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## Texas Go Math Grade 4 Lesson 5.4 Answer Key Use Benchmarks to Determine Reasonableness

**Essential Question**

How can you find and record sums and differences of fractions?

Answer:

- Step 1: Make sure the bottom numbers (the denominators) are the same.
- Step 2: Add the top numbers (the numerators), put that answer over the denominator.
- Step 3: Simplify the fraction (if possible)

- Make sure the bottom numbers (the denominators) are the same.
- Subtract the top numbers (the numerators). Put the answer over the same denominator.
- Simplify the fraction (if needed).

**Unlock the Problem**

A rover considers many possible paths before choosing the safest path toward its goal. A rover moved yard in a straight line, and then yard around a rock to reach its goal. How far did it travel?

Answer:

**Find the sum.**

**MODEL IT**

Use fraction strips.

Think: The rover moved 2 sixth yard and then 5 sixth yard. Shade 2 sixth-size pieces and then 5 sixth-size pieces.

So, the rover traveled _________ yards to reach its goal.

Answer:

So, the rover traveled \(\frac{7}{6}\) yards to reach its goal.

\(\frac{2}{6}\) + \(\frac{5}{6}\) = \(\frac{7}{6}\)

So, the rover traveled \(\frac{7}{6}\) yards to reach its goal.

**RECORD IT**

Write the sum.

_________ + _________ = \(\frac{7}{6}\)

Rename \(\frac{7}{6}\) as a mixed number.

Think: The model shows 1 whole yard and 1 sixth yard.

\(\frac{7}{6}\) = ___________

Answer:

\(\frac{2}{6}\) + \(\frac{5}{6}\) = \(\frac{7}{6}\)

Rename \(\frac{7}{6}\) as a mixed number.

Think: The model shows 1 whole yard and 1 sixth yard.

\(\frac{7}{6}\) = 1\(\frac{1}{6}\)

**Math Talk**

Mathematical Processes

Explain how you know \(\frac{5}{6}\) is greater than \(\frac{1}{2}\).

Answer:

**Determine whether the sum is reasonable.**

Compare the addends to the benchmarks 0, \(\frac{1}{2}\), and 1.

\(\frac{2}{6}\) is greater than \(\frac{1}{2}\). and less than \(\frac{1}{2}\)

The sum is greater than 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\) .

The sum is less than \(\frac{1}{2}\) + 1 = \(\frac{3}{2}\) .

So, 1\(\frac{1}{6}\) is a reasonable sum.

Answer:

\(\frac{5}{6}\) is Greater than \(\frac{1}{2}\) and lesser than 1.

**Example**

A rover must move \(\frac{5}{8}\) mile to reach its goal. The rover moves \(\frac{1}{8}\) mile toward its goal. How much farther must the rover move to reach its goal?

Answer:

\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)

(A) Find the difference.

\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)

\(\frac{4}{8}\) farther must the rover move to reach its goal

**MODEL IT**

Use fraction strips.

So, the rover must ___________ move mile farther.

Answer:

So, the rover must \(\frac{4}{8}\) move mile farther.

**RECORD IT**

Write the difference.

__________ – ____________ = \(\frac{4}{8}\)

Answer:

\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\)

(B) Determine whether the difference is reasonable.

Compare the fractions to the benchmarks 0, \(\frac{1}{4}\), \(\frac{3}{4}\), and 1.

\(\frac{1}{8}\) is greater than 0 and less than \(\frac{1}{4}\).

The difference is greater than 0 + \(\frac{1}{4}\) = __________.

The difference is less than \(\frac{1}{4}+\frac{3}{4}\) = ____________.

So, \(\frac{4}{8}\) is a reasonable difference.

Answer:

\(\frac{1}{8}\) is greater than 0 and less than \(\frac{1}{4}\).

The difference is greater than 0 + \(\frac{1}{4}\) = \(\frac{1}{4}\) .

The difference is less than \(\frac{1}{4}+\frac{3}{4}\) = 1.

So, \(\frac{4}{8}\) is a reasonable difference.

\(\frac{5}{8}\) is ____________ than \(\frac{1}{4}\) and __________ than \(\frac{3}{4}\).

Answer:

\(\frac{5}{8}\) is Greater than \(\frac{1}{4}\) and lesser than \(\frac{3}{4}\).

**Share and Show**

Question 1.

A rover needs to move \(\frac{9}{10}\) mile to a crater. It moves \(\frac{4}{10}\) mile ‘toward the crater. How much farther does it need to move to reach the crater?

- Model the difference.
- Write the difference.

\(\frac{9}{10}-\frac{4}{10}\) = ____________

Answer:

\(\frac{9}{10}-\frac{4}{10}\) = \(\frac{5}{10}\)

**Add or subtract. Determine whether your answer is reasonable.**

Question 2.

