Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Unit Test Lessons 15-17 will engage students and is a great way of informal assessment.
McGraw-Hill Math Grade 6 Unit Test Lessons 15-17 Answer Key
Restate in exponential form, then calculate.
Question 1.
2 × 2 × 2 × 2 + 3 × 3 × 3 _____________
Answer:
The given expression is 2 × 2 × 2 × 2 + 3 × 3 × 3.
The exponential form of above given expression is 24 + 33.
= 24 + 33
= 16 + 27
= 43
So, 24 + 33 is equal to 43.
Question 2.
4 × 4 × 4 × 4 – 5 × 5 × 5 _____________
Answer:
The given expression is 4 × 4 × 4 × 4 – 5 × 5 × 5.
The exponential form of above given expression is 44 – 53.
= 44 – 53
= 256 – 125
= 131
So, 44 – 53 is equal to 131.
Question 3.
2 × 2 × 2 × 2 × 2 × 2 + 6 × 6 – 5 × 5 _____________
Answer:
The given expression is 2 × 2 × 2 × 2 × 2 × 2 + 6 × 6 – 5 × 5.
The exponential form of above given expression is 26 + 62 – 52.
= 26 + 62 – 52
= 64 + 36 – 25
= 75
So, 26 + 62 – 52 is equal to 75.
Restate using scientific notation.
Question 4.
3,456,984.01 _____________
Answer:
The given number 3,456,984.01 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 3.45698401.
Now count how many places the decimal moved. In this case, the decimal moved 6 places to the left, which means the power is positive.
The scientific notation for 3,456,984.01 is 3.45698401 x 106.
Question 5.
8,694.1 _____________
Answer:
The given number 8,694.1 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 8.6941.
Now count how many places the decimal moved. In this case, the decimal moved 3 places to the left, which means the power is positive.
The scientific notation for 8,694.1 is 8.6941 x 103.
Question 6.
.00945 _____________
Answer:
The given number .00945 already has a decimal move. Move the decimal to the right until have a number between 1 and 10. So, the number is 9.45.
Now count how many places the decimal moved. In this case, the decimal moved 3 places to the right, which means the power is negative.
The scientific notation for .00945 is 9.45 x 10-3.
Question 7.
1,094,659,041 _____________
Answer:
Place a decimal at the far right and move the decimal to the left until have a number between 1 and 10. So, the number is 1.094659041.
Now count how many places the decimal moved. In this case, the decimal moved 9 places to the left, which means the power is positive.
The scientific notation for 1,094,659,041 is 1.094659041 x 109.
Question 8.
63.56 _____________
Answer:
The given number 63.56 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 6.356.
Now count how many places the decimal moved. In this case, the decimal moved 1 places to the left, which means the power is positive.
The scientific notation for 63.56 is 6.356 x 101.
Calculate using order of operations (PEMDAS).
Question 9.
3 × (6 – 4)2 + (15 – 5) × 5 + (5 – 3) × 4 + 33 ________________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
3 × (6 – 4)2 + (15 – 5) × 5 + (5 – 3) × 4 + 33 = ?
First solve the parts that are inside parenthesis.
3 × 22 + 10 × 5 + 2 × 4 + 33 = ?
Second solve the parts that have exponents.
3 × 4 + 10 × 5 + 2 × 4 + 27 = ?
Third perform multiplication operation.
12 + 50 + 8 + 27 = ?
Fourth perform Addition operation.
12 + 50 + 8 + 27 = 97
So, the expression 3 × (6 – 4)2 + (15 – 5) × 5 + (5 – 3) × 4 + 33 is equal to 97.
Question 10.
17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)2 ________________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)2 = ?
First solve the parts that are inside parenthesis.
17 – 14 + 2 × 2 + 52 = ?
Second solve the parts that have exponents.
17 – 14 + 2 × 2 + 25 = ?
Third perform multiplication operation.
17 – 14 + 4 + 25 = ?
