Go Math Answer Key

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.5 Solving Equations and Inequalities by Substitution will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.5 Solving Equations and Inequalities by Substitution

Exercises

Question 1.
Sydney has a dozen eggs. He wants to bake a cake, but his mother says she needs 9 of the 12 eggs. What equation could he write to see how many eggs he will be able to use for his cake?
Answer:
Number of eggs he will be able to use for his cake = 3.

Explanation:
Number of eggs Sydney has = 12.
Number of eggs his mom needs = 9.
Number of eggs he will be able to use for his cake = Number of eggs Sydney has – Number of eggs his mom needs
= 12 – 9
= 3.

Question 2.
If Sydney’s cake recipe calls for 4 eggs, will he have enough eggs to bake the cake?
Answer:
No, he doesn’t have enough eggs to bake the cake because number of eggs he will be able to have are less than his cake recipe.

Explanation:
Number of eggs he will be able to use for his cake = 3.
Number of eggs Sydney’s cake recipe calls = 4.

Question 3.
If Sydney decides instead to make brownies that require only 3 eggs, will he have enough eggs to make the brownies?
Answer:
Yes, he can make brownies because he has enough eggs with him.

Explanation:
Number of eggs he will be able to use for his cake = 3.
Number of eggs he needs to make brownies = 3.

Question 4.
Kai has 4 red marbles, 3 blue marbles, 3 green marbles, and 2 yellow marbles. Kai wants to play a game with his brother that requires 6 marbles that are all the same color. Kai’s brother says he can bring 2 marbles of any color. Which color should Kai bring?
Answer:
Red Marbles color his brother should get because it total matches the number of marbles he needs to play with his brother.

Explanation:
Number of red marble Kai has = 4.
Number of blue marble Kai has = 3.
Number of green marble Kai has = 3.
Number of yellow marble Kai has = 2.
Number of marbles he needs to play with his brother = 6.
Number of marbles his brother said will bring of any color = 2.
Marbles color his brother should get:
Number of marbles his brother said will bring of any color + Number of red marble Kai has
= 2 + 4
= 6.
Number of marbles his brother said will bring of any color + Number of blue marble Kai has
= 2 + 3
= 5.
Number of marbles his brother said will bring of any color + Number of green marble Kai has
= 2 + 3
= 5.
Number of marbles his brother said will bring of any color + Number of yellow marble Kai has
= 2 + 2
= 4.

Question 5.
Write an equation that describes the total number of marbles in the game in question 4, using the letter m for the number of marbles Kai should bring.
Answer:
Total number of marbles Kai should bring = m = 2 + 4 = 6.

Explanation:
Number of red marble Kai has = 4.
Number of blue marble Kai has = 3.
Number of green marble Kai has = 3.
Number of yellow marble Kai has = 2.
Total number of marbles Kai should bring = m = 6.
Number of marbles his brother said will bring of any color + Number of red marble Kai has
= 2 + 4
= 6.

Question 6.
If \(\frac{4}{k}\) = 2, which of the following could k be the value of k?
(A) 1
(B) 2
(C) 3
(D) 4
Answer:
If \(\frac{4}{k}\) = 2, then k = 2.
(B) 2

Explanation:
If \(\frac{4}{k}\) = 2
=> 4 = 2 × k
=> 4 ÷ 2 = k
=> 2 = k.

Question 7.
The Ferris wheel costs 4 tickets for each rider. Sarah and Sadie want to ride together. Sarah has only 3 tickets left. Sadie will need to have at least how many tickets for them to ride together?
Answer:
Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:
Cost of tickets the Ferris wheel costs for each rider = 4.
Number of tickets Sarah has left = 3.
Number of tickets needed for two riders = 2 × Cost of tickets the Ferris wheel costs for each rider
= 2 × 4
=8.
Number of tickets Sadie will need to have for them to ride together = Number of tickets needed for two riders – Number of tickets Sarah has left
= 8 – 3
= 5.