\(\frac{5}{12}+\frac{4}{12}\) = __________

Answer:

\(\frac{5}{12}+\frac{4}{12}\) = \(\frac{9}{12}\)

Explanation:

It is reasonable because \(\frac{9}{12}\) is lesser than 1 and greater than 0

Question 3.

\(\frac{4}{6}-\frac{2}{6}\) = __________

Answer:

\(\frac{4}{6}-\frac{2}{6}\) = \(\frac{2}{6}\)

Explanation:

It is reasonable because \(\frac{2}{6}\) is lesser than 1 and greater than 0

Question 4.

\(\frac{3}{8}+\frac{7}{8}\) = __________

Answer:

\(\frac{3}{8}+\frac{7}{8}\) = \(\frac{9}{8}\)

Explanation:

It is not reasonable because \(\frac{9}{8}\) is Greater than 1 and greater than 0

**Unlock the Problem**

Question 5.

**H.O.T.** Apply Multi-Step in our solar system, \(\frac{2}{8}\) of the planets have no moons, \(\frac{1}{8}\) have 1 moon, \(\frac{1}{8}\) have 2 moons, and \(\frac{1}{8}\) have 13 moons. What fraction of the planets have 0, 1, 2, or 13 moons?

(A) \(\frac{5}{8}\)

(B) \(\frac{4}{8}\)

(C) \(\frac{3}{8}\)

(D) \(\frac{2}{8}\)

Answer: A

Explanation:

\(\frac{2}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{5}{8}\)

\(\frac{5}{8}\) fraction of the planets have 0, 1, 2, or 13 moons

a. What do you need to know?

Answer:

fraction of the planets that have 0, 1, 2, or 13 moons.

b. What information are you given?

Answer:

In our solar system, \(\frac{2}{8}\) of the planets have no moons, \(\frac{1}{8}\) have 1 moon, \(\frac{1}{8}\) have 2 moons, and \(\frac{1}{8}\) have 13 moons. Is the information given

c. Write the addition problem you will use to solve this problem.

Answer:

\(\frac{2}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{5}{8}\)

d. Draw a model to help you solve the problem.

Answer:

e. Fill in the bubble for the correct answer choice above.

Answer:

Bubbled the correct the answer

**Daily Assessment Task**

Fill in the bubble completely to show your answer.

Question 6.

A man times the movement of a banana slug. It moves \(\frac{2}{6}\) foot during the first minute. It then moves \(\frac{3}{6}\) foot during the second minute. How far does the banana slug move in all?

(A) \(\frac{5}{12}\) foot

(B) \(\frac{1}{6}\) foot

(C) \(\frac{1}{12}\) foot

(D) \(\frac{5}{6}\) foot

Answer: D

Explanation:

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

\(\frac{5}{6}\) foot far does the banana slug move in all

Question 7.

One day \(\frac{3}{8}\) of the students in Jack’s class ate toast for breakfast. Another \(\frac{1}{8}\) of the students ate oatmeal. Jack added the fractions and found the sum was \(\frac{7}{8}\). Which statement best describes the sum \(\frac{7}{8}\)?

(A) It is reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).

(B) It is reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.

(C) It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).

(D) It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1.

Answer: C

Explanation:

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

It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\).

Question 8.

Multi-Step Ms. Ryan buys \(\frac{7}{8}\) yard of striped cloth. She uses \(\frac{3}{8}\) yard to make a bag. Then she uses \(\frac{1}{8}\) yard to make a belt. how much cloth does Ms. Ryan have left to make a hat?

(A) \(\frac{2}{8}\) yard

(B) \(\frac{4}{8}\) yard

(C) \(\frac{3}{8}\) yard

(D) \(\frac{6}{8}\) yard

Answer: C

Explanation:

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

\(\frac{7}{8}\) – \(\frac{4}{8}\) = \(\frac{3}{8}\) yard

\(\frac{3}{8}\) yard cloth does Ms. Ryan have left to make a hat

**TEXAS Test Prep**

Question 9.

Suppose a rover on Mars moved \(\frac{2}{6}\) yard in a straight line. Then it moved \(\frac{5}{6}\) yard around a rock, flow many more yards did the rover move around the rock than it moved in a straight line?

(A) \(\frac{3}{12}\) yard

(B) \(\frac{3}{6}\) yard

(C) \(\frac{7}{12}\) yard

(D) 1\(\frac{1}{6}\) yard

Answer: B

Explanation:

\(\frac{5}{6}\) – \(\frac{2}{6}\) = \(\frac{3}{6}\) yard

\(\frac{3}{6}\) more yards that the rover move around the rock than it moved in a straight line

### Texas Go Math Grade 4 Lesson 5.4 Homework and Practice Answer Key

Question 1.

Melina wants to finish \(\frac{6}{10}\) of her math homework problems before dinner. She finishes \(\frac{4}{10}\) of them. What fraction of her math problems does she still need to complete before dinner?

- Model the difference.
- Write the difference.

