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## Texas Go Math Grade 5 Lesson 5.3 Answer Key Estimate Fraction Sums and Differences

**Unlock the Problem**

Kimberly will be riding her bike to school this year. The distance from her house to the end of the Street is \(\frac{1}{62}\)mile. The distance from the end of the Street to the school is \(\frac{3}{8}\) mile. About how far is Kimberly’s house from school?

You can use benchmarks to find reasonable estimates by rounding fractions to 0, \(\frac{1}{2}\), or 1.

**One Way:**

Use a number line.

Estimate. \(\frac{1}{6}\) + \(\frac{3}{8}\)

STEP 1:

Place a point at \(\frac{1}{6}\) on the number line.

The fraction is between ________ and __________.

The fraction \(\frac{1}{6}\) is closer to the benchmark _________.

Round to ________.

STEP 2:

Place a point at \(\frac{3}{8}\) on the number line.

The fraction is between __________ and _________.

The fraction \(\frac{3}{8}\) is closer to the benchmark ___________.

Round to _________.

STEP 3:

Add the rounded fractions.

So, Kimberly’s house is about ________ mile from the school.

Answer:\(\frac{1}{6}\)

Use a number line.

Estimate. \(\frac{1}{6}\) + \(\frac{3}{8}\)

STEP 1:

Place a point at \(\frac{1}{6}\) on the number line.

The fraction is between \(\frac{0}{6}\) and \(\frac{6}{6}\)

The fraction \(\frac{1}{6}\) is closer to the benchmark \(\frac{0}{6}\)

Round to \(\frac{0}{6}\)

STEP 2:

Place a point at \(\frac{3}{8}\) on the number line.

The fraction is between \(\frac{0}{8}\) and \(\frac{3}{8}\)

The fraction \(\frac{3}{8}\) is closer to the benchmark \(\frac{4}{8}\)

Round to \(\frac{4}{8}\)

STEP 3:

Add the rounded fractions.

So, Kimberly’s house is about \(\frac{1}{2}\)mile from the school.

**Another Way**

Use mental math.

You can compare the numerator and the denominator to round a fraction and find a reasonable estimate.

Estimate. \(\frac{9}{10}\) – \(\frac{5}{8}\)

STEP 1:

Round \(\frac{9}{10}\).

Think: The numerator is about the same as the denominator.

Round the fraction \(\frac{9}{10}\) to __________.

Remember

A fraction with the same numerator and denominator, such as \(\frac{2}{2}, \frac{5}{5}, \frac{12}{12}\) or \(\frac{96}{96}\), is equal to 1.

STEP 2:

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

Think: The numerator is about half the denominator.

Round the fraction \(\frac{5}{8}\) to ___________.

STEP 3:

Subtract

So, \(\frac{9}{10}\) – \(\frac{5}{8}\) is about __________.

Answer:

STEP 1:

Round \(\frac{9}{10}\).

Think: The numerator is about the same as the denominator.

Round the fraction \(\frac{9}{10}\) to \(\frac{10}{10}\)

Remember

A fraction with the same numerator and denominator, such as \(\frac{2}{2}, \frac{5}{5}, \frac{12}{12}\) or \(\frac{96}{96}\), is equal to 1.

STEP 2:

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

Think: The numerator is about half the denominator.

Round the fraction \(\frac{5}{8}\) to \(\frac{4}{8}\)

STEP 3:

Subtract

So, \(\frac{9}{10}\) – \(\frac{5}{8}\) is about \(\frac{1}{2}\)

**Math Talk**

**Mathematical Processes**

Explain another way you could use benchmarks to estimate \(\frac{9}{10}\) – \(\frac{5}{8}\).

Answer:

\(\frac{9}{10}\) – \(\frac{5}{8}\) = \(\frac{1}{6}\)

\(\frac{1}{6}\) is very near to \(\frac{1}{5}\)

Explanation:

Used bench marks to find the sum

**Share and Show**

**Estimate the sum or difference.**

Question 1.

\(\frac{5}{6}\) + \(\frac{3}{8}\)

a. Round \(\frac{5}{6}\) to its closest benchmark.