Fourth perform Addition and subtraction operation from left to right.
17 – 14 + 4 + 25 = ?
3 + 4 + 25 = 32
So, the expression 17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)2 is equal to 32.
Question 11.
24 + (3 + 5) × 5 + (6 – 3)2 ______________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
24 + (3 + 5) × 5 + (6 – 3)2 = ?
First solve the parts that are inside parenthesis.
24 + 8 × 5 + 32 = ?
Second solve the parts that have exponents.
24 + 8 × 5 + 9 = ?
Third perform multiplication operation.
24 + 40 + 9 = ?
Fourth perform Addition operation.
24 + 40 + 9 = 73
So, the expression 24 + (3 + 5) × 5 + (6 – 3)2 is equal to 73.
Question 12.
33 – (4 – 2)3 + 6 × 2 + (5)2 – 3 ______________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
33 – (4 – 2)3 + 6 × 2 + (5)2 – 3 = ?
First solve the parts that are inside parenthesis.
33 – 23 + 6 × 2 + (5)2 – 3= ?
Second solve the parts that have exponents.
33 – 8 + 6 × 2 + 25 – 3= ?
Third perform multiplication operation.
33 – 8 + 12 + 25 – 3 = ?
Fourth perform Addition and subtraction operation from left to right.
33 – 8 + 12 + 25 – 3 = ?
25 + 12 + 25 – 3 = ?
37 + 25 – 3 = ?
62 – 3 = 59
So, the expression 33 – (4 – 2)3 + 6 × 2 + (5)2 – 3 is equal to 59.
What number property does each expression display?
Question 13.
3 + 4 + 5 = 5 + 4 + 3 ______________
Answer:
The expression 3 + 4 + 5 = 5 + 4 + 3 is commutative property of addition.
Explanation:
The commutative property of addition states that the addends are added in any order without changing the sum.
3 + 4 + 5 = 12
5 + 4 + 3 = 12
Question 14.
3(4 + 6) = 3(4) + 3(6) _______________
Answer:
The expression 3(4 + 6) = 3(4) + 3(6) is Distributive property of multiplication over addition.
Explanation:
The Distributive property of multiplication over addition states that when we multiply numbers, we have to multiply the numbers each separately and then add their products.
3(4 + 6) = 30
3(4) + 3(6) = 30
Question 15.
(15 + 16) + 18 = 15 + (16 + 18) ________________
Answer:
The expression (15 + 16) + 18 = 15 + (16 + 18) is Associative property of addition.
Explanation:
The Associative property of addition states that the addends are grouped in any way without changing the sum.
(15 + 16) + 18 = 49
15 + (16 + 18) = 49
Question 16.
34(1) = 34 _______________
Answer:
The expression 34(1) = 34 is Multiplication Identity property of 1.
Explanation:
In multiplication, the identity element is 1. Any factor or factors multiplying with 1 the product will not change.
34(1) = 34
Question 17.
3 + 0 = 3 _____________
Answer:
The expression 3 + 0 = 3 is Zero Identity of Addition.
Explanation:
In addition, the identity element is 0. Any addend + 0 will not change the total.
3 + 0 = 3
Question 18.
16(5 – 3) = (16 × 5) – (16 × 3) ______________
Answer:
The expression 16(5 – 3) = (16 × 5) – (16 × 3) is Distributive property of multiplication over subtraction.
Explanation:
The Distributive property of multiplication over subtraction states that when we multiply numbers, we have to multiply the numbers each separately and then subtract their products.
16(5 – 3) = 16(2) = 32
(16 × 5) – (16 × 3) = 80 – 48 = 32
Question 19.
15 × 5 = 5 × 15 _______________
Answer:
The expression 15 × 5 = 5 × 15 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the numbers are multiplied in any order without changing the product.
15 × 5 = 75
5 × 15 = 75
Question 20.
