Refer to our Texas Go Math Grade 5 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 5 Lesson 5.1 Answer Key Addition with Unequal Denominators.

## Texas Go Math Grade 5 Lesson 5.1 Answer Key Addition with Unequal Denominators

**Investigate**

Hilary is using red fabric to make a tote bag. She uses one piece that is \(\frac{1}{2}\) yard long. She uses another piece that is \(\frac{1}{4}\) yard long. How much red fabric does she use?

Materials; fraction strips; MathBoard

A. Find \(\frac{1}{2}\) + \(\frac{1}{4}\). Place a \(\frac{1}{2}\) strip and a \(\frac{1}{4}\) strip under the 1-whole strip on your MathBoard.

Answer:

B. Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{2}\) and \(\frac{1}{4}\) and fit exactly under the sum \(\frac{1}{2}\) + \(\frac{1}{4}\). Record the addends, using equal denominators.

Answer: 3/4

C. Record the sum in simplest form. \(\frac{1}{2}\) + \(\frac{1}{4}\) = ___________

So, Hilary uses ___________ yard of fabric.

Answer: So, Hilary uses \(\frac{3}{4}\) yard of fabric.

Record the sum in simplest form. \(\frac{1}{2}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)

**Math Talk**

**Mathematical Processes**

How can you tell if the sum of the fractions is less than 1?

Answer:

Fractions greater than 1 have numerators larger than their denominators; those that are less than 1 have numerators smaller than their denominators; the rest are equal to 1.

**Draw Conclusions**

Question 1.

Describe how you would determine what fraction strips, all with the same denominator, would fit exactly under \(\frac{1}{2}\) + \(\frac{1}{3}\). What are they?

Answer:

Explanation:

The denominator is 6

Which would fit exactly under \(\frac{1}{6}\) + \(\frac{1}{6}\)+ \(\frac{1}{6}\) + \(\frac{1}{6}\)+\(\frac{1}{6}\) + \(\frac{1}{6}\).

Question 2.

H.O.T. Explain the difference between finding fraction strips with the same denominator for \(\frac{1}{2}\) + \(\frac{1}{3}\) and \(\frac{1}{2}\) + \(\frac{1}{4}\).

Answer:

**Make Connections**

Sometimes, the sum of two fractions is greater than 1. When adding fractions with unequal denominators, you can use the 1-whole strip to help determine If a sum is greater than 1 or less than 1.

Use fraction strips to solve. \(\frac{3}{5}\) + \(\frac{1}{2}\)

STEP 1:

Work with another student. Place three \(\frac{1}{5}\) fraction strips under the 1-whole strip on your MathBoard. Then place a \(\frac{1}{2}\) fraction strip beside the three \(\frac{1}{5}\) strips.

STEP 2:

Find fraction strips, all with the same denominator, that are equivalent to \(\frac{3}{5}\) and \(\frac{1}{2}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.

\(\frac{3}{5}\) = __________ \(\frac{1}{2}\) = __________

STEP 3:

Add the fractions with equal denominators. Use the 1-whole strip to rename the sum in simplest form.

\(\frac{3}{5}\) + \(\frac{1}{2}\) = __________ + _________

= __________ or _________

Think: How many fraction strips with the same denominator are equal to 1 whole?

Answer:

step 1:

Explanation:

Placed three \(\frac{1}{5}\) fraction strips under the 1-whole strip on your MathBoard. Then place a \(\frac{1}{2}\) fraction strip beside the three \(\frac{1}{5}\) strips.

step 2:

Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.

\(\frac{3}{5}\) = 6\(\frac{1}{10}\)

\(\frac{1}{2}\) = 5\(\frac{1}{10}\)

step 3:

\(\frac{3}{5}\) + \(\frac{1}{2}\) = 6\(\frac {1}{10}\) + 5\(\frac{1}{10}\)

= \(\frac{11}{10}\)

**Math Talk**

**Mathematical Processes**

In what step did you find out that the answer is greater than 1? Explain.

Answer: In step 2

Explanation:

\(\frac{3}{5}\) =6\(\frac{1}{10}\)

\(\frac{1}{2}\) =5\(\frac{1}{10}\)

**Share and Show**

**Use fraction strips to find the sum. Write your answer in simplest form.**

Question 1.

Answer:

Explanation:

Place the fraction strips with the same denominator 8, that are equivalent to \(\frac{1}{2}\)

then Added

Question 2.

