathematical Practices

**Math Expressions Grade 4 Unit 7 Lesson 13 Homework**

**Write >, < or = to compare these numbers.**

Question 1.

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

Answer:

\(\frac{3}{4}\) > \(\frac{2}{8}\)

Explanation:

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

Simplify \(\frac{2}{8}\) with 2

We get \(\frac{1}{4}\)

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

When the denominators are common subtract the numerators to compare

\(\frac{3}{4}\) > \(\frac{1}{4}\)

Question 2.

\(\frac{4}{10}\) \(\frac{4}{5}\)

Answer:

\(\frac{4}{10}\) < \(\frac{4}{5}\)

Explanation:

\(\frac{4}{10}\) \(\frac{4}{5}\)

Simplify \(\frac{4}{10}\) with 2

We get \(\frac{2}{5}\)

\(\frac{2}{5}\) \(\frac{4}{5}\)

When the denominators are common subtract the numerators to compare

\(\frac{2}{5}\) < \(\frac{4}{5}\)

Question 3.

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

Answer:

1\(\frac{3}{6}\) < 2\(\frac{3}{6}\)

Explanation:

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

Convert the mixed fraction to whole fraction as

\(\frac{9}{6}\) \(\frac{15}{6}\)

Simplify with 3 on both sides

\(\frac{9 \div 3}{6 \div 3}\) \(\frac{15 \div 3}{6 \div 3}\)

\(\frac{3}{2}\) \(\frac{5}{2}\)

When denominators are common subtract the numerators to compare

\(\frac{3}{2}\) < \(\frac{5}{2}\)

1\(\frac{3}{6}\) < 2\(\frac{3}{6}\)

Question 4.

1\(\frac{1}{6}\) 1\(\frac{1}{4}\)

Answer:

1\(\frac{1}{6}\) < 1\(\frac{1}{4}\)

Explanation:

1\(\frac{1}{6}\) 1\(\frac{1}{4}\)

Convert the mixed fraction to whole fraction as

\(\frac{7}{6}\) \(\frac{5}{4}\)

Simplify on both sides to make common denominators

\(\frac{7×2}{6×2}\) = \(\frac{5×3}{4×3}\)

\(\frac{14}{12}\) = \(\frac{15}{12}\)

When the denominators are same subtract numerators to compare

So,1 \(\frac{1}{6}\) <1 \(\frac{1}{4}\)

Question 5.

2\(\frac{7}{8}\) 2\(\frac{3}{7}\)

Answer:

2\(\frac{7}{8}\) > 2\(\frac{3}{7}\)

Explanation:

2\(\frac{7}{8}\) 2\(\frac{3}{7}\)

Convert the mixed fraction to whole fraction as

\(\frac{23}{8}\) \(\frac{17}{7}\)

So,\(\frac{23}{8}\) > \(\frac{17}{7}\)

Question 6.

1\(\frac{4}{9}\) 1\(\frac{5}{10}\)

Answer:

1\(\frac{4}{9}\) < 1\(\frac{5}{10}\)

Explanation:

1\(\frac{4}{9}\) 1\(\frac{5}{10}\)

Convert the mixed fraction to whole fraction as

\(\frac{13}{4}\) \(\frac{15}{10}\)

Simplify on both sides to make common denominators

\(\frac{13×5}{4×5}\) = \(\frac{15×2}{10×2}\)

\(\frac{65}{20}\) = \(\frac{30}{20}\)

When the denominators are same subtract numerators to compare

\(\frac{13}{4}\) < \(\frac{15}{10}\)

So,1 \(\frac{1}{6}\) <1 \(\frac{1}{4}\)

**Complete.**

Question 7.

Answer:

Explanation:

By multiplying both the numerator and denominator with the same number, we can simplify as shown above. By multiplying with 5

Question 8.

Answer:

Explanation:

By multiplying both the numerator and denominator with the same number, we can simplify as shown above. By multiplying with 2

Question 9.

Answer:

Explanation:

By multiplying both the numerator and denominator with the same number, we can simplify as shown above. By multiplying with 8

Question 10.

Answer:

Explanation:

By dividing both the numerator and denominator with the same number, we can minimize or simplify as shown above.

Question 11.

Answer:

Explanation:

By dividing both the numerator and denominator with the same number, we can minimize or simplify as shown above.

Question 12.