Question 8.
Write the total number of tickets Sarah and Sadie need in question 7 as an inequality, using x for the number of tickets Sadie will need.
Answer:
Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:
Let the number of tickets Sadie will need to have for them to ride together be x.
Number of tickets needed for two riders = 8.
Number of tickets Sarah has left = 3.
Number of tickets needed for two riders – Number of tickets Sarah has left = x
= > 8 – 3 = x
=> 5 = x.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.4 Inequalities will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.4 Inequalities

Exercises
Can x be equal to 5?
Question 1.
x – 3 > 4
Answer:
No, x is not equal to 5 in x – 3 > 4.

Explanation:
x – 3 > 4
=> x > 4 + 3.
=> x > 7.
It means x is greater or equal to 7 but not less than to fulfill the equation.

Question 2.
x + 1 > 3 – 2
Answer:
No, x is not equal to 5 in x + 1 > 3 – 2.

Explanation:
x + 1 > 3 – 2
=> x + 1 > 1
=> x > 1 – 1
=> x > 0.
It means x is equal or greater to zero but not less than to fulfill the equation.

Question 3.
4 + x ≥ 9
Answer:
Yes, x is equal to 5 in 4 + x ≥ 9.

Explanation:
4 + x ≥ 9
=> x ≥ 9 – 4
=> x ≥ 5
It means x is equal to 5 and more than yet not less to fulfill the equation.

Question 4.
4x – 1 < 15
Answer:
No, x is not equal to 5 in 4x – 1 < 15.

Explanation:
4x – 1 < 15
=> 4x < 15 + 1
=> 4x < 16.
=> x < 16 ÷ 4
=> x < 4.
It means x is less than 4 yet not more to fulfill the equation.

Question 5.
x + 12 ≤ 35
Answer:
Yes, x can be 5 in x + 12 ≤ 35.

Explanation:
x + 12 ≤ 35
=> x  ≤ 35 – 12
=> x  ≤ 23
It means x is less than 24 yet not more to fulfill the equation.

Show the inequality on a number line.
Question 6.

x > 0

Answer:

Explanation:
x > 0
=> x is greater than 0.
=> x = 1, 2, 3,4,5,6,7and so on….

Question 7.
x ≥ 2

Answer:

Explanation:
x ≥ 2
=> x is equal to 2 and greater.
=> x = 2, 3, 4, 5, so on…

Question 8.
x < 7

Answer:

Explanation:
x < 7
=> x is less than 7.
=> x = 6, 5,4, 3, 2, 1, 0, -1, so on…

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.3 Solving Equations by Multiplication and Division will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.3 Solving Equations by Multiplication and Division

Exercises
SOLVE
Question 1.
3x + 10 = 19
Answer:
x = 3.

Explanation:
3x + 10 = 19
=> 3x = 19 – 10
=> 3x = 9
=> x = 9 ÷ 3
=> x = 3.

Question 2.
4 +7m = 32
Answer:
m = 4.

Explanation:
4 +7m = 32
=> 7m = 32 – 4
=> 7m = 28
=> m = 28 ÷ 7
=> m = 4.

Question 3.
10b+ 8 = 118
Answer:
b = 11.

Explanation:
10b+ 8 = 118
=> 10b = 118 – 8
=> 10 b = 110.
=> b = 110 ÷ 10
=> b = 11.

Question 4.
12 + 2p = 88
Answer:
p = 38.

Explanation:
12 + 2p = 88
=> 2p = 88 – 12
=> 2p = 76.
=> p = 76 ÷ 2
=> p = 38.

Question 5.
\(\frac{y}{7}\) = 49
Answer:
y = 343.

Explanation:
\(\frac{y}{7}\) = 49
=> y = 49 × 7
=> y = 343.

Question 6.
10 + 2u = 14 + u
Answer:
u = 4.

Explanation:
10 + 2u = 14 + u
=> 2u = 14 – 10 + u
=> 2u – u = 4
=> u = 4.

Question 7.
Lynda has twice as many cookies as Alex does. Together they have 12 cookies. Write an equation that can help you find the number of cookies Lynda has.
How many cookies does Lynda have? ____________
How many cookies does Alex have? _____________
Answer:
Number of cookies Lynda has = 8.
Number of cookies Alex has = 4.