Answer:

Explanation:

Place the fraction strips with the same denominator of 12, that are equivalent to \(\frac{3}{4}\) and \(\frac{1}{3}\). Then Added.

**Use fraction strips to find the sum. Write your answer in simplest form.**

Question 3.

\(\frac{2}{5}\) + \(\frac{3}{10}\) = __________

Answer: \(\frac{7}{10}\)

Explanation:

\(\frac{2}{5}\) + \(\frac{3}{10}\) = \(\frac{4}{10}\) + \(\frac{3}{10}\) = \(\frac{7}{10}\)

or

Question 4.

\(\frac{1}{4}\) + \(\frac{1}{12}\) = ___________

Answer: \(\frac{1}{3}\)

Explanation:

\(\frac{1}{4}\) + \(\frac{1}{12}\) = \(\frac{3}{12}\) + \(\frac{1}{12}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)

or

Question 5.

\(\frac{1}{2}\) + \(\frac{3}{10}\) = ____________

Answer: \(\frac{4}{5}\)

Explanation:

\(\frac{1}{2}\) + \(\frac{3}{10}\) = \(\frac{5}{10}\) + \(\frac{3}{10}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\)

**Problem Solving**

Question 6.

**H.O.T. Multi-Step** Maya makes trail mix by combining \(\frac{1}{3}\) cup mixed nuts, \(\frac{1}{4}\) cup of dried fruit, and \(\frac{1}{6}\) cup of chocolate morsels. What is the total amount of ingredients in her trail mix?

Answer: \(\frac{3}{4}\)

Explanation:

\(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{6}\)= \(\frac{4}{12}\) + \(\frac{3}{12}\) +\(\frac{2}{12}\) = \(\frac{9}{12}\) = \(\frac{3}{4}\)

Question 7.

**H.O.T. Pose a Problem** Write a new problem using different amounts for ingredients Maya used. Each amount should be a fraction with a denominator of 2, 3, or 4.

Answer:

Maya makes trail mix by combining \(\frac{1}{2}\) cup mixed nuts, \(\frac{1}{3}\) cup of dried fruit, and \(\frac{1}{4}\) cup of chocolate morsels. What is the total amount of ingredients in her trail mix?

Question 8.

**Use Diagrams** Solve the problem you wrote. Draw a picture of the fractions strips you use to solve your problem.

Answer: \(\frac{13}{12}\)

Question 9.

Explain why you chose the amounts you did for your problem.

Answer: in the question asked use different amounts for ingredients and Each amount should be a fraction with a denominator of 2, 3, or 4.

Question 10.

**Write Math** Explain how using fraction strips with equal denominators makes it possible to add fractions with unequal denominators.

Answer:

Think of the fruit analogy?

Does it make sense to add two bananas plus one watermelon? The units do not make sense for the sum.

BUT … we could think about changing both of them to common units, servings of fruit. If one banana serves one person and one watermelon serves ten people, then we could convert:

- two bananas + one watermelon =
- = two fruit servings + ten fruit servings =
- = twelve servings of fruit

Example:

**Daily Assessment Task**

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

Question 11.

In a garden, bluebonnets occupy \(\frac{7}{10}\) of the garden. After winter, the bluebonnets spread to cover another \(\frac{1}{5}\) of the garden. What fraction of the garden is now covered in bluebonnets?

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

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

(C) \(\frac{8}{10}\)

(D) \(\frac{9}{10}\)

Answer: D

Explanation:

\(\frac{7}{10}\) + \(\frac{1}{5}\) = \(\frac{9}{10}\)

Question 12.

Ling is using fraction strips to add \(\frac{2}{3}\) and \(\frac{7}{12}\). The sum is one whole, plus how many twelfths?

(A) 1

(B) 2

(C) 3

(D) 4

Answer: C

Explanation:

Question 13.

**Multi-Step** Juan uses \(\frac{1}{5}\) liter to water a small plant, and he uses \(\frac{1}{2}\) liter to water a large plant. Now he has \(\frac{2}{10}\) liter Left in the pitcher. How much water did Juan have in the beginning?

(A) \(\frac{3}{5}\) L

(B) \(\frac{9}{10}\) L

(C) \(\frac{1}{10}\) L

(D) \(\frac{3}{10}\) L

Answer: B

Explanation:

Juan uses \(\frac{1}{5}\) liter to water a small plant, and he uses \(\frac{1}{2}\) liter to water a large plant.