\(\frac{6}{10}-\frac{4}{10}\) = ___________

Answer:

\(\frac{6}{10}-\frac{4}{10}\) = \(\frac{2}{10}\)

**Add or subtract. Determine whether your answer is reasonable.**

Question 2.

\(\frac{1}{6}+\frac{4}{6}\) = ___________

Answer:

\(\frac{1}{6}+\frac{4}{6}\) = \(\frac{5}{6}\)

Explanation:

It is reasonable because \(\frac{5}{6}\) is lesser than 1 and greater than 0

Question 3.

\(\frac{3}{4}-\frac{1}{4}\) = ___________

Answer:

\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{2}{4}\)

Explanation:

It is reasonable because \(\frac{2}{4}\) is lesser than 1 and greater than 0

Question 4.

\(\frac{9}{12}-\frac{3}{12}\) = ___________

Answer:

\(\frac{9}{12}-\frac{3}{12}\) = \(\frac{6}{12}\)

Explanation:

It is reasonable because \(\frac{6}{12}\) is lesser than 1 and greater than 0

Question 5.

\(\frac{3}{6}+\frac{2}{6}\) = ___________

Answer:

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

Explanation:

It is reasonable because \(\frac{5}{6}\) is lesser than 1 and greater than 0

**Problem Solving**

Question 6.

In Joe’s family, \(\frac{2}{6}\) of the people have blue eves and \(\frac{3}{6}\) of the people have brown eyes. What fraction of people has either blue or brown eyes?

Answer:

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

\(\frac{5}{6}\) fraction of people has either blue or brown eyes

Question 7.

Kim wants to add drawings to \(\frac{5}{8}\) of the stories in her journal. So far she has completed drawings for \(\frac{2}{8}\) of the stories. How many more stories still need drawings?

Answer:

\(\frac{5}{8}\) – \(\frac{2}{8}\) = \(\frac{3}{8}\)

\(\frac{3}{8}\) more stories still need drawings

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 8.

**Add.** Determine if the answer is reasonable.

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

(A) \(\frac{4}{8}\)

(B) \(\frac{3}{8}\)

(C) \(\frac{5}{8}\)

(D) \(\frac{1}{8}\)

Answer: C

Explanation:

\(\frac{3}{8}+\frac{2}{8}\) = \(\frac{5}{8}\)

Question 9.

**Subtract.** Determine if the answer is reasonable.

\(\frac{10}{12}-\frac{1}{12}\)

(A) \(\frac{9}{12}\)

(B) \(\frac{11}{12}\)

(C) \(\frac{8}{12}\)

(D) \(\frac{7}{12}\)

Answer:

\(\frac{10}{12}-\frac{1}{12}\) = \(\frac{9}{12}\)

Question 10.

In Martha’s class, \(\frac{5}{8}\) of the students walk to school and \(\frac{1}{8}\) of the students ride the bus. Martha added the fractions and found the sum was \(\frac{1}{8}\). Which statement best describes the sum \(\frac{1}{8}\)?

(A) It is reasonable because \(v\frac{1}{2}\) + 0 = \(\frac{1}{2}\)

(B) It is reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

(C) It is not reasonable because \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\)

(D) It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

Answer: D

Explanation:

It is not reasonable because \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

Question 11.

Sabina walks dogs on Saturday. Last Saturday only \(\frac{7}{10}\) of the dogs needed to be walked. She walked \(\frac{5}{10}\) of them in the morning. What fractional part of the dogs does Sabina need to walk in the afternoon?

(A) \(\frac{2}{10}\)

(B) \(\frac{1}{10}\)

(C) \(\frac{3}{10}\)

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

Answer: A

Explanation:

\(\frac{7}{10}\) – \(\frac{5}{10}\) = \(\frac{2}{10}\)

\(\frac{2}{10}\) fractional part of the dogs that Sabina need to walk in the afternoon

Question 12.

**Multi-Step** Luke poured \(\frac{3}{4}\) cup yellow paint into a can and \(\frac{3}{4}\) cup of blue paint in a can. He mixed the colors to make green paint. Then used \(\frac{1}{4}\) cup of the green paint. how much green paint is left?

(A) \(\frac{7}{4}\)cup or 1\(\frac{3}{4}\) cup

(B) \(\frac{1}{4}\)cup

(C) \(\frac{3}{4}\)cup

(D) \(\frac{5}{4}\)cup or 1\(\frac{1}{4}\) cup

Answer: A

Explanation:

\(\frac{7}{4}\)cup or 1\(\frac{3}{4}\) of cup green paint is left

Question 13.

**Multi-Step** Andrew used \(\frac{2}{12}\) of a carton of eggs for a cake and \(\frac{5}{12}\) of a carton for egg salad, What fraction of the carton is remaining?

(A) \(\frac{4}{12}\)

(B) \(\frac{3}{12}\)

(C) \(\frac{5}{12}\)

(D) \(\frac{7}{12}\)

Answer: D

Explanation:

\(\frac{2}{12}\) + \(\frac{5}{12}\) = \(\frac{7}{12}\)