Answer: \(\frac{6}{6}\)

b. Round \(\frac{3}{8}\) to its closest benchmark.

Answer: \(\frac{4}{8}\)

c. Add to find the estimate. \(\frac{6}{6}\) +\(\frac{4}{8}\) = 1\(\frac{1}{2}\)

Answer: 1\(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 2.

\(\frac{5}{9}\) – \(\frac{3}{8}\)

Answer:

a. Round \(\frac{5}{9}\) to its closest benchmark.

Answer: \(\frac{5}{9}\)

b. Round \(\frac{3}{8}\) to its closest benchmark.

Answer: \(\frac{4}{8}\)

c. Add to find the estimate. \(\frac{5}{9}\) – \(\frac{4}{8}\) = 1\(\frac{1}{18}\)

Answer: 1\(\frac{1}{18}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 3.

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

Answer:

a. Round \(\frac{5}{6}\) to its closest benchmark.

Answer: \(\frac{6}{6}\)

b. Round \(\frac{2}{5}\) to its closest benchmark.

Answer: \(\frac{2}{5}\)

c. Add to find the estimate. \(\frac{6}{6}\) +\(\frac{2}{5}\) = 1\(\frac{1}{2}\)

Answer: 1\(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 4.

\(\frac{9}{10}\) – \(\frac{1}{9}\)

Answer:

a. Round \(\frac{9}{10}\) to its closest benchmark.

Answer: \(\frac{10}{10}\)

b. Round \(\frac{1}{9}\) to its closest benchmark.

Answer: \(\frac{0}{9}\)

c. Add to find the estimate. \(\frac{10}{10}\) – \(\frac{0}{9}\) = 1

Answer: 1

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

**Problem Solving**

Question 5.

How do you know whether your estimate for \(\frac{9}{10}\) + 3\(\frac{6}{7}\) would be greater than or less than the actual sum? Explain.

Answer: Greater than the actual sum

\(\frac{9}{10}\) + 3\(\frac{6}{7}\) =

close to bench marks \(\frac{10}{10}\) + 3\(\frac{7}{7}\) = 4

Explanation:

Is greater than the actual sum

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 6.

**Write Math** Nick estimated that \(\frac{5}{8}\) + \(\frac{4}{7}\) is about 2. Explain how you know his estimate is not reasonable.

Answer: \(\frac{5}{8}\) + \(\frac{4}{7}\)

close to benchmarks \(\frac{4}{8}\) + \(\frac{4}{7}\) = 1

Explanation:

Nick estimated that \(\frac{5}{8}\) + \(\frac{4}{7}\) is about 2.

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

so, his estimation is wrong

**Problem Solving**

Question 7.

Lisa and Valerie are picnicking in Trough Creek State Park in Pennsylvania. Lisa has brought a salad that she made with \(\frac{3}{4}\) cup of strawberries, \(\frac{7}{8}\) cup of peaches, and \(\frac{1}{6}\) cup of blueberries. About how many total cups of fruit are in the salad?

Answer:

\(\frac{3}{4}\) + \(\frac{7}{8}\) + \(\frac{1}{6}\) very close to bench marks

\(\frac{4}{4}\) + \(\frac{8}{8}\) + \(\frac{0}{6}\) =2 \(\frac{1}{2}\)

Explanation:

Lisa and Valerie are picnicking in Trough Creek State Park in Pennsylvania.

Lisa has brought a salad that she made with \(\frac{3}{4}\) cup of strawberries,

\(\frac{7}{8}\) cup of peaches, and \(\frac{1}{6}\) cup of blueberries.

2\(\frac{1}{2}\) total cups of fruit are in the salad

Question 8.

**Multi-Step** At Trace State Park in Mississippi, there is a 40-mile mountain bike trail. Tommy rode A of the trail on Saturday and \(\frac{1}{5}\) of the trail on Sunday. He estimates that he rode more than 22 miles over the two days. Is Tommy’s estimate reasonable?

