# McGraw Hill Math Grade 6 Lesson 16.4 Answer Key Zero Property, Equality Properties

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 16.4 Zero Property, Equality Properties will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 16.4 Zero Property, Equality Properties

Exercises
Identify the property.
Question 1.
5 × 0 = (4 + 1) × 0
5 × 0 = (4 + 1) × 0
Associative property.

Explanation:
The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.
5 × 0 = (4 + 1) × 0

Question 2.
$$\frac{(8 \times 1)}{2}$$ = $$\frac{(4+4)}{2}$$
$$\frac{(8 \times 1)}{2}$$ = $$\frac{(4+4)}{2}$$ = 4.
Commutative property.

Explanation:
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
$$\frac{(8 \times 1)}{2}$$ = $$\frac{(4+4)}{2}$$
= 4.

Question 3.
(2 + 3) × 0 = 0
(2 + 3) × 0 = 0.
Multiplication property.

Explanation:
The multiplication property of zero is that number multiplied by zero gives the product zero.
(2 + 3) × 0 = 0.

Question 4.
7 (0 + 0) = 0
7 (0 + 0) = 0.
Multiplication property.

Explanation:
The multiplication property of zero is that number multiplied by zero gives the product zero.
7 (0 + 0) = 0.

Question 5.
(7 × 4) + 0 = (14 × 2) + 0
(7 × 4) + 0 = (14 × 2) + 0 = 28.

Explanation:
Additive identity is the value when added to a number, results in the original number. When we add 0 to any real number, we get the same real number.
(7 × 4) + 0 = (14 × 2) + 0
= 28 + 0
= 28.

Question 6.
123.45 × 0 = 0
123.45 × 0 = 0.
Multiplication property.

Explanation:
The multiplication property of zero is that number multiplied by zero gives the product zero.
123.45 × 0 = 0.

Question 7.
(12 × 6) – 5 = (9 × 8) – 5
(12 × 6) – 5 = (9 × 8) – 5 = 67.
Associative property.

Explanation:
The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.
(12 × 6) – 5 = (9 × 8) – 5
= 72 – 5
= 67.

Question 8.
15 × 4 = (3 × 5) × 4
15 × 4 = (3 × 5) × 4 = 60.
Associative property.

Explanation:
The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.
15 × 4 = (3 × 5) × 4
= 15 × 4
= 60.

Question 9.
If 6 + 2 = 4 + 4, then does 4 (6 + 2) = 4 (4 + 4)?
Yes, If 6 + 2 = 4 + 4 then  4 (6 + 2) = 4 (4 + 4).

Explanation:
6 + 2 = 4 + 4.
4 (6 + 2)
= 4 × 8
= 32.
4 (4 + 4)
= 4 × 8
= 32.

Question 10.
If 5 × 8 = 4 × 10, then does $$\frac{(5 \times 8)}{4}$$ = $$\frac{(4 \times 10)}{4}$$?
Yes, 5 × 8 = 4 × 10 then $$\frac{(5 \times 8)}{4}$$ = $$\frac{(4 \times 10)}{4}$$.

Explanation:
5 × 8 = 4 × 10.
$$\frac{(5 \times 8)}{4}$$ = $$\frac{40}{4}$$ = 10.
$$\frac{(4 \times 10)}{4}$$ = $$\frac{40}{4}$$ = 10.

Question 11.
If 2 × 12 = 3 × 8, then does 4 – 2 × 12 = 3 × 8 – 4?
No, If 2 × 12 = 3 × 8, then 4 – 2 × 12 is not equal to  3 × 8 – 4.

Explanation:
2 × 12 = 3 × 8.
4 – 2 × 12
= 4 – 24
= -20.
3 × 8 – 4
= 24 – 4
= 20.

Question 12.
If 10 × 8 = 4 × 20, then does 10 × 8 – 2.53 = 4 × 20 – 2.53?
Yes, If 10 × 8 = 4 × 20, then 10 × 8 – 2.53 = 4 × 20 – 2.53.

Explanation:
10 × 8 = 4 × 20.
10 × 8 – 2.53
= 80 – 2.53
= 77.47.
4 × 20 – 2.53
= 80 – 2.53
= 77.47.

Question 13.
If $$\frac{3}{4}$$ = $$\frac{12}{16}$$, then does $$\frac{3}{4}$$ – 5 = $$\frac{12}{16}$$ – 5?
No, If $$\frac{3}{4}$$ = $$\frac{12}{16}$$, then $$\frac{3}{4}$$ – 5 is not equal to  $$\frac{12}{16}$$ – 5
$$\frac{3}{4}$$ = $$\frac{12}{16}$$
$$\frac{3}{4}$$ – 5
$$\frac{12}{16}$$ – 5 = [12 – (5 × 16)] ÷ 16
= –$$\frac{17}{4}$$