# Texas Go Math Grade 4 Lesson 5.6 Answer Key Add and Subtract Mixed Numbers

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## Texas Go Math Grade 4 Lesson 5.6 Answer Key Add and Subtract Mixed Numbers

Essential Question

How con you add and subtract mixed numbers with like denominators?
Answer: First convert the mixed fraction to the fraction
if the denominators are same then you can directly add or subtract the numerators.

Unlock the Problem

After a party, there were 1$$\frac{4}{6}$$ quesadillas left on one tray and 2$$\frac{3}{6}$$ quesadillas left on another tray. How much otthe quesadillas were left?
Answer:

Example Add mixed numbers.

Answer:

Answer:

Answer:

So, _____________ quesadillas were left.
Answer:
So, 4$$\frac{1}{6}$$  quesadillas were left.

Math Talk

Mathematical Processes
When modeling sums such as $$\frac{4}{6}$$ and $$\frac{3}{6}$$, why is it helpful to combine parts into wholes when possible? Explain.
Answer: It is easy to add the numbers than fractions
If we make a whole then adding the remaining fractions will be easy.

Example Subtract mixed numbers.

Alejandro had 3$$\frac{4}{6}$$ quesadillas. His family ate 2$$\frac{3}{6}$$ of the quesadillas. How many quesadillas are left?

Find 3$$\frac{4}{6}$$ – 2$$\frac{3}{6}$$

Model

Shade the model to show 3$$\frac{4}{6}$$.
Then cross out 2$$\frac{3}{6}$$ to model the subtraction.

The difference is $$\frac{1}{6}$$.
So, there are __________ quesadillas left.

Answer:

The difference is _________ .
So, there are 1$$\frac{1}{6}$$.quesadillas left.
Explanation:
Add the fractions first
$$\frac{4}{6}$$. – $$\frac{3}{6}$$.
$$\frac{1}{6}$$.
Then subtract the wholes
3 – 2 = 1 Converted $$\frac{1}{6}$$. to 1$$\frac{1}{6}$$.

Record

Subtract the fractional parts of the mixed numbers.
Then subtract the whole-number parts of the mixed numbers.

Answer:

Explanation:
Subtracted the fractions first
$$\frac{4}{6}$$. – $$\frac{3}{6}$$.
$$\frac{1}{6}$$.
Then subtract the wholes
3 – 2 = 1 Converted $$\frac{1}{6}$$. to 1$$\frac{1}{6}$$.

Share and Grow

Write the sum as a mixed number with the fractional part less than 1.

Question 1.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Question 2.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Question 3.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Find the difference.

Question 4.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Question 5.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Question 6.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Math Talk

Mathematical Processes
Explain how adding and subtracting mixed numbers is different from adding and Subtracting fractions.
Answer:
In fractions first we make denominators equal
then add or subtract the fractions directly
Explanation:
In mixed fractions first add or subtract the wholes
then add or subtract the fractions

Problem Solving

Solve. Write your answer as a mixed number.

Question 7.
The driving distance from Alex’s house to the museum is 6$$\frac{7}{10}$$ miles. What is the round-trip distance?
Answer: 13$$\frac{4}{10}$$ is the round trip distance
Explanation:
6$$\frac{7}{10}$$ + 6$$\frac{7}{10}$$
first add the fractions
$$\frac{7}{10}$$ + $$\frac{7}{10}$$  = $$\frac{14}{10}$$
Then add the wholes
6 + 6 = 12
6 + 6 + 1 + $$\frac{4}{10}$$ = 13$$\frac{4}{10}$$

Question 8.
H.O.T. Apply Multi-Step The driving distance from the sports arena to Kristina’s house is 10$$\frac{9}{10}$$ miles. The distance from the sports arena to Luke’s house is 2$$\frac{7}{10}$$ miles. How much greater is the driving distance between the sports arena and Kristina’s house than between the sports arena and Luke’s house?
Answer: 8$$\frac{2}{10}$$
Explanation:
10$$\frac{9}{10}$$ – 2$$\frac{7}{10}$$ miles.
Subtract the wholes 10 – 2 = 8
then subtract the fractions $$\frac{9}{10}$$ – $$\frac{7}{10}$$
8$$\frac{2}{10}$$ is the driving distance between the sports arena and Kristina’s house than between the sports arena and Luke’s house

Question 9.
Benji biked from his house to the nature preserve, a distance of 23$$\frac{4}{5}$$ miles. Jade hiked from her house to the lake, a distance of 12$$\frac{2}{5}$$ miles. How many fewer miles did Jade bike than Benji?
Answer: 11$$\frac{2}{5}$$ fewer miles did Jade bike than Benji
Explanation:
23$$\frac{4}{5}$$ – 12$$\frac{2}{5}$$
Subtract the wholes 23 – 12 = 11
then subtract the fractions $$\frac{4}{5}$$  – $$\frac{2}{5}$$ = $$\frac{2}{5}$$
11$$\frac{2}{5}$$

