We included **HMH Into Math Grade 5 Answer Key PDF** **Module 14 Lesson 6 Use Strategies Reasoning to Add and Subtract **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 14 Lesson 6 Answer Key Use Strategies Reasoning to Add and Subtract

I Can add and subtract decimals by using reasoning and strategies involving addition properties or friendly numbers.

**Step It Out**

Question 1.

Kyle finds two games that he wants to buy.

A. What amount does Kyle pay for the two games?

Find friendly numbers. Add $0.03 to the price of Dark Embers. Subtract $0.03 from the price of Golden Scythe. What are the new prices?

Answer:

New prices Dark Embers – $16,

Golden Scythe- $13.44,

Explanation:

Given Dark Embers – $15.97, Golden Scythe- $13.47,

Now adding $0.03 to the price of Dark Embers.

Subtracting $0.03 from the price of Golden Scythe.

The new prices are Dark Embers is

$15.97

+ $0.03

$16.00

Golden Scythe is

$13.47

-$0.03

$13.44

What is the cost for both games?

Answer:

$29.44,

Explanation:

The total cost of both games Dark Embers – $16 and

Golden Scythe- $13.44 is

$16.00

+$13.44

$29.44

Is this the same as 15.97 + 13.47? How do you know?

Answer:

Yes, Same,

Explanation:

Yes, the total cost is the same as 15.97 + 13.47 as

we are adding and subtracting with same amount

of value there won’t be any change in the total.

B. How much more does Dark Embers cost than Golden Scythe?

Find friendly numbers. Subtract 0.47 from the price of each game. What are the new prices?

Answer:

New prices: Dark Embers – $15.5,

Golden Scythe- $13,

Explanation:

Subtract 0.47 from the price of each game.

The new prices are Dark Embers –

$15.97

– $0.47

$15.5 and

Golden Scythe –

$13.47

$ 0.47

$13.

What is the difference in price?

Answer:

$2.5,

Explanation:

The difference in the price is

$15.5 – $13 = $2.5.

Is this the same as 15.97 – 13.47? How do you know?

Answer:

Yes,Same,

Explanation:

Yes the same as we are subtracting same value

0.47 from the price of each game.

So the difference will be the same.

**Turn and Talk** How could you find the sum and difference in a different way?

Answer:

Results of sum and difference will be different,

Explanation:

The sum will be the result of adding numbers,

while the difference will be the result of subtracting them.

For example, in the math problem 4 + 3 – 5,

the sum of 4 and 3 will be 7 and

the difference between 7 and 5 will be 2.

Question 2.

Kyle wants to buy three accessories for his club’s gaming system. He writes 32.75 + 11.98 + 24.25 to find the total cost.

A. Kyle notices that 0.75 and 0.25 from the first and third addends have a sum of 1.00. He uses the Commutative Property of Addition and the Associative Property of Addition to regroup the addends to add them first.

(32.75 + 11.98) + 24.25 = 32.75 + (11.98 + 24.25) Associative Property

= 32.75 + (24.25 + 11.98) Commutative Property

= (32.75 + 24.25) + 11.98 Associative Property

Rewrite the sum as an expression with two addends. ___________

Answer:

Expression: (32 + 24 + 1) + 11.98,

Explanation:

Given Kyle wants to buy three accessories for his

club’s gaming system. He writes 32.75 + 11.98 + 24.25 and

Kyle notices that 0.75 and 0.25 from the first and

third addends have a sum of 1.00. So the sum as an

expression with two addends is (32 + 24 + 1) + 11.98.

B. What is the cost of all three accessories?

Answer:

$68.98,

Explanation:

The cost of three accessories for his club’s gaming system is

$32.75 + $11.98 + $24.25 or ($32 + $24 + $1) + $11.98 is

$32.75

$11.98

+$24.25

$68.98 or

$57

+$11.98

$68.98 therefore same.

**Turn and Talk** Explain why addition properties can make solving an addition problem easier than using friendly numbers.

Answer:

The properties of addition make it easier to work with

numbers by allowing us to regroup them so that an

equation is easier to solve.

Explanation:

Understanding the properties of addition can help us

to work with numbers more effectively than using

friendly numbers which is typically a multiple of

10, 100, or 100 then we add on the remainder.

**Check Understanding**

Question 1.

Use the table above to write and solve an equation to find how much more a headset costs than a racing wheel. How can using friendly numbers help you?

Answer:

Equation: m = $24.25 – $11.98,

Much more a headset costs than a racing wheel is $12.27,

Explanation:

Using the table above to write and solve an equation to

find how much more a headset costs than a racing wheel is

headset $24.25 and racing wheel $11.98, let m be more

a headset costs than a racing wheel so equation:

m = $24.25 – $11.98, solving using user friendly we make

$11.98 as $10 by subtracting $1.98 we get $10 and

even subtracting from $24.25 – $1.98 = $22.27,

So now we get $22.27 – $10 = $12.27.

**Add or subtract. Explain what strategy you used.**

Question 2.

27.86 + 31.44 + 12.14

Answer:

71.44,

Explanation:

Given to add 27.86 + 31.44 + 12.14 we get

1,1

27.86

31.44

+12.14

71.44

Question 3.

79.32 – 42.05

Answer:

37.27,

Explanation:

Given to subtract 79.32 – 42.05 we get

79.32

-42.05

37.27

**On Your Own**

Question 4.

**Reason** At the department store, Ms. Jarvis finds two winter coats that she likes. What is the cost to buy both coats? Explain your reasoning.