33(0) + (33 + 0) = 0 + 33 = 33 ______________
Answer:
The expression 33(0) + (33 + 0) = 0 + 33 = 33 is Zero property of addition and multiplication.
Explanation:
Zero property of addition and multiplication states that any addend + 0 will not change the total and any number multiplied with 0 is equal to 0.
33(0) + (33 + 0) = 0 + 33 = 33
Question 21.
(7 × 4) × 20 = 7 × (4 × 20) _____________
Answer:
The expression (7 × 4) × 20 = 7 × (4 × 20) is Associative property of Multiplication.
Explanation:
The Associative property of multiplication states that the numbers are grouped in any way without changing the product.
(7 × 4) × 20 = 560
7 × (4 × 20) = 560
Solve for x.
Question 22.
4 + x = 7
Answer:
Given equation is 4 + x = 7.
To calculate x value we need to subtract both sides of the equation with 4.
x + 4 – 4= 7 – 4
x = 3
Question 23.
x – 5 = 12
Answer:
Given equation is x – 5 = 12
To calculate x value we need to add both sides of the equation with 5.
x – 5 + 5 = 12 + 5
x = 17
Question 24.
29 – x = 25
Answer:
Given equation is 29 – x = 25
To calculate x value we need to subtract both sides of the equation with 29.
29 – x – 29 = 25 – 29
– x = -4
x = 4
Question 25.
x + 30 = 90
Answer:
Given equation is x + 30 = 90
To calculate x value we need to subtract both sides of the equation with 30.
x + 30 – 30= 90 – 30
x = 60
Question 26.
4x + 5 = 13
Answer:
Given equation is 4x + 5 = 13
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 5 from 13 the difference is equal to 8.
4x = 13 – 5
4x = 8
x = 8/4
x = 2
Question 27.
3x – 5 = 13
Answer:
Given equation is 3x – 5 = 13
To calculate x value first we need to perform addition operation and then division operation.
Add 13 with 5 the sum is equal to 18
3x = 13 + 5
3x = 18
x = 18/3
x = 6
Question 28.
5x + 4 = 39
Answer:
Given equation is 5x + 4 = 39
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 4 from 39 the difference is equal to 35.
5x = 39 – 4
5x = 35
x = 35/5
x = 7
Question 29.
3x + 4 = 28
Answer:
Given equation is 3x + 4 = 28
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 4 from 28 the difference is equal to 24.
3x = 28 – 4
3x = 24
x = 24/3
x = 8
Question 30.
-4x + 4 = -28
Answer:
Given equation is -4x + 4 = -28
To calculate x value first change all numbers to one sides and variable to another side.
28 + 4 = 4x
Second perform addition operation and then division operation.
32 = 4x
32/4 = x
x = 8
Question 31.
\(\frac{x}{4}\) + 5 = 25
Answer:
Given equation is \(\frac{x}{4}\) + 5 = 25
To calculate x value first we have to perform subtraction operation and then multiplication operation.
\(\frac{x}{4}\) = 25 – 5
\(\frac{x}{4}\) = 20
x = 20 x 4
x = 80
Question 32.
\(\frac{x}{2}\) – 5 = 30
Answer:
Given equation is \(\frac{x}{2}\) – 5 = 30
To calculate x value first we have to perform addition operation and then multiplication operation.
\(\frac{x}{2}\) = 30 + 5
\(\frac{x}{2}\) = 35
x = 35 x 2
x = 70
Question 33.
\(\frac{2}{3}\)x – 4 = 26
Answer:
Given equation is \(\frac{2}{3}\)x – 4 = 26
To calculate x value first we have to perform addition operation, second multiplication operation and then division operation.
\(\frac{2}{3}\)x = 26 + 4
\(\frac{2}{3}\)x = 30
2x = 30 x 3
2x = 90
x = 90/2
x = 45
Find all the factors.
Question 34.
