We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 4 Lesson 4 Use Grouping Symbols** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 4 Lesson 4 Answer Key Use Grouping Symbols

I Can describe how to use grouping symbols in a numerical expression and place parentheses so an expression has a given value.

**Step It Out**

1. Justine is making jewelry for her friends. She makes 4 of the bracelets shown. To determine the number of beads she needs, she writes the numerical expression 5 + 3 + 6 × 4.

A. Use the order of operations to evaluate Justine’s numerical expression.

B. Which part of Justine’s numerical expression models the number of beads she uses for 1 bracelet?

C. How can you use your answer from Part B to find how many beads she uses for 4 bracelets?

D. How many beads does she need to make 4 bracelets? How does your answer compare to the answer you found in Part A?

E. How can you rewrite 5 + 3 + 6 × 4 with parentheses so that it models the number of beads she needs to make 4 bracelets?

Answer:

A. Parentheses, addition and multiplication,

B. Part A -(5 + 3 + 6),

C. By calculating,

D. 42 beads does she need to make 4 bracelets,

by number of beads multiply by 4 times,

E. (5 + 3 + 6) × 4,

Explanation:

Given Justine is making jewelry for her friends. She makes 4 of the bracelets shown.

To determine the number of beads she needs, she writes the numerical expression 5 + 3 + 6 × 4.

A. The order of operations to evaluate Justine’s numerical expression is (5 + 3 + 6) X 4.

First Parentheses, addition and multiplication,

B. Part A of Justine’s numerical expression models the number of beads she uses for 1 bracelet is (5 + 3 + 6).

C. By calculating Iuse my answer from Part B to find how many beads she uses for 4 bracelets.

D. 42 beads does she need to make 4 bracelets, By comparing to the answer I found in Part A (5 + 3 + 6) multiply by 4 times to make 4 bracelets.

E. Rewriting 5 + 3 + 6 × 4 with parentheses so that it models the number of beads she needs to make 4 bracelets is (5 + 3 + 6) × 4.

**Turn and Talk **

Where can you place one pair of parentheses in the numerical expression 5 × 8 – 4 + 2 to get the least possible value? Explain how you know.

Answer:

5 x (8 – 4) + 2,

Explanation:

First we check placing a pair of parentheses in the numerical expressions 5 × 8 – 4 + 2 to get the least possible value as

1. (5 X 8) – 4 + 2 = 40 – 4 + 2 = 36 + 2 = 38,

2. 5 x (8 – 4) + 2 = 5 X 4 + 2 = 20 + 2 = 22,

3. 5 X 8 – (4 + 2) = 40 – 6 = 34,

So the least possible value is by placing parentheses as 5 x (8 – 4) + 2.

**Step It Out**

2. Mr. Finn makes gift boxes with 4 green bracelets, 1 gold bracelet, and 1 necklace. Each bracelet costs $2 to make, and each necklace costs $5. He has $90 to spend on gift boxes. How can you model the number of gift boxes Mr. Finn can make using a numerical expression?

A. Parentheses (): Write an expression in parentheses to represent the total number of bracelets in one gift box.

(___ + ___)

B. Brackets [ ]: Write an expression in brackets to represent the total cost of the bracelets in one gift box.

[___ × (__ + ___)]

C. Braces {}: Write an expression in braces to represent the total cost of the bracelets and the necklace in one gift box.

{[___ × (___ + __)] + ___}

D. Write and evaluate an expression to show how many gift boxes Mr. Finn can make with $90.

__ ÷ {[__ × (___ + ___)] + ___}

_________

Answer:

A. (4 + 1),

B. [$2 × (4 +1)],

C. {[$2 × (4 +1)] + 1 X $5},

D. $90 ÷ {[$2 × (4 +1)] + 1 X $5},

Mr Finn can make 6 gift boxes,

Explanation:

Given Mr. Finn makes gift boxes with 4 green bracelets, 1 gold bracelet, and 1 necklace. Each bracelet costs $2 to make, and each necklace costs $5. He has $90 to spend on gift boxes.

A. Expression in parentheses to represent the total number of bracelets in one gift box is (4 + 1).

B. An expression in brackets to represent the total cost of the bracelets in one gift box is [$2 × (4 + 1)].

C. An expression in braces to represent the total cost of the bracelets and the necklace in one gift box.

{[$2 × (4 +1)] + 1 X $5},

D. An expression to show how many gift boxes Mr. Finn can make with $90 is

$90 ÷ {[$2 × (4 +1)] + 1 X $5} =

$90 ÷ {[$2 × (5)] + $5} = $90 ÷ {[$10] + $5} = $90 ÷ {$15} = 6,

therefore, Mr Finn can make 6 gift boxes.