Explanation:
Total number of cookies they have = 12.
Lynda has twice as many cookies as Alex does.
=> Let number of cookies Alex be x.
Number of cookies Lynda has = 2 × number of cookies Alex
= 2 × x
=> 2x.
2x + x = 12.
=> 3x = 12
=> x = 12 ÷ 3
=> x = 4.
Number of cookies Lynda has = 2x = 2 × 4 = 8.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.2 Solving Equations by Addition and Subtraction will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.2 Solving Equations by Addition and Subtraction

Exercises
SOLVE
Question 1.
w + 3 = 10
Answer:
w = 7.

Explanation:
w + 3 = 10
=> w = 10 – 3
=> w = 7.

Question 2.
12 = q + 8
Answer:
q = 4.

Explanation:
12 = q + 8
=> 12 – 8 = q
=> 4 = q.

Question 3.
2 + y = 34
Answer:
y = 32.

Explanation:
2 + y = 34
=> y = 34 – 2
=> y = 32.

Question 4.
7 – e = 4
Answer:
e = 3.

Explanation:
7 – e = 4
=> 7 – 4 = e
=> 3 = e.

Question 5.
s + 17 = 50
Answer:
s = 33.

Explanation:
s + 17 = 50
=> s = 50 – 17
=> s = 33.

Question 6.
d – 4 = 11
Answer:
d = 15.

Explanation:
d – 4 = 11
=> d = 11 + 4
=> d = 15.

Question 7.
z + 10 = 25
Answer:
z = 15.

Explanation:
z + 10 = 25
=> z = 25 – 10
=> z = 15.

Question 8.
23 = 5 + r
Answer:
r = 18.

Explanation:
23 = 5 + r
=> 23 – 5 = r
=>18 = r.

Question 9.
m + 45 = 54
Answer:
m = 9.

Explanation:
m + 45 = 54
=> m = 54 – 45
=> m = 9.

Question 10.
15 + f = 33
Answer:
f = 18.

Explanation:
15 + f = 33
=> f = 33 – 15
=> f = 18.

Question 11.
45 – g = 30
Answer:
g = 15.

Explanation:
45 – g = 30
=> 45 – 30 = g
=> 15 = g.

Question 12.
3 – f = 1
Answer:
f = 2.

Explanation:
3 – f = 1
=> 3 – 1 = f
=> 2 = f.

Question 13.
Chris scored 26 points more than Valerie did in their game of one-on-one basketball. The game ended with a total score of 108. Write an equation that can help you find the number of points Valerie scored.
How many points did Valerie score? ______________
How many points did Chris score? ______________
Answer:
Number of points Chris scored = 67.
Number of points Valerie scored = 41.

Explanation:
Chris scored 26 points more than Valerie did in their game of one-on-one basketball.
Total score game ended = 108.
Let the points scored by Valerie  be x.
=> (x + 26) + x = 108.
=> 2x = 108 – 26
=> 2x = 82
=> x = 82 ÷ 2
=> x = 41.
Number of points Chris scored = x + 26
=> 41 + 26
=> 67.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.1 Understanding Variable Expressions will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.1 Understanding Variable Expressions

Exercises
EXPRESS
Write each expression in word form.

Question 1.
\(\frac{b}{6}\)
Answer:
\(\frac{b}{6}\) = b divided by 6.

Explanation:
Word form:
\(\frac{b}{6}\) = b divided by 6.

Question 2.
x + 4
Answer:
Sum of x and 4 = x + 4.

Explanation:
Word form:
x + 4 = Adding x and 4.

Question 3.
2d + 10
Answer:
Word form of 2d + 10 = Sum of 2 times d added to 10.

Explanation:
2d + 10 = Sum of 2 times d added to 10.

Question 4.
5q – 5
Answer:
Word form of 5q – 5 = 5times q subtracted by 5.

Explanation:
5q – 5 = 5times q subtracted by 5.

Question 5.
\(\frac{(z-5)}{33}\)
Answer:
Word form of \(\frac{(z-5)}{33}\) = Difference between z and 5 divided by 33.

Explanation:
\(\frac{(z-5)}{33}\) = Subtraction between z and 5 whole divided by 33.

Question 6.
(3h + 4) 10
Answer:
Word form of (3h + 4) 10 = 3 times h added to 4 multiplied 10 times.

Explanation:
(3h + 4) 10 = Sum of 3 times h multiplied 10 times.

Write each phrase as an algebraic expression.
Question 7.
two times a number less three
Answer:
two times a number less three = 2x – 3.