Answer: yes

Explanation:

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

20 + 20 = 40

one represents the whole

so, his estimation is reasonable

Question 9.

**H.O.T** Explain how you know that \(\frac{5}{8}\) + \(\frac{6}{10}\) is greater than 1.

Answer: No

Explanation:

Close to the bench marks

\(\frac{8}{8}\) + \(\frac{5}{10}\) = 1

actual sum is greater than 1

**Daily Assessment Task**

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

Question 10.

Mia uses \(\frac{1}{5}\) of a bag of gravel in the morning and \(\frac{11}{12}\) of a bag in the afternoon. About how much gravel does she use in one day?

(A) 0 bags

(B) \(\frac{1}{2}\) bag

(C) 1 bag

(D) 2\(\frac{1}{2}\) bags

Answer: C

\(\frac{1}{5}\) + \(\frac{11}{12}\)

nearest benchmarks are

\(\frac{0}{5}\) + \(\frac{12}{12}\) = 1

Explanation:

Mia uses \(\frac{1}{5}\) of a bag of gravel in the morning and \(\frac{11}{12}\) of a bag in the afternoon.

she use 1 bag of gravel

Question 11.

Evaluate Reasonableness Hector and Veronica are going hiking. They made a trail mix that has \(\frac{2}{3}\) cup of almonds, \(\frac{7}{8}\) cup of peanuts, and \(\frac{4}{5}\) cup of raisins in it. Hector estimates that they made about 3 cups of trail mix. Is the estimate greater than or less than the actual sum? How do you know?

(A) The estimate is greater because each fraction is rounded up to a benchmark.

(B) The estimate is less because each fraction is rounded down to a benchmark.

(C) The estimate is greater because they really made more than 3 cups.

(D) The estimate is less because each fraction is rounded up to a benchmark.

Answer: A

Explanation:

\(\frac{2}{3}\) + \(\frac{7}{8}\) + \(\frac{4}{5}\)

rounded to nearest benchmarks

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

Evaluated Reasonableness Hector and Veronica are going hiking.

They made a trail mix that has \(\frac{2}{3}\) cup of almonds, ”

\(\frac{7}{8}\) cup of peanuts,

and \(\frac{4}{5}\) cup of raisins in it.

Hector estimates that they made about 3 cups of trail mix.

Question 12.

**Multi-Step** Amanda picked \(\frac{3}{5}\) pound of blueberries at her local farm yesterday. She used \(\frac{3}{8}\) pound of blueberries. Today she picked \(\frac{4}{5}\) pound of blueberries. About how many pounds of blueberries does Amanda have now?

(A) \(\frac{1}{5}\)lb

(B) 1 lb

(C) \(\frac{1}{2}\)lb

(D) 1\(\frac{1}{2}\)lbs

Answer: B

Explanation:

what she bought is that she used yesterday

in today marked to nearest benchmarks \(\frac{4}{5}\) is \(\frac{5}{5}\)

that is 1

**Texas Test Prep**

Question 13.

Jake added \(\frac{1}{8}\) cup of sunflower seeds and \(\frac{4}{5}\) cup of banana chips to his sundae. Which is the best estimate of the total amount of toppings Jake added to his sundae?

(A) about 2 cups

(B) about 1 cup

(C) about 1\(\frac{1}{2}\) cups

(D) about \(\frac{1}{2}\) cup

Answer: B

Explanation:

Jake added \(\frac{1}{8}\) cup of sunflower seeds and

\(\frac{4}{5}\) cup of banana chips to his sundae.

The best estimate of the total amount of toppings Jake added to his sundae is 1 cup

### Texas Go Math Grade 5 Lesson 5.3 Homework and Practice Answer Key

**Estimate the sum or difference.**

Question 1.

\(\frac{3}{8}\) + \(\frac{4}{5}\) = ___________

Answer:

\(\frac{3}{8}\) + \(\frac{4}{5}\) rounded to the nearest benchmarks

\(\frac{4}{8}\) + \(\frac{5}{5}\) = 1 \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 2.