Question 10.
H.O.T. Apply During the Samson family trip, they drove from home to a ski lodge, a distance of 55$$\frac{4}{5}$$ miles, and then drove an additional 12$$\frac{4}{5}$$ miles to visit friends. If the family drove the same route back home, what was the distance traveled during their trip?
Answer: 68$$\frac{3}{5}$$
55$$\frac{4}{5}$$ + 12$$\frac{4}{5}$$
add the wholes 55 + 12 = 67
Add the fractions
$$\frac{4}{5}$$ + $$\frac{4}{5}$$ = $$\frac{8}{5}$$ = 1$$\frac{3}{5}$$
68$$\frac{3}{5}$$

Daily Assessment Task

Fill in the bubble completely to show your answer.

Question 11.
A chameleon’s body is 1$$\frac{4}{6}$$ feet long. Its tongue is 2$$\frac{5}{6}$$ feet long. How much longer is the chameleon’s tongue than its body?
(A) 2$$\frac{3}{6}$$
(B) 1$$\frac{3}{6}$$
(C) 1$$\frac{1}{6}$$
(D) 2$$\frac{1}{6}$$
Answer: C
Explanation:
2$$\frac{5}{6}$$ – 1$$\frac{4}{6}$$  = 1$$\frac{1}{6}$$ longer is the chameleon’s tongue than its body

Question 12.
Jill rides her horse 5$$\frac{6}{12}$$ miles on a horse trail. She will ride 4$$\frac{5}{12}$$ miles more to reach the end of the trail. How long is the horse trail?
(A) 1$$\frac{1}{12}$$
(B) 1$$\frac{11}{12}$$
(C) 9$$\frac{1}{12}$$
(D) 9$$\frac{11}{12}$$
Answer: D
Explanation:
5$$\frac{6}{12}$$ + 4$$\frac{5}{12}$$ = 9$$\frac{11}{12}$$ is the horse trail

Question 13.
Multi-Step Students bring 8$$\frac{7}{8}$$ gallons of lemonade to a picnic. They drink 5$$\frac{2}{8}$$ gallons with lunch. Then they drink 2$$\frac{1}{8}$$ gallons with an afternoon snack. How much lemonade is left?
(A) 3$$\frac{5}{8}$$ gallons
(B) 6$$\frac{3}{4}$$gallons
(C) 5$$\frac{3}{4}$$gallons
(D) 1$$\frac{1}{2}$$gallons
Answer: D
Explanation:
5$$\frac{2}{8}$$ + 2$$\frac{1}{8}$$ = 7$$\frac{3}{8}$$
8$$\frac{7}{8}$$ – 7$$\frac{3}{8}$$ = 1$$\frac{4}{8}$$
= 1$$\frac{1}{2}$$gallons lemonade is left

TEXAS Test Prep

Question 14.
Jeff used 4$$\frac{7}{8}$$ cups of orange juice and 3$$\frac{1}{8}$$ cups of pineapple juice to make a tropical punch. How much more orange juice than pineapple juice did Jeff use?
(A) $$\frac{3}{4}$$
(B) 1$$\frac{3}{4}$$
(C) 1$$\frac{7}{8}$$
(D) 8 cups
Answer: B
Explanation:
4$$\frac{7}{8}$$ – 3$$\frac{1}{8}$$ = 1$$\frac{6}{8}$$
1$$\frac{3}{4}$$ more orange juice than pineapple juice that Jeff use

### Texas Go Math Grade 4 Lesson 5.6 Homework and Practice Answer Key

Write the sum as a mixed number with the fractional part less than 1.

Question 1.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Question 2.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Question 3.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Question 4.

Answer:

Explanation:
Added the wholes then added the fractions
written the sum

Find the difference

Question 5.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Question 6.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Question 7.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Question 8.

Answer:

Explanation:
subtracted the wholes then subtracted the fractions
written the Difference

Problem Solving

Question 9.
Mrs. Baker drove 2$$\frac{4}{10}$$ hours to visit her mother. It took her 3$$\frac{6}{10}$$ hours to get home. How much longer did it take Mrs. Baker to get home?
Answer: 1$$\frac{2}{10}$$
Explanation:
3$$\frac{6}{10}$$ – 2$$\frac{4}{10}$$  = 1$$\frac{2}{10}$$
1$$\frac{2}{10}$$ longer that take Mrs. Baker to get home

Question 10.
Monica’s recipe calls for 2$$\frac{3}{4}$$ cup of water and 3$$\frac{3}{4}$$ cup of milk. What is the total amount of liquid in the recipe?
Answer:  6$$\frac{2}{4}$$
2$$\frac{3}{4}$$ + 3$$\frac{3}{4}$$ = 6$$\frac{2}{4}$$
6$$\frac{2}{4}$$ is the total amount of liquid in the recipe

Lesson check

Fill in the bubble completely to show your answer.