Answer:

Explanation:

By dividing both the numerator and denominator with the same number, we can minimize or simplify as shown above.

**Solve. Show your work.**

Question 13.

Cole lives 2.4 miles from the library. Gwen lives 2.04 miles from the library. Xander lives 2.40 miles from the library. Who lives closest to the library: Cole, Gwen, or Xander?

Answer:

Gwen lives closest to the library (2.04 miles from the library)

Explanation:

We know zero after decimal has no value

So, 2.4 and 2.40 are same

with reference to the number line from 0

smaller number = 2.04

Greater number = 2.4

So, 2.04 is smaller then 2.4

Question 14.

After making his art project, Robbie has \(\frac{2}{10}\) yard of rope left. What is \(\frac{2}{10}\) written as a decimal?

Answer: 0.2

Explanation:

Divide 2 with 10, we get

\(\frac{2}{10}\) = 0.2

**Math Expressions Grade 4 Unit 7 Lesson 13 Remembering**

**Solve. Show your work.**

Question 1.

A 2-quart bottle of juice has 1,040 calories. Each serving is 1 cup. How many calories are in each serving of the juice?

Answer:

130 calories;

Explanation:

1 quart = 4 servings in cup

2 quart = 8 servings in cup

\(\frac{1040}{8}\) = 130 calories

Question 2.

The perimeter of a photograph is 20 inches. The longer side of the photograph is 6 inches. What is the length of the shorter side?

Answer:

4 inches of length

Explanation:

20 inches = 2(6 + x) = 12 + 2x

20 – 12 = 2x

8 = 2x

x = 4

**Write an equation. Then solve.**

Question 3.

Peggy needs \(\frac{3}{4}\) cup of flour for each batch of pancakes. If she makes 5 batches of pancakes, how many cups of flour does she use?

Answer:

5 x \(\frac{3}{4}\) = \(\frac{23}{4}\)

Explanation:

1 batch of pancakes is \(\frac{3}{4}\)

5 batches of pancakes is 5 x \(\frac{3}{4}\)

So, number cups she uses is \(\frac{5×3}{4}\)

= \(\frac{23}{4}\)

**Compare. Use < or >.**

Question 4.

26.3 8.3

Answer:

26.3 > 8.3

Explanation:

with reference to the number line from 0

smaller number = 8.3

Greater number = 26.3

So, 26.3 is greater then 8.3

Question 5.

5.09 5.9

Answer:

5.09 < 5.9

Explanation:

with reference to the number line from 0

smaller number = 5.09

Greater number = 5.9

So, 5.09 is smaller then 5.9

Question 6.

1.7 7.1

Answer:

1.7 < 7.1

Explanation:

with reference to the number line from 0

smaller number = 1.7

Greater number = 7.1

So, 1.7 is smaller then 7.1

Question 7.

84.2 8.42

Answer:

84.2 > 8.42

Explanation:

with reference to the number line from 0

smaller number = 8.42

Greater number = 84.2

So, 84.2 is greater then 8.42

Question 8.

9.40 9.04

Answer:

9.40 > 9.04

Explanation:

with reference to the number line from 0

smaller number = 9.04

Greater number = 9.40

So, 9.40 is greater then 9.04

Question 9.

57 5.7

Answer:

57 > 5.7

Explanation:

with reference to the number line from 0

smaller number = 5.7

Greater number = 57

So, 57 is greater then 5.7

Question 10.

11.28 12.8

Answer:

11.28 < 12.8

Explanation:

with reference to the number line from 0

smaller number = 11.28

Greater number = 12.8

So, 11.28 is smaller then 12.8

Question 11.

6.31 6.13

Answer:

6.31 > 6.13

Explanation:

with reference to the number line from 0

smaller number = 6.13

Greater number = 6.31

So, 6.31 is greater then 6.13

Question 12.

**Stretch Your Thinking** On the first day of a trip, the Brenner family hikes 2.8 miles. On the second day, they hike 1\(\frac{2}{5}\) miles along a trail. They take a break, and hike back to where they started. Did they hike more the first day or the second day? Explain.

Answer:

They hiked the same amount on both days.

2.8 miles

Explanation:

First day : 2.8 miles

Second day : 1\(\frac{2}{5}\) = 1.4 miles

2.8 = 2(1.4) =2.8

They hiked the same amount on both days.

2.8 miles.