So total water he used \(\frac{7}{10}\) L.

Now he has \(\frac{2}{10}\) liter Left in the pitcher.

So Juan have water in the beginning is \(\frac{9}{10}\) L. Since

**Texas Test Prep**

Question 14.

Wilhelm is making a pie. He uses \(\frac{1}{2}\) cup of blueberries and \(\frac{2}{3}\) cup of raspberries. What is the total amount of berries in Wilhelm’s pie?

(A) \(\frac{3}{5}\) cup

(B) \(\frac{2}{6}\) cup

(C) \(\frac{7}{6}\) cups

(D) \(\frac{3}{6}\) cup

Answer: \(\frac{7}{6}\) cups

Explanation:

He uses \(\frac{1}{2}\) cup of blueberries and \(\frac{2}{3}\) cup of raspberries.

Sum of \(\frac{1}{2}\) + \(\frac{2}{3}\) = \(\frac{7}{6}\)

### Texas Go Math Grade 5 Lesson 5.1 Homework and Practice Answer Key

**Use fraction strips to find the sum. Write your answer in the simplest form.**

Question 1.

Answer:

Explanation:

To add the given fractions, did the denominator equal first then added

Question 2.

Answer:

Explanation:

To add the given fractions, did the denominator equal first then added

Question 3.

\(\frac{1}{6}\) + \(\frac{3}{4}\) = ____________

Answer:\(\frac{11}{12}\)

Explanation:

To add the given fractions, did the denominator equal first then added

Question 4.

\(\frac{5}{6}\) + \(\frac{1}{2}\) = ____________

Answer: \(\frac{8}{6}\)

Explanation:

To add the given fractions, did the denominator equal first then added

Question 5.

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

Answer: \(\frac{9}{10}\)

Explanation:

To add the given fractions, did the denominator equal first then added

Question 6.

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

Answer: \(\frac{11}{12}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{1}{4}\) + \(\frac{2}{3}\) = \(\frac{3}{12}\) + \(\frac{8}{12}\) = \(\frac{11}{12}\)

Question 7.

\(\frac{1}{3}\) + \(\frac{5}{6}\) = _____________

Answer: \(\frac{7}{6}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{1}{3}\) + \(\frac{5}{6}\) = \(\frac{2}{6}\) + \(\frac{5}{6}\) = \(\frac{7}{6}\)

Question 8.

\(\frac{3}{5}\) + \(\frac{3}{10}\) = ______________

Answer: \(\frac{9}{10}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{3}{5}\) + \(\frac{3}{10}\) = \(\frac{6}{10}\) + \(\frac{3}{10}\) = \(\frac{9}{10}\)

Question 9.

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

Answer: \(\frac{7}{8}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{1}{8}\) + \(\frac{3}{4}\) = \(\frac{1}{8}\) + \(\frac{6}{8}\) = \(\frac{7}{8}\)

Question 10.

\(\frac{7}{10}\) + \(\frac{1}{2}\) = _____________

Answer: \(\frac{7}{8}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{7}{10}\) + \(\frac{1}{2}\) = \(\frac{7}{10}\) + \(\frac{5}{10}\) = \(\frac{12}{10}\) = \(\frac{6}{5}\)

Question 11.

\(\frac{5}{6}\) + \(\frac{1}{12}\) = _____________

Answer: \(\frac{11}{12}\)

Explanation:

To add the given fractions, did the denominator equal first then added

\(\frac{5}{6}\) + \(\frac{1}{12}\) = \(\frac{10}{12}\) + \(\frac{1}{12}\) = \(\frac{11}{12}\)

**Problem Solving**

Question 12.

Cooper is grating cheese for the family taco dinner. He grates \(\frac{1}{2}\) cup of cheddar cheese and \(\frac{3}{4}\) cup of monterey jack cheese. How much cheese does Cooper grate?

Answer: Cooper grate \(\frac{5}{4}\) cup of cheese

Explanation:

Cooper grates \(\frac{1}{2}\) cup of cheddar cheese and \(\frac{3}{4}\) cup of monterey jack cheese. then total cheese is sum of \(\frac{1}{2}\) cup of cheddar cheese and \(\frac{3}{4}\) cup of monterey jack cheese. So Total cheese is \(\frac{5}{4}\)

\(\frac{1}{2}\)+\(\frac{3}{4}\) =\(\frac{2}{4}\)+\(\frac{3}{4}\) = \(\frac{5}{4}\)

Question 13.