Question 11.
Kimberly’s kite tail is 5$$\frac{5}{6}$$ feet long. Margaret’s kite tail is 4$$\frac{3}{6}$$ feet long. How much longer is Kimberly’s kite tail than Margaret’s kite tail?
(A) 1$$\frac{2}{3}$$feet
(B) 1$$\frac{1}{3}$$feet
(C) 2$$\frac{1}{3}$$feet
(D) 2$$\frac{2}{3}$$feet
Answer: B
Explanation:
5$$\frac{5}{6}$$ – 4$$\frac{3}{6}$$  = 1$$\frac{2}{6}$$
1$$\frac{1}{3}$$feet  longer is Kimberly’s kite tail than Margaret’s kite tail.

Question 12.
Wayne recorded his exercise for two months. He walked 2$$\frac{8}{10}$$ miles the first day. He walked 1$$\frac{5}{10}$$ miles the second day. What is the total distance he walked during the two days?
(A) 4$$\frac{3}{10}$$ miles
(B) 4$$\frac{2}{10}$$ miles
(C) 3$$\frac{3}{10}$$ miles
(D) 3$$\frac{2}{10}$$ miles
Answer: A
Explanation:
2$$\frac{8}{10}$$ + 1$$\frac{5}{10}$$ = 3$$\frac{13}{10}$$ = 4$$\frac{3}{10}$$ miles is the total distance he walked during the two days

Question 13.
Kris used 7$$\frac{5}{12}$$ inches of tape to wrap her brother’s gift and 6$$\frac{9}{12}$$ inches of tape to wrap her sister’s gift. What is the total amount of tape Kris used to wrap the gifts?
(A) 13$$\frac{1}{6}$$ inches
(B) 14$$\frac{1}{6}$$ inches
(C) 13$$\frac{1}{12}$$ inches
(D) 14$$\frac{1}{12}$$ inches
Answer:
Explanation:
7$$\frac{5}{12}$$ + 6$$\frac{9}{12}$$  = 13$$\frac{14}{12}$$ = 14$$\frac{2}{12}$$ is the total amount of tape Kris used to wrap the gifts

Question 14.
The mall is 6$$\frac{6}{10}$$ miles from Miranda’s house. The nearest grocery store is 4$$\frac{2}{10}$$ miles from her house. How much farther is the mall than the grocery store from Miranda’s house?
(A) 2$$\frac{2}{5}$$ miles
(B) 4$$\frac{4}{5}$$ mi1es
(C) 2$$\frac{2}{5}$$ miles
(D) 8$$\frac{2}{5}$$ miles
Answer: A
Explanation:
6$$\frac{6}{10}$$ – 4$$\frac{2}{10}$$ = 2$$\frac{4}{10}$$ = 2$$\frac{2}{5}$$ miles
2$$\frac{2}{5}$$ miles farther is the mall than the grocery store from Miranda’s house

Question 15.
Multi-Step A tank has 5$$\frac{3}{4}$$ gallons of water in it. Today, 4$$\frac{1}{4}$$ gallons of the water is used. Then, the tank is filled with another 6$$\frac{3}{4}$$ gallons of water. What is the amount of water in the tank now?
(A) 8$$\frac{1}{4}$$ gallons
(B) 1$$\frac{1}{2}$$ gallons
(C) 8$$\frac{1}{4}$$ gal1ons
(D) 1$$\frac{3}{4}$$ gallons
Answer: A
5$$\frac{3}{4}$$ – 4$$\frac{1}{4}$$  = 1$$\frac{2}{4}$$
1$$\frac{2}{4}$$ + 6$$\frac{3}{4}$$  = 7$$\frac{5}{4}$$ = 8$$\frac{1}{4}$$ gallons
8$$\frac{1}{4}$$ gallons is the amount of water in the tank now

Question 16.
Multi-Step For a candy recipe, Karen will need 4$$\frac{3}{8}$$ cups of dark chocolate chips, 5$$\frac{5}{8}$$ cups milk chocolate chips, and 3$$\frac{4}{8}$$ cups white chocolate chips. What is the total amount of chips needed for the candy recipe?
(A) 12$$\frac{1}{2}$$ cups
(B) 12$$\frac{2}{3}$$ cups
(C) 13$$\frac{2}{3}$$ cups
(D) 13$$\frac{1}{2}$$ cups
Answer: D
Explanation:
First add the wholes 4 + 5 + 3 = 12
Then add the fractions
$$\frac{3}{8}$$ + $$\frac{5}{8}$$ + $$\frac{4}{8}$$  = $$\frac{12}{8}$$
1$$\frac{4}{8}$$
so, the fraction is 13$$\frac{1}{2}$$ cups

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