All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 8 Multiplication Properties will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 8 Multiplication Properties
Math in My World
Example 1
A coach had 16 players in each of 2 groups. Each player scored 5 goals. Find the total number of goals scored.
Find (16 × 2) × 5.
Since you can easily multiply 2 and 5, change the way the numbers are grouped.
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
It is easier to find 2 × 5 than 16 × 2. You can group the numbers differently to find 2 × 5 first.
So, the total number of goals scored is _____________.
Answer:
160 goals.
Explanation:
A coach had 16 players in each of 2 groups = 16 x 2 = 32
Each player scored 5 goals.
The total number of goals scored = 32 x 5 = 160 goals.
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
Example 2
Find the unknown in the equation
35.5 × __________ = 17 × 35.5.
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
So, the unknown is ___________.
Answer:
17
Explanation:
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
35.5 × 17 = 17 × 35.5
603.5 = 603.5
So, the unknown is 7
Example 3
Find the unknown in the equation 17 × __________ = 17.
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
So, the unknown is __________.
Answer:
Unknown number is 1.
Explanation:
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
17 x 1 = 17
So, the unknown is 1.
Guided Practice
Draw lines to match the multiplication property used in each equation.
Answer:
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
Talk Math
Explain how you could use mental math and multiplication properties to find (5.5 × 50) × 2.
Answer:
550
Explanation:
The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.
(5.5 × 50) × 2 = 5.5 x (50 x 2)
275 x 2 = 5.5 x 100
550 = 550
Independent Practice
Use properties of multiplication to find each product mentally. Show your steps and identify the properties that you used.
Question 4.
(5.1 × 2) × 50 = ____________
Answer:
510
Explanation:
The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.
(5.1 x 2) x 50 = 5.1 x (50 x 2)
10.2 x 50 = 5.1 x 100
510 = 510
(5.1 × 2) × 50 = 510 or 5.1 x (50 x 2) = 510.
Question 5.
4 × (2.5 × 6) = ____________
Answer:
60
Explanation:
The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.
4 x (2.5 x 6) = (4 x 6) x 2.5
4 x 15 = 24 x 2.5
60 = 60
4 x (2.5 x 6) = 60 or (4 x 6) x 2.5 = 60.
Question 6.
(9.8 × 500) × 2 = ____________
Answer:
9,800
Explanation:
The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.
(9.8 x 500) x 2 = 9.8 x (2 x 500)
4900 x 2 = 9.8 x 1000
9800 = 9800
(9.8 x 500) x 2 = 9800 or 9.8 x (2 x 500) = 9800
Question 7.
(1.4 × 50) × 20 = ____________
Answer:
1400
Explanation:
The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.
(1.4 x 50) x 20 = 1.4 x ( 20 x 50)
7 x 50 = 1.4 x 1000
1400 = 1400
(1.4 × 50) × 20 = 1400 or 1.4 x ( 20 x 50) = 1400
Mathematical PRACTICE Use Algebra Find the unknown in each equation. Circle which property you used.
Question 8.
19.5 × 
= 19.5
= ____________
Commutative Property
Associative Property
Identity Property
Answer:
Explanation:
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
19.5 x 1 = 19.5
Question 9.
34 × 65 = 65 ×
= _____________
Commutative Property
Associative Property
Identity Property
Answer:
Explanation:
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
34 x 65 = 65 x 34
Question 10.
2.1 × = 4.3 × 2.1
= _____________
Commutative Property
Associative Property
Identity Property
Answer:
Explanation:
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
2.1 x 4.3 = 4.3 x 2.1
Question 11.
(17 × 2) × 5 = 17 × ( × 5)
= ______________
Commutative Property
Associative Property
Identity Property
Answer:
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
(17 × 2) × 5 = 17 × (2 × 5)
Problem Solving
Question 12.
Elijah and 2 of his friends are each paid $20 per afternoon for stuffing envelopes. If they work 5 afternoons, what is the total amount of their earnings?
Answer:
$300
Explanation:
Elijah and 2 of his friends are each paid $20 per afternoon for stuffing envelopes.
3 x $20 = $60
If they work 5 afternoons.
The total amount of their earnings,
(3 x 20) x 5
$60 x 5 = $300
Associative property is applied.