**Turn and Talk** Look at the placement of the parentheses, brackets, and braces. How would you describe to someone the order of evaluating based on their position?

Answer:

1st parentheses, 2nd brackets and then braces,

Explanation:

The order of evaluation based on their position will be the values of 1st parentheses, 2nd brackets and then braces will be evaluated.

**Check Understanding Math Board**

Question 1.

Liza is making 3 necklaces. Each necklace has 4 pink beads, 6 purple beads, and 10 blue beads. Use parentheses to rewrite the numerical expression 3 × 4 + 6 + 10 so that it models the number of beads Liza needs to make 3 necklaces.

Answer:

3 X (4 + 6 + 10),

Explanation:

Given Liza is making 3 necklaces. Each necklace has 4 pink beads, 6 purple beads, and 10 blue beads.

Using parentheses to rewrite the numerical expression 3 × 4 + 6 + 10 so that it models the number of beads Liza needs to make 3 necklaces are first necklace needs the number of beads 4 + 6 + 10 then for making 3 necklaces are 3 X (4 + 6 + 10).

**On Your Own**

Question 2.

**Model with Mathematics** During a conference, a group makes the same lunch order shown in the table each day for 4 days. Use parentheses to rewrite the numerical expression to have a value of $308.

4 × 8 × 6 + 7 × 2 + 3 × 5

Answer:

4 X [(8 X 6) + (7 X 2) + (3 x 5)],

Explanation:

Given during a conference, a group makes the same lunch order shown in the table each day for 4 days.

Using parentheses to rewrite the numerical expression

4 × 8 × 6 + 7 × 2 + 3 × 5 to have a value of $308 is 4 X [(8 X 6) + (7 X 2) + (3 x 5)].

Question 3.

**Reason** When the numerical expression 80 – 20 ÷ 4 is rewritten with parentheses, it can have a value of 15 or 75. Explain.

Answer:

15,

Explanation:

Given to find the numerical expression 80 – 20 ÷ 4 is rewritten with parentheses, it can have a value of 15 or 75.

It will have 15 why because while the order of writing first we take parentheses from left to right

so it can have a value is (80 – 20) ÷ 4 = 60 ÷ 4 = 15.

**Use parentheses to rewrite the expression to have the given value.**

Question 4.

7 × 5 – 4 + 2

value: 9

Answer:

(7 x (5 – 4)) + 2,

Explanation:

Given the expression 7 × 5 – 4 + 2 to have given value 9 we need to check

1. If ((7 x 5) – 4) + 2 = 35 – 4 + 2 = 31 + 2 = 33 ≠ 9,

2. If (7 x (5 – 4)) + 2 = 7 X 1 + 2 = 7 + 2 = 9 = 9,

3. If (7 X 5) – (4 + 2) = 35 – 6 = 29 ≠ 9,

therefore the expression to have the given value 9 using parentheses is (7 x (5 – 4)) + 2.

Question 5.

8 + 12 ÷ 4 + 2

value: 10

Answer:

8 + (12 ÷ (4 + 2)),

Explanation:

Given the expression 8 + 12 ÷ 4 + 2 to have given value 10 we need to check

1. If ((8 + 12) ÷ 4) + 2 = 20 ÷ 4 + 2 = 5 + 2 = 7 ≠ 10,

2. If 8 + ((12 ÷ 4) + 2) = 8 + 3 + 2 = 8 + 5 = 13 ≠ 10 ,

3. If 8 +(12 ÷ (4 + 2)) = 8 + 12 ÷ 6 = 8 + 2 = 10 = 10,

therefore the expression to have the given value 10 using parentheses is 8 + (12 ÷ (4 + 2)).

Question 6.

2 + 6 × 5 – 4

value: 36

Answer:

((2 + 6) X 5) – 4,

Explanation:

Given the expression 2 + 6 X 5 – 4 to have given value 36 we need to check

1. If ((2 + 6) X 5) – 4 = 8 X 5 – 4 = 40 – 4 = 36 = 36,

2. If 2 + ((6 X 5) – 4) = 2 + 30 – 4 = 2 + 26 = 28 ≠ 36 ,

3. If 2 + (6 X (5 – 4)) = 2 + 6 X 1 = 2 + 6 = 8 ≠ 36,

therefore the expression to have the given value 36 using parentheses is ((2 + 6) X 5) – 4.

Question 7.