Jasmine has to mix \(\frac{3}{4}\) cup of flour and \(\frac{3}{8}\) cup of cornmeal. She has a container that holds 1 cup. Can Jasmine mix the flour and cornmeal in the container? Explain.

Answer: Jasmine Can not mix the flour and cornmeal in the container. Since total mix of flour and cornmeal is 1/8 cup more than cup.

Explanation:

Jasmine has to mix \(\frac{3}{4}\) cup of flour and \(\frac{3}{8}\) cup of cornmeal. So Sum of flour and cornmeal is \(\frac{9}{8}\)

if divide in to fraction strips of same denominator the \(\frac{8}{8}\) + \(\frac{1}{8}\). \(\frac{8}{8}\) is equals to 1 cup. So she can not mix in the container.

**Lesson Check**

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

Question 14.

Julio spent \(\frac{1}{10}\) of his weekly allowance on a set of markers and \(\frac{2}{5}\) of it on a book. What fraction of Julio’s allowance is this altogether?

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

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

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

(D) \(\frac{1}{5}\)

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

Explanation:

\(\frac{1}{10}\) + \(\frac{2}{5}\) = \(\frac{1}{10}\) + \(\frac{4}{10}\) =\(\frac{5}{10}\) = \(\frac{1}{2}\)

Question 15.

Kate is using fraction strips to add \(\frac{4}{10}\) and \(\frac{4}{5}\). She uses one whole strip to represent the sum. How many fifths strips does she need to complete the sum?

(A) 1

(B) 2

(C) 5

(D) 8

Answer: A

Explanation:

one extra strip is needed to complete the sum

Question 16.

Which fraction correctly completes the equation?

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

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

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

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

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

Answer: D

Explanation:

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

Question 17.

An apple was cut into 8 equal-size pieces. Stacy ate \(\frac{1}{4}\) of the apple. Tony ate \(\frac{3}{8}\) of the apple. What part of the apple did Stacy and Tony eat in all?

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

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

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

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

Answer: B

Explanation:

Equal the all denominators:

Stacy ate \(\frac{1}{4}\) of the apple = \(\frac{1}{4}\) = \(\frac{2}{8}\)

Tony ate \(\frac{3}{8}\) of the apple = \(\frac{3}{8}\)

Stacy and Tony ate = \(\frac{3}{8}\) + \(\frac{2}{8}\)= \(\frac{5}{8}\)

Question 18.

**Multi-Step** Last weekend, Beatrice walked her poodle \(\frac{2}{3}\) mile on Saturday and \(\frac{5}{6}\) mile on Sunday. Fiona walked her beagle \(\frac{1}{3}\) mile on Saturday and \(\frac{1}{2}\) mile on Sunday. How much farther did the poodle walk last weekend than the beagle?

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

(B) 1\(\frac{1}{3}\) miles

(C) \(\frac{2}{3}\) mile

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

Answer: C

Explanation:

Last weekend, Beatrice walked her poodle \(\frac{2}{3}\) mile on Saturday

and \(\frac{5}{6}\) mile on Sunday.

Fiona walked her beagle \(\frac{1}{3}\) mile on Saturday

and \(\frac{1}{2}\) mile on Sunday.

\(\frac{2}{3}\) + \(\frac{5}{6}\) = \(\frac{4}{6}\) + \(\frac{5}{6}\) = \(\frac{9}{6}\) = \(\frac{3}{2}\)

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

\(\frac{3}{2}\) – \(\frac{5}{6}\) = \(\frac{9}{6}\) – \(\frac{5}{6}\) = \(\frac{2}{3}\)

Question 19.

**Multi-Step** Rick worked in his garden on Friday. He pulled weeds for \(\frac{5}{6}\) hour, planted seeds for \(\frac{1}{2}\) hour, and watered for \(\frac{1}{6}\) hour. How much time did Rick spend working in his garden on Friday?

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

(B) 1 hour

(C) 1\(\frac{1}{3}\) hours

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

Answer: D

Explanation:

\(\frac{5}{6}\) +\(\frac{1}{2}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\) +\(\frac{3}{6}\) +\(\frac{1}{6}\) = \(\frac{9}{6}\) = \(\frac{6}{6}\) +\(\frac{3}{6}\) = 1 + \(\frac{1}{2}\)