Question 13.
Replace the in (8.7 × ) × 5 with a number greater than 10 so that the product is easy to find mentally. Explain.
Answer:
20
Explanation:
20 is greater then 10.
So, that the product is easy to find mentally.
8.7 x 20 x 5
8.7 x (20 x 5) = 8.7 x 100 = 870
Question 14.
Mathematical PRACTICE Draw a Conclusion Each juice box contains 6.4 ounces. Each value pack of juice holds 10 juice boxes. If you have fifty value packs, how many ounces of juice do you have?
Answer:
3,200 ounces.
Explanation:
Each juice box contains 6.4 ounces.
Each value pack of juice holds 10 juice boxes.
6.4 x 10 = 64 ounces.
If you have fifty value packs,
50 x 64 = 3200 ounces.
HOT Problems
Question 15.
Mathematical PRACTICE Use Number Sense Which two properties can you use to find (3.4 × 4) × (25 × 1) mentally? Explain. Remember that the parentheses tell you which factors to multiply first.
Answer:
Associative Property and Identity Property.
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
(3.4 × 4) × (25 × 1)
13.6 x 25 = 340
Question 16.
Building on the Essential Question How do the multiplication properties help me to find products mentally?
Answer:
When two numbers are multiplied we get a product.
When the places of numbers are interchanged, their product remains the same,
i.e., 3 × 5 = 5 × 3 = 15.
The different types of properties are,
Commutative Property.
Associative Property.
Identity Property.
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
McGraw Hill My Math Grade 5 Chapter 6 Lesson 8 My Homework Answer Key
Practice
Use properties of multiplication to find each product mentally. Show your steps and identify the properties that you used.
Question 1.
(1.6 × 2) × 5 = ____________
Answer:
16
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
(1.6 × 2) × 5
3.2 x 5 = 16
Question 2.
(27 × 2.5) × 4 = _____________
Answer:
270
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
(27 × 2.5) × 4
67.5 x 4 = 270
Algebra Find each unknown.
Question 3.
× 5.5 = 5.5
= ______________
Answer:
1
Explanation:
x × 5.5 = 5.5
x = 5.5 ÷ 5.5
x = 1
The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.
Question 4.
49 × 201 = × 49
= ______________
Answer:
201
Explanation:
49 x 201 = x × 49
x = (49 x 201) ÷ 49
x = 201
The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.
Problem Solving
Question 5.
For a party, Shandra and James each bought 5 packages of hot dog buns that each cost $1.50. How much did the hot dog buns cost altogether?
Answer:
$7.5
Explanation:
Shandra and James each bought 5 packages of hot dog buns.
Each cost $1.50.
Total cost of hot dog buns, 5 x $1.50 = $7.5
Question 6.
Eva needs to find: (6 × 1.5) × 2. Give the product and name the property she could use.
Answer:
18
Associative Property.
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
(6 × 1.5) × 2
6 x 1.5 = 9
9 x 2 = 18
Question 7.
Write a multiplication sentence to show how the Associative Property can help you solve a problem mentally. Explain.
Answer:
(17 × 2) × 5 = 17 × (2 × 5)
The associative property of multiplication helps us to multiply numbers faster.
Instead of multiplying a list of numbers in the order in which they’re written,
group them differently to multiply in an order according to the convenient.
Explanation:
(17 × 2) × 5 = 17 × (2 × 5)
34 x 5 = 17 x 10
170 = 170
Question 8.
Mathematical PRACTICE Reason Without calculating, is the equation (1.8 × 3) × 2.1 = 3 × (1.8 × 2.1) true or false? Explain your reasoning.
Answer:
True.
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
(1.8 × 3) × 2.1 = 3 × (1.8 × 2.1)
5.4 x 2.1 = 3 x 3.78
11.34 = 11.34
Test Practice
Question 9.
Which multiplication property is shown in the equation below?
3.1 × (2 × 9) = (3.1 × 2) × 9
(A) Identity Property
(B) Commutative Property
(C) Zero Property
(D) Associative Property
Answer:
Option(D)
Explanation:
The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.
3.1 × (2 × 9) = (3.1 × 2) × 9
3.1 x 18 = 6.2 x 9
55.8 = 55.8