Explanation:
Algebraic expression:
two times a number less three = 2x – 3.

Question 8.
a number minus twenty-two, times fourteen
Answer:
Algebraic expression of a number minus twenty-two, times fourteen = (x – 22) 14.

Explanation:
a number minus twenty-two, times fourteen = (x – 22) 14.

Question 9.
twenty-two minus three, times a number, plus two
Answer:
Algebraic expression of twenty-two minus three, times a number, plus two = (22 – 3)x + 2.

Explanation:
twenty-two minus three, times a number, plus two = (22 – 3)x + 2.

Question 10.
ten times a number minus three times another number
Answer:
Algebraic expression of ten times a number minus three times another number = 10x – 3y.

Explanation:
ten times a number minus three times another number = 10x – 3y.

Question 11.
nine times a number divided by ten times the same number minus two
Answer:
Algebraic expression of nine times a number divided by ten times the same number minus two = 9x ÷ (10x -2).

Explanation:
nine times a number divided by ten times the same number minus two = 9x ÷ (10x -2).

Question 12.
one-half of a number plus one-fourth of the same number
Answer:
Algebraic expression of one-half of a number plus one-fourth of the same number = (1x ÷ 2) + (1x ÷ 4).

Explanation:
one-half of a number plus one-fourth of the same number = (1x ÷ 2) + (1x ÷ 4).

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 16.5 Factors and Multiples will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 16.5 Factors and Multiples

Exercises
FIND THE LEAST COMMON MULTIPLE
Question 1.
8 and 12 ______________
Answer:
Least common multiply of 8 and 12 = 24.

Explanation:
Multiplies of 8 and 12:
2 × 2 × 2 = 8.
2 × 2 × 3 = 12.
=> LCM = 2 × 2 × 2 × 3 = 8 × 3 = 24.

Question 2.
6 and 10 ______________
Answer:
Least common multiply of 6 and 10 = 60.

Explanation:
Multiplies of 6 and 10:
2 × 3 = 6.
2 × 5 = 10.
=> LCM = 2 × 3 × 5 = 6 × 10 = 60.

Question 3.
2 and 7 ______________
Answer:
Least common multiply of 2 and 7 = 14.

Explanation:
Multiplies of 2 and 7:
2 × 1 = 2.
7 × 1 = 7.
=> LCM = 2 × 7 = 14.

Question 4.
3 and 5 ______________
Answer:
Least common multiply of 3 and 5 = 15.

Explanation:
Multiplies of 3 and 5:
3 × 1 = 3.
5 × 1 = 5.
=> LCM = 3 × 5 = 15.

Question 5.
18 and 36 ______________
Answer:
Least common multiply of 18 and 36 = 36.

Explanation:
Multiplies of 18 and 36:
2 × 9 = 18.
2 × 2 × 9 = 36.
=> LCM = 2 × 9 × 2 = 18 × 2 = 36.

Question 6.
9 and 6 ______________
Answer:
Least common multiply of 9 and 6 = 18.

Explanation:
Multiplies of 9 and 6:
3 × 3 = 9.
2 × 3 = 6.
=> LCM = 3 × 3 × 2 = 18.

Question 7.
24 and 36 ______________
Answer:
Least common multiply of 24 and 36 = 72.

Explanation:
Multiplies of 24 and 36:
2 × 2 × 2 × 3 = 24.
2 × 2 × 3 × 3 = 36.
=> LCM = 2 × 2 × 3 × 3 × 2 = 72.

Question 8.
6 and 32 ______________
Answer:
Least common multiply of 6 and 32 = 96.

Explanation:
Common multiplies of 6 and 32:
2 × 3 = 6.
2 × 2 × 2 × 2 × 2 = 32.
=> LCM = 2 × 3 × 2 × 2 × 2 × 2 = 96.

FIND THE GREATEST COMMON FACTOR
Question 9.
8 and 24 ______________
Answer:
Greatest common factor of 8 and 24 = 8.

Explanation:
Factors of 8 and 24:
8: 1,2, 4, 8.
24: 1,2,3,4,6,8,12,
=> GCF = 8.

Question 10.
12 and 24 ______________
Answer:
Greatest common factor of 12 and 24 = 12.

