Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Posttest and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 5 Posttest Answers Key
Check What You Learned
Expressions and Equations
Write each power as a product of factors.
Question 1.
a. 35 _____
Answer:
Given value is 35
It can be written as a product of 3 x 3 x 3 x 3 x 3
= 243
Therefore the value of 35 is 243.
b. 122 _____
Answer:
Given value is 122
It can be written as a product of 12 x 12
=144
Therefore the value of 122 is 144.
c. 64 _____
Answer:
Given value is 64
It can be written as a product of 6 x 6 x 6 x 6
=1296
Therefore the value of 64 is 1296.
Question 2.
a. 54 _____
Answer:
Given value is 54
It can be written as a product of 5 x 5 x 5 x 5
= 625
Therefore the value of 54 is 625.
b. 73 _____
Answer:
Given value is 73
It can be written as a product of 7 x 7 x 7
= 343
Therefore the value of 73 is 343.
c. 85 _____
Answer:
Given value is 85
It can be written as a product of 8 x 8 x 8 x 8 x 8
= 32768
Therefore the value of 85 is 32768.
Question 3.
a. 45 _____
Answer:
Given value is 45
It can be written as a product of 4 x 4 x 4 x 4 x 4
= 1024
Therefore the value of 45 is 1024.
b. 29 _____
Answer:
Given value is 29
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 512
Therefore the value of 29 is 512.
c. 93 _____
Answer:
Given value is 93
It can be written as a product of 9 x 9 x 9
= 729
Therefore the value of 93 is 729 .
Use exponents to rewrite each expression.
Question 4.
a. 2 × 2 × 2 × 2 × 2 = ____
Answer:
Given 2 × 2 × 2 × 2 × 2
It can be written as 25
= 32
Therefore the value of 2 × 2 × 2 × 2 × 2 is 25 which is equal to 32.
b. 8 × 8 × 8 =_____
Answer:
Given 8 × 8 × 8
It can be written as 83
= 512
Therefore the value of 8 × 8 × 8 is 83 which is equal to 512.
c. 25 × 25 = ____
Answer:
Given 25 x 25
It can be written as 252
= 625
Therefore the value of 25 x 25 is 252 which is equal to 625.
Question 5.
a. 4 × 4 × 4 = ____
Answer:
Given 4 × 4 × 4
It can be written as 43
= 64
Therefore the value of 4 × 4 × 4 is 43 which is equal to 64.
b. 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = _____
Answer:
Given 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5
It can be written as 58
= 390,625
Therefore the value of 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 is 58which is equal to 390625 .
c. 15 × 15 × 15 = _____
Answer:
Given 15 × 15 × 15
It can be written as 153
= 3375
Therefore the value of 15 × 15 × 15 is 153which is equal to 3375.
Identify each of the following as an expression or on equation.
Question 6.
a. 7 + x _____
Answer:
It is an Expression which contains a one numerical value and it doesn’t contain any Equality(=) symbol.
b. 9 + 4 = 13 ____
Answer:
The given Example is an Equation which is having an Equality(=) Symbol indicating the equality.
c. 85 × n = ____
Answer:
It is an Expression which contains a one numerical value and it doesn’t contain any Equality(=) symbol.
For each term below, identify the coefficient (C) and the variable (V).
Question 8.
a. 9y C ____ V ____
Answer:
Given term is 9y.
Variable (V) : y
Coefficient (C)= 9
b. 4b C ____ V _____
Answer:
Given term is 4b.
Variable (V) : b
Coefficient (C)= 4
c. m C ____ V ____
Answer:
Given term is m.
Variable (V) : m
Coefficient (C)= 1
Write the expression for each statement.
Question 9.
the product of 2 and the difference between 7 and 3 _____________
Answer:
Given values are 2, 7 and 3
Difference between 7 and 3 is : (7-3)
Therefore the Expression for product of 2 and difference of 7 and 3 is = 2.(7-3)
Question 10.
3 increased by the product of 9 and 2 _____________
Answer:
Given values are 3, 9 and 2
Product of 9 and 2 is : (9.2)
Then f 3 is increased by the product of 9 and 2 is : 3 + (9.2)
Question 11.
the difference between 12 and the product of 9 and 3 ________
Answer:
Given 12, 9 and 3
Product of 9 and 3 is : (9. 3)
Therefore the difference between 12 and the product of 9 and 3 is : 12-(9.3)
Question 12.
the quotient of 20 and 5 increased by 16 _____________
Answer:
Given 20, 5 and 16
Firstly Quotient of 20 and 5 is : 20 ÷ 5 = 4
Therefore the Quotient of 20 and 5 is increased by 16 = 4 + 16 = 20
Question 13.
the product of 7 and 2 divided by 3 ________
Answer:
Given 7, 2 and 3
Product of 7 and 2 is : (7 x 2) = 14
When the product is divided by 3 = 14 ÷ 3
Therefore the the product of 7 and 2 divided by 3 is 14 ÷ 3 = 4.666
Question 14.
twice the quotient of 45 and 9 ________
Answer:
Given 45 and 9
Firstly, the Quotient of 45 and 9 is : 45 ÷ 9 = 5
Therefore , twice the Quotient of 45 and 9 is = 2 x 5 = 10
Question 15.
the difference between 15 and the product of 4 and 2 ________
Answer:
Given 15 , 4 and 2
Product of 4 and 2 is : 4 x 2 = 8
Therefore difference between 15 and the product of 4 and 2 is : 15 – (4 x 2)
= 15 – 8
= 7
Question 16.
triple the sum of 16 and 9 ________
Answer:
Firstly, the sum of 16 and 9 is : 16 + 9 = 25
Therefore , When the sum of 16 and 9 is tripled = 3 x 25 = 73
Question 17.
a. x – 5 = 3 _____
Answer:
Given values are x , 5 and 3
Therefore the given Expression is difference between x and 5 is Equal to five.
b. x + 5 = 8 ____
Answer:
Given values are x , 5 and 8
Therefore the given Expression is sum of x and 5 is Equal to Eight.
c. y – 4 = 0 ____
Answer:
Given values are y , 4 and 0
Therefore the given Expression is difference between y and 4 is Equal to four.