\(\frac{9}{10}\) – \(\frac{3}{8}\) = ___________

Answer:

\(\frac{9}{10}\) – \(\frac{3}{8}\) rounded to the nearest benchmarks

\(\frac{10}{10}\) – \(\frac{4}{8}\) = \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 3.

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

Answer:

\(\frac{5}{8}\) + \(\frac{2}{5}\) rounded to the nearest benchmarks

\(\frac{4}{8}\) + \(\frac{2}{5}\) = 1

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 4.

\(\frac{6}{7}\) + \(\frac{3}{5}\) = ___________

Answer:

\(\frac{6}{7}\) + \(\frac{3}{5}\) rounded to the nearest benchmarks

\(\frac{7}{7}\) + \(\frac{2}{5}\) = 1\(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 5.

\(\frac{3}{8}\) – \(\frac{1}{6}\) = ___________

Answer:

\(\frac{3}{8}\) – \(\frac{1}{6}\) rounded to the nearest benchmarks

\(\frac{4}{8}\) – \(\frac{0}{6}\) = \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 6.

\(\frac{7}{12}\) + \(\frac{1}{7}\) = ___________

Answer:

\(\frac{7}{12}\) + \(\frac{1}{7}\) rounded to the nearest bench marks

\(\frac{6}{12}\) + \(\frac{0}{7}\) = \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 7.

\(\frac{4}{9}\) – \(\frac{5}{8}\) = ___________

Answer:

\(\frac{4}{9}\) – \(\frac{5}{8}\) rounded to the nearest benchmarks

\(\frac{5}{9}\) – \(\frac{4}{8}\) = 0

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 8.

\(\frac{1}{9}\) + \(\frac{5}{6}\) = ___________

Answer:

\(\frac{1}{9}\) + \(\frac{5}{6}\) rounded to the nearest benchmark

\(\frac{0}{9}\) + \(\frac{6}{6}\) = 1

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 9.

\(\frac{7}{8}\) + \(\frac{4}{7}\) = ___________

Answer:

\(\frac{7}{8}\) + \(\frac{4}{7}\) rounded to the nearest bench mark

\(\frac{8}{8}\) + \(\frac{4}{7}\) =1\(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 10.

\(\frac{1}{5}\) + \(\frac{3}{8}\) = ___________

Answer:

\(\frac{1}{5}\) + \(\frac{3}{8}\) rounded to the nearest benchmark

\(\frac{0}{5}\) + \(\frac{4}{8}\) = \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 11.

\(\frac{7}{9}\) – \(\frac{2}{6}\) = ___________

Answer:

\(\frac{7}{9}\) – \(\frac{2}{6}\) rounded to the nearest benchmark

\(\frac{9}{9}\) – \(\frac{3}{6}\) = \(\frac{1}{2}\)

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 12.

\(\frac{9}{10}\) – \(\frac{7}{8}\) = ___________

Answer:

\(\frac{9}{10}\) – \(\frac{7}{8}\) rounded to the bench marks

\(\frac{10}{10}\) – \(\frac{8}{8}\) = 0

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 13.

Explain how you can estimate the sum of \(\frac{4}{5}\) and \(\frac{1}{6}\).

Answer:

\(\frac{4}{5}\) + \(\frac{1}{6}\) rounded to the nearest bench marks

\(\frac{5}{5}\) + \(\frac{0}{6}\) = 1

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

**Problem Solving**

Question 14.

Jena uses \(\frac{7}{8}\) cup of raisins for muffins and \(\frac{5}{8}\) cup of raisins for a bowl of oatmeal. Does lena need more than or less than 1 cup of raisins to make muffins and oatmeal? Explain.

Answer: more than 1 cup of raisins

Explanation:

Jena uses \(\frac{7}{8}\) cup of raisins for muffins and

\(\frac{5}{8}\) cup of raisins for a bowl of oatmeal.

\(\frac{7}{8}\) + \(\frac{5}{8}\) rounded the benhmark

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

Question 15.

A group of students ate \(\frac{5}{12}\) of a cheese pizza, \(\frac{7}{8}\) of a pepperoni pizza, and \(\frac{5}{8}\) of a veggie pizza. About how many pizzas were eaten?

