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

Answer:

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.

\(\frac{(8 \times 1)}{2}\) = \(\frac{(4+4)}{2}\)

Answer:

\(\frac{(8 \times 1)}{2}\) = \(\frac{(4+4)}{2}\) = 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

Answer:

(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

Answer:

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

Answer:

(7 × 4) + 0 = (14 × 2) + 0 = 28.

Additive identity.

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

Answer:

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

Answer:

(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

Answer:

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.

**Answer yes or no.
**Question 9.

If 6 + 2 = 4 + 4, then does 4 (6 + 2) = 4 (4 + 4)?

Answer:

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 \(\frac{(5 \times 8)}{4}\) = \(\frac{(4 \times 10)}{4}\)?

Answer:

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?

Answer:

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?

Answer:

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?

Answer:

No, If \(\frac{3}{4}\) = \(\frac{12}{16}\), then \(\frac{3}{4}\) – 5 is not equal to \(\frac{12}{16}\) – 5

Explanation:

\(\frac{3}{4}\) = \(\frac{12}{16}\)

\(\frac{3}{4}\) – 5

\(\frac{12}{16}\) – 5 = [12 – (5 × 16)] ÷ 16

= (12 – 80) ÷ 16

= -68 ÷ 16

= –\(\frac{17}{4}\)