Question 18.
a. x – 19 = 8 ____
Answer:
Given values are x , 19 and 8
Therefore the given Expression is difference between x and 19 is Equal to Eight.
b. x – 12 = 4 ____
Answer:
Given values are x , 12 and 4
Therefore the given Expression is difference between x and 12 is Equal to four.
c. n + 8 = 8 ____
Answer:
Given values are x , 8 and 8
Therefore the given Expression is sum of x and 8 is Equal to Eight.
Question 19.
a. b – 7 = 0 ____
Answer:
Given values are b, 7 and 0
Therefore the given Expression is difference between b and 7 is Equal to Zero.
b. n + 3 = 3 ____
Answer:
Given values are n , 3 and 3
Therefore the given Expression is sum of x and 3 is Equal to three.
c. x + 2 = 8 ____
Answer:
Given values are x , 2 and 8
Therefore the given Expression is sum of x and 2 is Equal to Eight.
Question 20.
a. \(\frac{x}{3}\) = 3 ____
Answer:
Given x / 3 = 3
\(\frac{x}{3}\) = 3
To Evaluate the given n value ,Try to undo division by 3, multiply by 3.
\(\frac{x}{3}\) × \(\frac{3}{1}\) = 3 × 3
x = 9
Therefore the value of x is 9.
b. n × 5 = 5 ______
Answer:
To Evaluate the given n value ,Try to perform the undo multiplication by 5, divide by 5.
\(\frac{n5}{5}\) = \(\frac{5}{5}\)
n = 1
Therefore the value of n is 1.
c. \(\frac{b}{2}\) = 1 ____
Answer:
Given b / 2 = 1
\(\frac{b}{2}\) = 1
To Evaluate the given b value ,Try to undo division by 2, multiply by 2.
\(\frac{b}{2}\) × \(\frac{2}{1}\) = 1 × 2
b = 2
Therefore the value of b is 2.
Question 21.
a. b × 8 = 12 ______-
Answer:
To Evaluate the given b value ,Try to perform the undo multiplication by 8, divide by 8.
\(\frac{b.8}{8}\) = \(\frac{12}{8}\)
b = 1.5
Therefore the value of b is 1.5.
b. \(\frac{x}{3}\) = 3 ____
Answer:
Given x / 3 = 3
\(\frac{x}{3}\) = 3
To Evaluate the given x value ,Try to perform the undo division by 3, multiply by 3.
\(\frac{x}{3}\) × \(\frac{3}{1}\) = 3 × 3
x = 9
Therefore the value of x is 9
c. a × 2 = 3 ______
Answer:
To Evaluate the given a value ,Try to perform the undo multiplication by 2, divide by 2.
\(\frac{a.2}{2}\) = \(\frac{3}{2}\)
a = 1.5
Therefore the value of a is 1.5.
Question 22.
a. \(\frac{n}{4}\) = 4 ____
Answer:
Given n/ 4 = 4
\(\frac{n}{4}\) = 4
To Evaluate the given n value ,Try to perform the undo division by 4, multiply by 4.
\(\frac{n}{4}\) × \(\frac{4}{1}\) = 4 × 4
n = 16
Therefore the value of n is 16
b. n × 8 = 8 ______
Answer:
To Evaluate the given a value ,Try to perform the undo multiplication by 8, divide by 8.
\(\frac{n.8}{8}\) = \(\frac{8}{8}\)
n = 1
Therefore the value of n is 1.
c. b × 3 = 18 ______
Answer:
To Evaluate the given b value ,Try to perform the undo multiplication by 3, divide by 3.
\(\frac{b.3}{3}\) = \(\frac{18}{3}\)
b = 6
Therefore the value of b is 6.
Solve each problem.
Question 23.
Patrick paid $72.60 for some computer games. Each game cost $24.20. How many games did Patrick buy?
What is the unknown number? _____________________
Equation: ___________________ n = _____________
Answer:
Amount paid by Patrick to few Computer games = $72.60
Cost of Each Computer game = $24.20
Number of Computer games That Patrick buys = ?
Let the unknown number = n
Equation : n = $72.60 ÷ $24.20
It implies n = 3
Therefore Patrick buys three Games.
Question 24.
Noelle and Gina have a combined height of 130 inches. Noelle is 4 inches taller than Gina. How tall is each girl?
Let n stand for Noelle’s height.
Equation: _________________________
Noelle is ________________ inches tall.
Gina is _____ inches tall.
Answer:
Height of both Noelle and Gina Height = 130 inches
Number of inches that Neolle is taller than Gina = 4
Equation : n + g = 130………Equation (1)
4+g+g = 130
4 + 2g = 130
2g = 130 – 4
2g = 128
g = 128 / 2
g = 64
n = 4 + 64 = 68
Therefore , Neolle height = 68 inches
Gina height = 64 inches