Answer:

\(\frac{5}{12}\) + \(\frac{7}{8}\) + \(\frac{5}{8}\) rounded to the nearest benchmark

\(\frac{6}{12}\) + \(\frac{8}{8}\) + \(\frac{4}{8}\) = 2

Explanation:

A group of students ate \(\frac{5}{12}\) of a cheese pizza,

\(\frac{7}{8}\) of a pepperoni pizza,

and \(\frac{5}{8}\) of a veggie pizza.

2 pizzas were eaten in whole.

**Lesson Check**

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

Question 16.

On Saturday, the scouts hiked \(\frac{4}{5}\) mile up the mountain. On Sunday, they hiked \(\frac{1}{4}\) mile up the mountain. About how far did the scouts hike up the mountain in all?

(A) \(\frac{1}{2}\) mile

(B) 1 mile

(C) 1\(\frac{1}{2}\) miles

(D) 2 miles

Answer:

\(\frac{4}{5}\) + \(\frac{1}{4}\) rounded to nearest benchmark

\(\frac{5}{5}\) + \(\frac{0}{4}\) is 1 mile

Explanation:

On Saturday, the scouts hiked \(\frac{4}{5}\) mile up the mountain.

On Sunday, they hiked \(\frac{1}{4}\) mile up the mountain.

1 mile far the scouts hike up the mountain in all

Question 17.

Which of the following best describes the difference for \(\frac{11}{12}\) – \(\frac{7}{10}\) ?

(A) less than \(\frac{1}{2}\)

(B) greater than \(\frac{1}{2}\)

(C) greater than 1

(D) greater than 1\(\frac{1}{2}\)

Answer: A

Explanation:

\(\frac{11}{12}\) – \(\frac{7}{10}\) is 0

that is less than \(\frac{1}{2}\)

Question 18.

Which sum is greatest? Use estimation to decide.

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

(B) \(\frac{1}{10}\) + \(\frac{3}{8}\)

(C) \(\frac{1}{6}\) + \(\frac{1}{8}\)

(D) \(\frac{2}{9}\) + \(\frac{1}{8}\)

Answer: A

Explanation:

\(\frac{2}{7}\) + \(\frac{3}{8}\) = 1

Question 19.

Which statement is not correct? Use estimation to decide.

Answer: B

Explanation:

used benchmarks to find reasonable estimates

by rounding fractions to 0, \(\frac{1}{2}\), or 1.

Question 20.

**Multi-Step** Michaela has \(\frac{11}{12}\) yard of orange fabric and \(\frac{7}{8}\) yard of green fabric. She uses \(\frac{1}{2}\) yard of each color for her sewing project. About how much fabric does Michaela have left if she combines the two colors?

(A) 1 yard

(B) \(\frac{1}{2}\) yard

(C) 1 \(\frac{1}{2}\) yards

(D) 2 yards

Answer: D

\(\frac{11}{12}\) + \(\frac{7}{8}\) rounded to nearest bench marks

\(\frac{12}{12}\) + \(\frac{8}{8}\) = 2

Explanation:

2 yards fabric uses Michaela have left if she combines the two colors.

Question 21.

**Multi-Step** Dustin buys \(\frac{9}{10}\) yard of striped fabric. He uses \(\frac{3}{8}\) yard. He buys \(\frac{7}{8}\) yard more. About how much fabric does Dustin have now?

(A) 1 yard

(B) \(\frac{1}{2}\) yard

(C) 1\(\frac{1}{2}\) yards

(D) 2 yards

Answer: C

Explanation:

Dustin buys \(\frac{9}{10}\) yard of striped fabric.

He uses \(\frac{3}{8}\) yard.

He buys \(\frac{7}{8}\) yard more.

\(\frac{9}{10}\) + \(\frac{3}{8}\) + \(\frac{7}{8}\) rounded to nearest benchmarks

\(\frac{10}{10}\) – \(\frac{4}{8}\) + \(\frac{8}{8}\) = 1\(\frac{1}{2}\) yards