Spectrum Math Grade 6 Chapter 5 Lesson 6 Answer Key Solving 1-Step Equations: Multiplication & Division

Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.6 Solving 1-Step Equations: Multiplication & Division and get the proper assistance needed during your homework.

Spectrum Math Grade 6 Chapter 5 Lesson 5.6 Solving 1-Step Equations: Multiplication & Division Answers Key

Division Property of Equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal.
3y = 21
To undo multiplication by 3, divide by 3.
\(\frac{3 y}{3}\) = \(\frac{21}{3}\)
y = 7

Multiplication Property of Equality
If you multiply each side of an equation by the same number, the two sides remain equal.
\(\frac{a}{4}\) = 4
To undo division by 4, multiply by 4.
\(\frac{a}{4}\) × \(\frac{4}{1}\) = 5 × 4
a = 20

Write the operation that would undo the operation in each equation.

Question 1.
a. 5 × n = 40 _____
Answer:
Given 5n = 40
To Evaluate the given n value ,Try to undo multiplication by 5, divide by 5.
\(\frac{5n}{5}\) = \(\frac{40}{5}\)
n = 8
Therefore the value of n is 8.

b. \(\frac{y}{5}\) = 80 _____
Answer:
Given y / 5 = 80
\(\frac{y}{5}\) = 80
To Evaluate the given n value ,Try to undo division by 5, multiply by 5.
\(\frac{y}{5}\) × \(\frac{5}{1}\) = 80 × 5
y = 400
Therefore the value of y is 400.

Question 2.
a. \(\frac{x}{2}\) = 8 _______
Answer:
Given x / 2 = 8
\(\frac{x}{2}\) = 8
To Evaluate the given n value ,Try to perform the undo division by 2, multiply by 2.
\(\frac{x}{2}\) × \(\frac{2}{1}\) = 8 × 2
x = 16
Therefore the value of x is 16

b. a × 7 = 42 ____
Answer:
To Evaluate the given a value ,Try to perform the undo multiplication by 7, divide by 7.
\(\frac{a7}{7}\) = \(\frac{42}{7}\)
a = 6
Therefore the value of a is 6.

Solve each equation.

Question 3.
a. 3 × a = 9 ____
Answer:
To Evaluate the given a value ,Try to perform the undo multiplication by 3, divide by 3.
\(\frac{3a}{3}\) = \(\frac{9}{3}\)
a = 3
Therefore the value of a is 3.

b. \(\frac{x}{5}\) = 5 ________
Answer:
\(\frac{x}{5}\) = 5
To Evaluate the given x value ,Try to perform the undo division by 5, multiply by 5.
\(\frac{x}{5}\) × \(\frac{5}{1}\) = 5 × 5
x = 25
Therefore the value of x is 25

c. \(\frac{n}{4}\) = 3 _____
Answer:
\(\frac{n}{4}\) = 3
To Evaluate the given n value ,Try to perform the undo division by 4, multiply by 4.
\(\frac{n}{4}\) × \(\frac{4}{1}\) = 3 × 4
n = 12
Therefore the value of n is 12

Question 4.
a. \(\frac{x}{3}\) = 3 _____
Answer:
\(\frac{x}{3}\) = 3
To Evaluate the given x value, Try to perform the undo division by 3, and multiply by 3.
\(\frac{x}{3}\) × \(\frac{3}{1}\) = 3 × 3
x = 9
Therefore the value of x is 9.

b. n × 4 = 4 ____
Answer:
To Evaluate the given n value, Try to perform the undo multiplication by 4, and divide by 4.
\(\frac{n4}{4}\) = \(\frac{4}{4}\)
n = 1
Therefore the value of n is 1.

c. 3 × y = 24 ____
Answer:
To Evaluate the given y value, Try to perform the undo multiplication by 3, and divide by 3.
\(\frac{3.y}{3}\) = \(\frac{24}{3}\)
y = 8
Therefore the value of y is 8.

Question 5.
a. 5 × b = 10 ____
Answer:
To Evaluate the given b value, Try to perform the undo multiplication by 5, and divide by 5.
\(\frac{5.b}{5}\) = \(\frac{10}{5}\)
b = 2
Therefore the value of b is 2.

b. \(\frac{b}{8}\) = 2 _____
Answer:
\(\frac{b}{8}\) = 2
To Evaluate the given b value, Try to perform the undo division by 8, and multiply by 8.
\(\frac{b}{8}\) × \(\frac{8}{1}\) = 2 × 8
b = 16
Therefore the value of b is 16.

c. 4 × a = 20 ____
Answer:
To Evaluate the given a value ,Try to perform the undo multiplication by 4, divide by 4.
\(\frac{4.a}{4}\) = \(\frac{20}{4}\)
a = 5
Therefore the value of a is 5.