Explanation:
Factors of 12 and 24:
12: 1,2,3,4,6,12.
24:1,2,3,4,6,8,12,24.
=> GCF = 12.

Question 11.
12 and 30 ______________
Answer:
Greatest common factor of 12 and 30 = 6.

Explanation:
Factors of 12 and 30:
12: 1,2,3,4,6,12.
30: 1,2,3,5,6,10,15,30.
=> GCF = 6.

Question 12.
9 and 12 ______________
Answer:
Greatest common factor of 9 and 12 = 3.

Explanation:
Factors of 9 and 12:
9: 1,3,9.
12: 1,2,3,4,6,12.
=> GCF = 3.

Question 13.
4 and 10 ______________
Answer:
Greatest common factor of 4 and 10 = 2.

Explanation:
Factors of 4 and 10:
4: 1,2,4.
10: 1,2,5,10.
=> GCF = 2.

Question 14.
16 and 80 ______________
Answer:
Greatest common factor of 16 and 80 = 8.

Explanation:
Factors of 16 and 80:
16: 1, 2,4,8.
80: 1,2,4,5,8,10,16,20,40.
=> GCF = 8.

Question 15.
8 and 60 ______________
Answer:
Greatest common factor of 8 and 60 = 4.

Explanation:
Factors of 8 and 60:
8: 1,2,4,8.
60: 1,2,3,4,5,12,15,20,30.
=> GCF = 4.

Question 16.
6 and 40 ______________
Answer:
Greatest common factor of 6 and 40 = 2.

Explanation:
Factors of 6 and 40:
6: 1,2,3,6.
40: 1,2,4,5,8,10,20,40.
=> GCF = 2.

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
= –\(\frac{17}{4}\)

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.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 16.2 Commutative and Associative Properties will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 16.2 Commutative and Associative Properties

Exercises

IDENTIFY THE PROPERTY
Question 1.
3 × 4 × 2 = 2 × 4 × 3
Answer:
3 × 4 × 2 = 2 × 4 × 3 = 24.
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.
3 × 4 × 2 = 2 × 4 × 3
= 8 × 3
= 24.

Question 2.
1 + 9 + 22 = 22 + 9 + 1
Answer:
1 + 9 + 22 = 22 + 9 + 1 = 32.
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.
1 + 9 + 22 = 22 + 9 + 1
= 31 + 1
= 32.

Question 3.
2 + 3 + 3 + 2 = 2 + (3 + 3) + 2
Answer:
2 + 3 + 3 + 2 = 2 + (3 + 3) + 2 = 10.
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 + 3 + 2 = 2 + (3 + 3) + 2
= 2 + 6 + 2
= 8 + 2
= 10.

Question 4.
4 × 2 + 2 × 3 = 2 × 4 + 3 × 2
Answer:
4 × 2 + 2 × 3 = 2 × 4 + 3 × 2 = 14.
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.
4 × 2 + 2 × 3 = 2 × 4 + 3 × 2
= 8 + 6
= 14.

Question 5.
7 × 2 × 7 = 7 × (2 × 7)
Answer:
7 × 2 × 7 = 7 × (2 × 7) = 98.
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 × 2 × 7 = 7 × (2 × 7)
= 7 × 14
= 98.

Question 6.
7 × 7 × 8 × 7 = 8 × 7 × 7 × 7
Answer:
7 × 7 × 8 × 7 = 8 × 7 × 7 × 7 = 2,744.
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 × 7 × 8 × 7 = 8 × 7 × 7 × 7
= 56 × 49
= 2,744.

Question 7.
(9 + 7) + 6 = 9 + (7 + 6)
Answer:
(9 + 7) + 6 = 9 + (7 + 6) = 22.
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.
(9 + 7) + 6 = 9 + (7 + 6)
= 9 + 13
= 22.

Question 8.
4 × 5 × 5 × 4 = 5 × 5 × 4 × 4
Answer:
4 × 5 × 5 × 4 = 5 × 5 × 4 × 4 = 400.
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.
4 × 5 × 5 × 4 = 5 × 5 × 4 × 4
= 25 × 16
= 400.