2 + 7 – 2 × 4

value: 22

Answer:

2 + ((7 – 2) X 4),

Explanation:

Given the expression 2 + 7 – 2 X 4 to have given value 22 we need to check

1. If ((2 + 7) – 2) X 4 = 9 – 2 X 4 = 7 X 4 = 28 ≠ 22,

2. If 2 + ((7 – 2) X 4) = 2 + 5 X 4 = 2 + 20 = 22 = 22,

3. If (2 + 7) – (2 X 4) = 2 + 7 – 8 = 9 – 8 = 1 ≠ 22,

therefore the expression to have the given value 22 using parentheses is 2 + ((7 – 2) X 4).

Question 8.

90 – 30 ÷ 6

value: 10

Answer:

(90 – 30) ÷ 6,

Explanation:

Given the expression 90 – 30 ÷ 6 to have given value 10 we need to check

1. If (90 – 30) ÷ 6 = 60 ÷ 6 =10 = 10,

2. If 90 – (30 ÷ 6) = 90 – 5 = 85 ≠ 10,

therefore the expression to have the given value 10 using parentheses is (90 – 30) ÷ 6.

Question 9.

12 + 24 ÷ 6 – 3

value: 3

Answer:

((12 + 24) ÷ 6) – 3,

Explanation:

Given the expression 12 + 24 ÷ 6 – 3 to have given value 3 we need to check

1. If ((12 + 24) ÷ 6) – 3 = 36 ÷ 6 – 3 = 6 – 3 = 3 = 3,

2. If 12 + ((24 ÷ 6) – 3) = 12 + 4 – 3 = 12 + 1 = 13 ≠ 3,

3. If 12 +(24 ÷ (6 – 3)) = 12 + 24 ÷ 3 = 12 + 8 = 20 ≠ 3,

therefore the expression to have the given value 3 using parentheses is ((12 + 24) ÷ 6) – 3.

**On Your Own**

Question 10.

**Model with Mathematics** Nayla works at a health food store. The store has the bins shown, On Monday, the bins are full. The store sells 13 pounds of granola by Friday. Nayla wants to evenly divide the remaining granola in the 7 bins. Use parentheses to rewrite the numerical expression to model the amount that will be in each bin, 2 pounds.

4 × 3 + 3 × 5 – 13 ÷ 7

Answer:

((4 × 3) + (3 × 5) – 13) ÷ 7,

Explanation:

Given Nayla works at a health food store.

The store has the bins shown, On Monday, the bins are full.

The store sells 13 pounds of granola by Friday.

Nayla wants to evenly divide the remaining granola in the 7 bins. Using parentheses to rewrite the numerical expression to model the amount that will be in each bin, 2 pounds is for 4 × 3 + 3 × 5 – 13 ÷ 7,

((4 × 3) + (3 × 5) – 13) ÷ 7 = ((12 + 15) – 13) ÷ 7,

(27 – 13) ÷ 7 = 14 ÷ 7 = 2, So the expression is

((4 × 3) + (3 × 5) – 13) ÷ 7.

Question 11.

**Critique Reasoning** Deshawn says that he can evaluate the numerical expression 7 + (3 × 8) – 5 without parentheses and get the same answer. Is Deshawn correct? Explain how you know.

Answer:

Deshawn is incorrect,

Explanation:

Given Deshawn says that he can evaluate the numerical expression 7 + (3 × 8) – 5 without parentheses and get the same answer. Checking using parentheses

7 + ( 24) – 5 = 7 + 19 = 26, without using parentheses 7 + 3 X 8 – 5 = 10 X 8 – 5 = 80 – 5 = 75. Deshawn is incorrect as the values are differing by using using parentheses and without using parentheses.

Question 12.

**Reason** Describe how you would evaluate the numerical expression 48 ÷ {[2 × (1 + 3)] + 4}.

Answer:

4,

Explanation:

Given to evaluate numerical expression 48 ÷ {[2 × (1 + 3)] + 4}, first we evaluate parentheses then brackets and braces so

48 ÷ {[2 × 4)] + 4} = 48 ÷ {[8] + 4} =48 ÷ {12} = 4.

Question 13.

**Reason** Use parentheses to rewrite 16 + 4 × 4 – 3 to have a value of 20. Then rewrite the expression to have a value of 77.

Answer:

1. For value of 20 : (16 + 4) X (4 – 3),

2. For value of 77 : ((16 + 4) X 4) – 3,

Explanation:

Given to rewrite 16 + 4 × 4 – 3 to have a value of 20.

Then rewrite the expression to have a value of 77.

1. To have value of 20 the expression 16 + 4 X 4 – 3 can be written as (16 + 4) X (4 – 3) = 20 X 1 = 20 ,

2. To have value of 77 the expression is ((16 + 4) X 4) – 3 = (20 X 4) – 3 = 80 – 3 = 77.