Question 6.
a. \(\frac{m}{3}\) = 1 _____
Answer:
\(\frac{m}{3}\) = 1
To Evaluate the given m value ,Try to perform the undo division by 3, multiply by 3.
\(\frac{m}{3}\) × \(\frac{3}{1}\) = 1 × 3
m = 3
Therefore the value of m is 3.

b. 8 × n = 20 ____
Answer:
To Evaluate the given n value ,Try to perform the undo multiplication by 8, divide by 8.
\(\frac{8.n}{8}\) = \(\frac{20}{8}\)
n = 2.5
Therefore the value of n is 2.5

c. \(\frac{x}{5}\) = 2 _____
Answer:
\(\frac{x}{5}\) = 2
To Evaluate the given x value ,Try to perform the undo division by 5, multiply by 5.
\(\frac{x}{5}\) × \(\frac{5}{1}\) = 2 × 5
x = 10
Therefore the value of x is 3.

Question 7.
a. 4 × n = 1 ____
Answer:
To Evaluate the given n value, Try to perform the undo multiplication by 4, and divide by 4.
\(\frac{4.n}{4}\) = \(\frac{1}{4}\)
n = \(\frac{1}{4}\)
Therefore the value of n is \(\frac{1}{4}\)

b. \(\frac{n}{4}\) = 5 _____
Answer:
\(\frac{n}{4}\) = 5
To Evaluate the given n value, Try to perform the undo division by 4, and multiply by 4.
\(\frac{n}{4}\) × \(\frac{4}{1}\) = 5 × 4
n = 20
Therefore the value of n is 20.

c. \(\frac{b}{3}\) = 27 _____
Answer:
\(\frac{b}{3}\) = 27
To Evaluate the given b value ,Try to perform the undo division by 3, multiply by 3.
\(\frac{b}{3}\) × \(\frac{3}{1}\) = 27 × 3
b = 81
Therefore the value of b is 81.

Question 8.
a. n × 15 = 30 ____
Answer:
Given n x 15  = 30
To Evaluate the given n value ,Try to undo multiplication by 15, divide by 15.
\(\frac{15.n}{15}\) = \(\frac{30}{15}\)
n = 2
Therefore the value of n is 2.

b. \(\frac{n}{4}\) = 10 _____
Answer:
Given n / 4 = 10
\(\frac{n}{4}\) = 10
To Evaluate the given n value ,Try to undo division by 4, multiply by 4.
\(\frac{n}{4}\) × \(\frac{4}{1}\) = 10 × 4
n = 40
Therefore the value of n is 40.

c. n × 12 = 36 ____
Answer:
Given n x 12 = 36
To Evaluate the given n value ,Try to undo multiplication by 12, divide by 12.
\(\frac{12.n}{12}\) = \(\frac{36}{12}\)
n = 3
Therefore the value of n is 3.

Question 9.
a. \(\frac{n}{18}\) = 2 _____
Answer:
Given n / 18 = 2
\(\frac{n}{18}\) = 2
To Evaluate the given n value ,Try to undo division by 4, multiply by 4.
\(\frac{n}{18}\) × \(\frac{18}{1}\) = 2 × 18
n = 36
Therefore the value of n is 36.

b. n × 3 = 18 ____
Answer:
Given n x 3 = 18
To Evaluate the given n value ,Try to undo multiplication by 3, divide by 3.
\(\frac{3.n}{3}\) = \(\frac{18}{3}\)
n = 6
Therefore the value of n is 6.

c. n × 2 = 20 ____
Answer:
Given n x 2 = 20
To Evaluate the given n value ,Try to undo multiplication by 2, divide by 2.
\(\frac{2.n}{2}\) = \(\frac{20}{2}\)
n = 10
Therefore the value of n is 10.

Question 10.
a. \(\frac{n}{2}\) = 20 _____
Answer:
Given n / 2 = 20
\(\frac{n}{2}\) = 20
To Evaluate the given n value ,Try to undo division by 2, multiply by 2.
\(\frac{n}{2}\) × \(\frac{2}{1}\) = 20 x 2
n = 40
Therefore the value of n is 40.

b. \(\frac{n}{16}\) = 1 _____
Answer:
Given n / 16 = 1
\(\frac{n}{16}\) = 1
To Evaluate the given n value ,Try to undo division by 16, multiply by 16.
\(\frac{n}{16}\) × \(\frac{16}{1}\) = 1 x 16
n = 16
Therefore the value of n is 16.

c. n × 3 = 3 ____
Answer:
Given n x 3 = 3
To Evaluate the given n value ,Try to undo multiplication by 3, divide by 3.
\(\frac{3.n}{3}\) = \(\frac{3}{3}\)
n = 1
Therefore the value of n is 1.