Question 9.
2 + 6 + 8 + 3 = 6 + 3 + 8 + 2
Answer:
2 + 6 + 8 + 3 = 6 + 3 + 8 + 2 = 19.
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.
2 + 6 + 8 + 3 = 6 + 3 + 8 + 2
= 9 + 8 + 2
= 17 + 2
= 19.

Question 10.
(6 × 4) × 2 = 6 × (4 × 2)
Answer:
(6 × 4) × 2 = 6 × (4 × 2) = 48.
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.
(6 × 4) × 2 = 6 × (4 × 2)
= 6 × 8
= 48.

Question 11.
12 + 13 + 13 + 12 = 12 + 12 + 13 + 13
Answer:
12 + 13 + 13 + 12 = 12 + 12 + 13 + 13 = 50.
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.
12 + 13 + 13 + 12 = 12 + 12 + 13 + 13
= 24 + 13 + 13
= 37 + 13
= 50.

Question 12.
7 × 8 + 8 × 7 = 8 × 7 + 8 × 7
Answer:
7 × 8 + 8 × 7 = 8 × 7 + 8 × 7 = 112.
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 × 8 + 8 × 7 = 8 × 7 + 8 × 7
= 56 + 56
= 112.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 16.1 Order of Operations will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 16.1 Order of Operations

Exercises
SOLVE
Question 1.
5 – (4 – 3) + 5 × 4
Answer:
5 – (4 – 3) + 5 × 4 = 24.

Explanation:
5 – (4 – 3) + 5 × 4
= 5 – (4 – 3) + 20
= 25 – (4 – 3)
= 25 – 1
= 24.

Question 2.
(3 × 2)² × 2 – 2 + 4
Answer:
(3 × 2)² × 2 – 2 + 4 = 74.

Explanation:
(3 × 2)² × 2 – 2 + 4
= 36 × 2 – 2 + 4
= 72 – 2 + 4
= 76 – 2
= 74.

Question 3.
(3 + 2)² × 4 – 3 + \(\frac{4}{2}\)
Answer:
(3 + 2)² × 4 – 3 + \(\frac{4}{2}\) = 99.

Explanation:
(3 + 2)² × 4 – 3 + \(\frac{4}{2}\)
= (5 × 5) × 4 – 3 + \(\frac{4}{2}\)
= 25 × 4 – 3 + \(\frac{4}{2}\)
= 100 – 3 + \(\frac{4}{2}\)
= 100 – 3 + 2
= 102 – 3
= 99.

Question 4.
5 – 7 + 4 × 2 – 3
Answer:
5 – 7 + 4 × 2 – 3 = 3.

Explanation:
5 – 7 + 4 × 2 – 3
= 5 – 7 + 8 – 3
= 13 – 7 – 3
= 6 – 3
= 3.

Question 5.
55 – 2 × \(\frac{3}{2}\) – 10²
Answer:
55 – 2 × \(\frac{3}{2}\) – 10^{2 = 152.}

Explanation:
55 – 2 × \(\frac{3}{2}\) – 10²
= 55 – 2 × 1.5 – 100
= 55 – 3 – 100
= 155 – 3
= 152.

Question 6.
(2 + 3 + 4)^3-1
Answer:
(2 + 3 + 4)^3-1 = 81.

Explanation:
(2 + 3 + 4)^3-1
= (5+ 4)^3-1
= (9)2
= 9 × 9
= 81.

Question 7.
(2 – 2)² + (4 – 2)²
Answer:
(2 – 2)² + (4 – 2)²  = 4.

Explanation:
(2 – 2)² + (4 – 2)²
= (0)² + (4 – 2)²
= 0 + (2)²
= 2 × 2
= 4.

Question 8.
(3 – 4) + 3² × 3 + 2
Answer:
(3 – 4) + 3² × 3 + 2 = 28.

Explanation:
(3 – 4) + 3² × 3 + 2
= (3 – 4) + 9 × 3 + 2
= (3 – 4) + 27 + 2
= (3 – 4) + 29
= -1 + 29
= 28.

Question 9.
4 × (11 – 7) – (44 + 28)
Answer:
4 × (11 – 7) – (44 + 28) = 44.

Explanation:
4 × (11 – 7) – (44 + 28)
= 4 × (11 – 7) – 72
= 4 × 4 – 72
= 28 – 72
= 44.