Answer:

The cost to buy both coats is $83.54,

Explanation:

Given at the department store, Ms. Jarvis finds two winter coats

that she likes. The cost to buy both coats is

$48.98

+$34.56

$83.54.

Question 5.

**Critique Reasoning** Ina claims she can find 58.42 – 16.95 by solving the equation 58.47 – 17.00 = n. Is she correct? Justify your reasoning.

Answer:

Ina is correct,

Explanation:

Given Ina claims she can find 58.42 – 16.95 by solving the

equation 58.47 – 17.00 = n. Yes she is correct because

58.42

-16.95

41.47 and

58.47

-17.00

41.47 upon solving both are same.

**Add or subtract.**

Question 6.

37.41 – 29.08

Answer:

8.33,

Explanation:

Given to subtract 37.41 – 29.08 we get

37.41

-29.08

8.33

Question 7.

437.60 – 321.75

Answer:

115.85,

Explanation:

Given to subtract 437.60 – 321.75 we get

437.60

-321.75

115.85

Question 8.

138.62 + 567.88 + 319.38

Answer:

1025.88

Explanation:

Given to add 138.62 + 567.88 + 319.38 we get

2 ,2,1,1

138.62

567.88

+319.38

1025.88

Question 9.

817.62 – 408.03

Answer:

409.59,

Explanation:

Given to subtract 817.62 – 408.03 we get

817.62

-408.03

409.59

Question 10.

The table shows the price of some school supplies.

How much more do pencils cost than a notebook?

Answer:

0.42,

Explanation:

More do pencils cost than a notebook is

$1.71

-$1.29

$0.42

What is the cost to buy one package each of erasers, paper clips, and pencils?

Answer:

The cost to buy one package each of

erasers, paper clips, and pencils is $45.70,

Explanation:

Given to find the cost to buy one package each of

erasers, paper clips, and pencils it is

$1.30

$1.56

+$1.71

$4.57

How much do three notebooks cost?

Answer:

The cost of three notebooks is $3.87,

Explanation:

Given to find the cost of three notebooks is

3 X $1.29 = $3.87.

Describe how you can use friendly numbers to find how much more pencils cost than paper clips.

Answer:

Much more pencils cost than paper clips is $0.15,

Explanation:

We can use friendly numbers to find how much more

pencils cost($1.71) than paper clips($1.56) as adding

$0.44 to $1.56 we get $2 and adding$0.44 to $1.71 we get

$2.15, now much more pencils cost than paper clips is

$2.15

-$2.00

$0.15.

Question 11.

The dimensions of a polygon are given.

What is the perimeter of the polygon?

Answer:

The perimeter of the polygon is 21 cm,

Explanation:

The perimeter of the polygon is

4.13 cm + 3.87 cm + 4.29 cm + 8.71 cm = 21 cm.

How much longer is the longest side than the shortest side?

Answer:

4.84 cm,

Explanation:

Longer is the longest side than the shortest side is

8.71 cm

– 3.87 cm

4.84 cm

Question 12.

**Use Structure** Yuan is given the following problem.

37.5 + (15.32 + 12.5)

How can Yuan use the Commutative Property of Addition and the Associative Property of Addition to simplify the problem?

Answer:

Commutative Property of Addition:

37.5 + (15.32 + 12.5) = (37.5 + 15.32) + 12.5,

Associative Property of Addition:

(37.5 + 15.32) + 12.5 = 37.5 + (15.32 + 12.5),

Result is 65.32,

Explanation:

Yuan is given the following problem.

37.5 + (15.32 + 12.5), Yuan can use the

Commutative Property of Addition as

Changing the order of addends does not

change the sum so 37.5 + (15.32 + 12.5) = (37.5 + 15.32) + 12.5 and

the Associative Property of Addition is Changing the grouping of

addends does not change the sum (37.5 + 15.32) + 12.5 = 37.5 + (15.32 + 12.5),

result is 65.32.

How can he use friendly numbers to simplify the problem?

Answer:

(37.5 + 12.5 + 0.32) + 15.32 – 0.32 = 65.32,

Explanation:

Adding 0.32 and subtracting 0.32 using as

friendly number will not change the value of the result.

What is the sum?

Answer:

Sum is 65.32,

Explanation:

The total sum is

1,1

37.5

12.5

+0.32

50.32

+15.32

65.64

-0.32

65.32

Question 13.

Margot has $21.50 to spend at the Street fair. She buys roasted peanuts for $4.75 and a hot dog for $2.99. How much money does she have left?

Answer:

$13.76,

Explanation:

Given Margot has $21.50 to spend at the Street fair.

She buys roasted peanuts for $4.75 and a hot dog for $2.99.

Margot have left with $21.50 – ($4.75 + $2.99) = $13.76.

Question 14.

**Open-Ended** When is it better to use friendly numbers to solve a decimal addition problem, and when is it better to use the properties of addition to solve?

Answer:

Friendly numbers as a number that is

easy to work with,

The properties of addition and subtraction make it

easier to work with numbers by allowing you to

regroup them so that an equation is easier to solve,

Explanation:

Friendly numbers as a number that is easy to work with.

For example, multiples of 10 are “friendly” because they are

easy to work with when we add or subtract.

When we use the “friendly number” strategy for addition,

it helps us work with big numbers.

The properties of addition and subtraction make it

easier to work with numbers by allowing you to

regroup them so that an equation is easier to solve.

Understanding the properties of addition and

subtraction can help you to work with numbers more effectively.