Question 11.
a. 5 × b = 30 ____
Answer:
Given 5 x b = 30
To Evaluate the given b value ,Try to undo multiplication by 5, divide by 5.
\(\frac{5.b}{5}\) = \(\frac{30}{5}\)
b = 6
Therefore the value of b is 6.

b. \(\frac{b}{5}\) = 30 _____
Answer:
Given b / 5 = 30
\(\frac{b}{5}\) = 30
To Evaluate the given b value ,Try to undo division by 5, multiply by 5.
\(\frac{b}{5}\) × \(\frac{ 5}{1}\) = 30 x 5
b = 150
Therefore the value of b is 150.

c. n × 8 = 24 ____
Answer:
Given n x 8 = 24
To Evaluate the given n value ,Try to undo multiplication by 8, divide by 8.
\(\frac{8.n}{8}\) = \(\frac{24}{8}\)
n = 3
Therefore the value of n is 3.

Question 12.
a. \(\frac{n}{4}\) = 1 _____
Answer:
Given n / 4 = 1
\(\frac{n}{4}\) = 1
To Evaluate the given n value ,Try to undo division by 4, multiply by 4.
\(\frac{n}{4}\) × \(\frac{4}{1}\) = 1 × 4
n = 4
Therefore the value of n is 4.

b. \(\frac{b}{2}\) = 2 _____
Answer:
Given b / 2 = 2
\(\frac{b}{2}\) = 2
To Evaluate the given b value ,Try to undo division by 2, multiply by 2.
\(\frac{b}{2}\) × \(\frac{2}{1}\) = 2 × 2
b = 4
Therefore the value of b is 4.

c. n × 6 = 48 ____
Answer:
Given n x 6 = 48
To Evaluate the given n value ,Try to undo multiplication by 6, divide by 6.
\(\frac{6.n}{ 6}\) = \(\frac{48}{6}\)
n = 8
Therefore the value of n is 8.

Solve each equation.

Question 1.
a. 2 × d = 18 ____
Answer:
Given 2 x d = 18
To Evaluate the given d value ,Try to undo multiplication by 2, divide by 2.
\(\frac{2d}{2}\) = \(\frac{18}{2}\)
d = 9
Therefore the value of d is 9.

b. a × 4 = 20 ____
Answer:
Given a x 4 = 20
To Evaluate the given a value ,Try to undo multiplication by 4, divide by 4.
\(\frac{a.4}{4}\) = \(\frac{20}{4}\)
a = 5
Therefore the value of a is 5.

c. 5 × n = 30 ____
Answer:
Given 5 x n = 30
To Evaluate the given n value ,Try to undo multiplication by 5, divide by 5.
\(\frac{5n}{5}\) = \(\frac{30}{5}\)
n = 6
Therefore the value of n is 6.

Question 2.
a. y ÷ 3 = 4 ____
Answer:
Given y / 3 = 4
\(\frac{y}{3}\) = 4
To Evaluate the given y value ,Try to undo division by 3, multiply by 3.
\(\frac{y}{3}\) × \(\frac{3}{1}\) = 4 × 3
y = 12
Therefore the value of y is 12.

b. t ÷ 9 = 3 ____
Answer:
Given t / 9 = 3
\(\frac{t}{9}\) = 3
To Evaluate the given t value ,Try to undo division by 9, multiply by 9.
\(\frac{t}{9}\) × \(\frac{9}{1}\) = 9 × 3
t = 27
Therefore the value of t is 27.

c. \(\frac{a}{5}\) = 3 ____
Answer:
Given a / 5 = 3
\(\frac{a}{5}\) = 3
To Evaluate the given a value ,Try to undo division by 5, multiply by 5.
\(\frac{a}{5}\) × \(\frac{5}{1}\) = 3 × 5
a = 15
Therefore the value of a is 15.

Question 3.
a. 8 × s = 64 ____
Answer:
Given 8 x s = 64
To Evaluate the given s value ,Try to undo multiplication by 8, divide by 8.
\(\frac{8.s}{8}\) = \(\frac{64}{8}\)
s = 8
Therefore the value of s is 8.

b. p × 16 = 16 ____
Answer:
Given p x 16 = 16
To Evaluate the given p value ,Try to undo multiplication by 16, divide by 16.
\(\frac{p.16}{16}\) = \(\frac{16}{16}\)
p = 1
Therefore the value of p is 1.

c. 7 × r = 42 ____
Answer:
Given 7 x r = 42
To Evaluate the given r value ,Try to undo multiplication by 7, divide by 7.
\(\frac{7.r}{7}\) = \(\frac{42}{7}\)
r = 6
Therefore the value of r is 6.

