Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 16.3 Distributive Property and Identity will engage students and is a great way of informal assessment.
McGraw-Hill Math Grade 6 Answer Key Lesson 16.3 Distributive Property and Identity
Exercises
IDENTIFY THE PROPERTY
Question 1.
0 + 5 = 5
Answer:
0 + 5 = 5.
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.
0 + 5 = 5.
Question 2.
2(3 + 2 + 3) = 2 × 3 + 2 × 2 + 2 × 3
Answer:
2(3 + 2 + 3) = 2 × 3 + 2 × 2 + 2 × 3 = 16.
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.
2(3 + 2 + 3) = 2 × 3 + 2 × 2 + 2 × 3
= 6 + 4 + 6
= 10 + 6
= 16.
Question 3.
20 × 1 = 20
Answer:
20 × 1 = 20.
Identity property of Multiplication..
Explanation:
The identity property of 1 says that any number multiplied by 1 keeps its identity.
20 × 1 = 20.
Question 4.
2 × 3 + 2 × 7 = 2(3 + 7)
Answer:
2 × 3 + 2 × 7 = 2(3 + 7) = 20.
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.
2 × 3 + 2 × 7 = 2(3 + 7)
= 6 + 14
= 20.
Question 5.
\(\frac{(7+6)}{4}\) = \(\frac{7}{4}\) + \(\frac{6}{4}\)
Answer:
\(\frac{(7+6)}{4}\) = \(\frac{7}{4}\) + \(\frac{6}{4}\) = 3.25.
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.
\(\frac{(7+6)}{4}\) = \(\frac{7}{4}\) + \(\frac{6}{4}\)
= 1.75 + 1.5
= 3.25.
Question 6.
7(23 – 14) = 7 × 23 – 7 × 14
Answer:
7(23 – 14) = 7 × 23 – 7 × 14 = 63.
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.
7(23 – 14) = 7 × 23 – 7 × 14
= 161 – 98
= 63.
USE THE DISTRIBUTIVE PROPERTY
Express each of the following as a multiple of the sum of two whole numbers with no common factors. For example, 24 + 30 = 6 (4 + 5)
Question 7.
12 + 14
Answer:
12 + 14 = 2(6 + 7)
Explanation:
12 + 14 = 2(6 + 7)
= 26.
Question 8.
15 + 25
Answer:
15 + 25 = 5(3 + 5)
Explanation:
15 + 25 = 5(3 + 5)
= 40.
Question 9.
18 + 9
Answer:
18 + 9 = 9(2 + 1)
Explanation:
18 + 9 = 9(2 + 1)
= 27.
Question 10.
27 + 12
Answer:
27 + 12 = 3(9 + 4)
Explanation:
27 + 12 = 3(9 + 4)
= 39.