24
Answer:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Explanation:
The numbers that divide 24 exactly without leaving a remainder are the factors of 24. The number 24 is an even number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Question 35.
15
Answer:
The factors of 15 are 1, 3, 5 and 15.
Explanation:
The numbers that divide 15 exactly without leaving a remainder are the factors of 15. The number 15 is an odd number. The factors of 15 are 1, 3, 5 and 15.
Question 36.
20
Answer:
The factors of 20 are 1, 2, 4, 5, 10 and 20.
Explanation:
The numbers that divide 20 exactly without leaving a remainder are the factors of 20. The number 20 is an even number. The factors of 20 are 1, 2, 4, 5, 10 and 20.
Question 37.
8
Answer:
The factors of 8 are 1, 2, 4 and 8.
Explanation:
The numbers that divide 8 exactly without leaving a remainder are the factors of 8. The number 8 is an even number. The factors of 8 are 1, 2, 4 and 8.
Question 38.
13
Answer:
The factors of 13 are 1, 13.
Explanation:
The numbers that divide 13 exactly without leaving a remainder are the factors of 13. The number 13 is an odd number. The factors of 13 are 1,13.
Question 39.
21
Answer:
The factors of 21 are 1, 3, 7 and 21.
Explanation:
The numbers that divide 21 exactly without leaving a remainder are the factors of 21. The number 21 is an odd number. The factors of 21 are 1, 3, 7 and 21.
List the first five multiples.
Question 40.
5
Answer:
The first five multiples of 5 are 5,10,15, 20, 25.
Question 41.
3
Answer:
The first five multiples of 3 are 3, 6, 9, 12, 15.
Question 42.
7
Answer:
The first five multiples of 7 are 7,14, 21, 28, 35.
Question 43.
11
Answer:
The first five multiples of 11 are 11, 22, 33, 44, 55.
Solve the inequalities.
Question 44.
2x ≤ 14
Answer:
The given equation is 2x ≤ 14.
Divide both sides of the equation by 2.
2x/2 ≤ 14/2
x ≤ 7
The value of x should be less than or equal to 7.
Question 45.
x + 8 ≥ 2
Answer:
The given equation is x + 8 ≥ 2.
Subtract both sides of the equation with 8.
x + 8 – 8 ≥ 2 – 8
x ≥ – 6
The value of x should be greater than or equal to -6.
Question 46.
3 < \(\frac{x}{6}\)
Answer:
The given equation is 3 < \(\frac{x}{6}\).
Multiply both sides of the equation with 6.
3 x 6 < \(\frac{x}{6}\) x 6
18 < x
The value of x should be greater than 18.
Question 47.
x – 7 > 4
Answer:
The given equation is x – 7 > 4.
Add both sides of the equation with 7.
x – 7 + 7 > 4 + 7
x > 11
The value of x should be greater than 11.
Question 48.
x + 3x > 16
Answer:
The given equation is x + 3x > 16.
4x > 16
Divide both sides of the equation by 4.
4x/4 > 16/4
x > 4
The value of x should be greater than 4.
Question 49.
Elba has four tiles marked 1, 2, 3, and 4. If she needs to choose a tile that solves the equation x – 1 > 2, which one will she choose?
Answer:
Elba has four tiles marked 1, 2, 3, and 4.
If she choose a tile 1 then the equation becomes 0 > 2. So, she will not choose tile 1.
If she choose a tile 2 then the equation becomes 1 > 2. So, she will not choose tile 2.
If she choose a tile 3 then the equation becomes 2 > 2. So, she will not choose tile 3.
If she choose a tile 4 then the equation becomes 3 > 2. So, she will choose tile 4.
Question 50.
Vicki’s mother tells her to pack at least 4 shirts for a trip. Write an inequality that expresses that command, using the letter x for the number of shirts.
Answer:
Vicki’s mother tells her to pack at least 4 shirts for a trip. Which means 4 shirts or more.
The inequality that expresses the command is x ≥ 4.