Question 4.
a. \(\frac{n}{5}\) = 10 ____
Answer:
Given n / 5 = 10
\(\frac{n}{5}\) = 10
To Evaluate the given n value ,Try to undo division by 5, multiply by 5.
\(\frac{n}{5}\) × \(\frac{5}{1}\) = 10 × 5
n = 50
Therefore the value of n is 50.

b. n ÷ 3 = 12 _____
Answer:
Given n / 3 = 12
\(\frac{n}{3}\) = 12
To Evaluate the given n value ,Try to undo division by 3, multiply by 3.
\(\frac{n}{3}\) × \(\frac{3}{1}\) = 12 × 3
n = 36
Therefore the value of n is 36.

c. a ÷ 8 = 6 _____
Answer:
Given a / 8 = 6
\(\frac{a}{8}\) = 6
To Evaluate the given a value ,Try to undo division by 8, multiply by 8.
\(\frac{a}{8}\) × \(\frac{8}{1}\) = 6 × 8
n = 48
Therefore the value of n is 48.

Question 5.
a. 25 = 5 × d ____
Answer:
Given d x 5 = 25
To Evaluate the given d value ,Try to undo multiplication by 5, divide by 5.
\(\frac{5.d}{5}\) = \(\frac{25}{5}\)
d = 5
Therefore the value of d is 5.

b. 0 = a × 57 ____
Answer:
Given 0 = a x 57
To evaluate the given value, try to undo multiplication by 57, divide by 57
\(\frac{a.57}{57}\) = \(\frac{0}{57}\)
a = 0

c. 32 = b × 2 ____
Answer:
Given b x 2 = 32
To Evaluate the given b value ,Try to undo multiplication by 2, divide by 2.
\(\frac{2.b}{2}\) = \(\frac{32}{2}\)
b = 16
Therefore the value of b is 16.

Question 6.
a. 19 = \(\frac{x}{1}\) _______
Answer:
Given x / 1 = 19
\(\frac{x}{1}\) = 19
To Evaluate the given x value ,Try to undo division by 1, multiply by 1.
\(\frac{x}{1}\) × \(\frac{19}{1}\) = 19 × 1
x = 19
Therefore the value of x is 19.

b. 7 = b ÷ 4 _____
Answer:
Given b / 4 = 7
\(\frac{b}{4}\) = 7
To Evaluate the given b value ,Try to undo division by 4, multiply by 4.
\(\frac{b}{4}\) × \(\frac{4}{1}\) = 7 × 4
b = 28
Therefore the value of b is 28.

c. 9 = \(\frac{c}{7}\) _______
Answer:
Given c / 7 = 9
\(\frac{c}{7}\) = 9
To Evaluate the given c value ,Try to undo division by 7, multiply by 7.
\(\frac{c}{7}\) × \(\frac{7}{1}\) = 9 × 7
c = 63
Therefore the value of c is 63.

Write an equation for each problem. Then, solve the equation.

Question 7.
Taryn practiced piano the same amount of time every day for 6 days. If she practiced a total of 12 hours, how many hours did she practice each day?
____________ She practiced ________ hours each day.
Answer:
Number of hours Taryn practiced piano = 12 hours
From the given data Taryn practiced the same amount of time for 6 days i.e. 12/6 = 2 hours
Therefore, Taryn practiced 2 hours for 6 days.

Question 8.
A group of friends decided to equally share a package of trading cards. If there were 48 cards in the package and each person received 12, how many friends were in the group?
________ There were _____ friends in the group.
Answer:
Number of cords in the package = 48
Number of cords received by each persons = 12
Number of friends present in the Group =
?
Equation : 48 ÷ 12 = 4
Therefore four friends are present in the Group.

Question 9.
Twenty-five cars can take the ferry across the river at one time. If 150 cars took the ferry, and it was full each time, how many times did the ferry cross the river?
_____ The ferry crossed the river ____ times.
Answer:
Twenty-five cars can take the ferry across the river at one time
Number of cars that took the ferry = 150
How many times the ferry crosses the river = number of cars that took the ferry/ number of cars that take to cross ferry at 1 time
= 150/25
= 6
Therefore, the ferry crossed 6 times the river.

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