Math 101 Final
Find the LCM of 12 and 30.
If we list the multiples of each number, we get
12:12,24,36,48,60
30:30,60
We see that the least common multiple is 60.
Find the prime factorization of 44 using a factor tree.
The prime factorization is 2⋅2⋅11.
Simplify: ∣8⋅−4∣
First simplify inside the absolute value sign. ∣8⋅−4∣=∣−32∣Then take the absolute value.
Remember the absolute value of a number is its distance from 0 on the number line. So
∣8∗−4∣=32
What is the sum of 9, −5, and 5?
This question is asking us to add three numbers: 9+−5+5. Note that −5 and 5 are opposites,
and add up to zero. So 9+−5+5=9+0=9.
Simplify: 5 squared−6squared
Following the order of operations, we should simplify powers before subtracting. Thus we
have
5squared−6squared=25−36.
The difference 25−36=−11 is negative because 36 is more negative than 25 is positive. -11
Divide: (−48)÷(6)
When we divide a negative by a positive number or a positive number by a negative number,
the quotient will be negative. So (−48)÷(6)=−8
Multiply: (−1)(5)
When we multiply a negative times a positive number, the product will be negative. So
(−1)(5)=−5
Convert the following mixed number to a reduced improper fraction:
9 3/7
66/7
66 over 7
,Which of the following equivalent to 5/4 5 over 4
10/8
10 over 8
Convert the following fraction to a percent: 13/50
13 over 50
26%
Convert the following decimal to a fraction: 0.953. Simplify when possible.
953/1000
What is the decimal form of 1 31/36?
1.861⎯⎯⎯
Find the reciprocal of 4/2
2/4
Divide the following. Give your answer as a reduced improper fraction if necessary.
6÷1/8
48
Multiply the following fractions, and give your answer as a reduced fraction.
2/7⋅5/6
5/21
Add or subtract: 1+7/8.
15/8
Add the following fractions, and give your answer as a reduced improper fraction.
11/13+4/7
129/91
Sean bought 3/4 of a pound of cherries and then he bought 1/3 of a pound more. When he
got home, he saw that he still had 1/2 of a pound of cherries in his cupboard. How many total
pounds of cherries does he have? Give your answer as an exact simplified improper fraction,
not as a mixed number. Do not include units.
19/12
, Add or subtract: 9/13−4/13.Enter your answer as a reduced fraction.
5/13
Use the order of operations to simplify the given expression.
3−12⋅2+19
-2
Simplify the given expression:
5−8+3×9
24
Simplify the following expression by expanding and collecting like terms.
−(7x+6)+3(−5x−3)
Give your answer in the form ax+b.
−22x−15
Evaluate the following expression at x=1 and y=7.
5x+9y−6
62
Simplify the following expression.
(p−1q−3/r)3
=1/p3q9r3
Simplify: 10//8.
10 to the 12th power
Simplify: −7 to the 3rd power
-343
Find the LCM of 12 and 30.
If we list the multiples of each number, we get
12:12,24,36,48,60
30:30,60
We see that the least common multiple is 60.
Find the prime factorization of 44 using a factor tree.
The prime factorization is 2⋅2⋅11.
Simplify: ∣8⋅−4∣
First simplify inside the absolute value sign. ∣8⋅−4∣=∣−32∣Then take the absolute value.
Remember the absolute value of a number is its distance from 0 on the number line. So
∣8∗−4∣=32
What is the sum of 9, −5, and 5?
This question is asking us to add three numbers: 9+−5+5. Note that −5 and 5 are opposites,
and add up to zero. So 9+−5+5=9+0=9.
Simplify: 5 squared−6squared
Following the order of operations, we should simplify powers before subtracting. Thus we
have
5squared−6squared=25−36.
The difference 25−36=−11 is negative because 36 is more negative than 25 is positive. -11
Divide: (−48)÷(6)
When we divide a negative by a positive number or a positive number by a negative number,
the quotient will be negative. So (−48)÷(6)=−8
Multiply: (−1)(5)
When we multiply a negative times a positive number, the product will be negative. So
(−1)(5)=−5
Convert the following mixed number to a reduced improper fraction:
9 3/7
66/7
66 over 7
,Which of the following equivalent to 5/4 5 over 4
10/8
10 over 8
Convert the following fraction to a percent: 13/50
13 over 50
26%
Convert the following decimal to a fraction: 0.953. Simplify when possible.
953/1000
What is the decimal form of 1 31/36?
1.861⎯⎯⎯
Find the reciprocal of 4/2
2/4
Divide the following. Give your answer as a reduced improper fraction if necessary.
6÷1/8
48
Multiply the following fractions, and give your answer as a reduced fraction.
2/7⋅5/6
5/21
Add or subtract: 1+7/8.
15/8
Add the following fractions, and give your answer as a reduced improper fraction.
11/13+4/7
129/91
Sean bought 3/4 of a pound of cherries and then he bought 1/3 of a pound more. When he
got home, he saw that he still had 1/2 of a pound of cherries in his cupboard. How many total
pounds of cherries does he have? Give your answer as an exact simplified improper fraction,
not as a mixed number. Do not include units.
19/12
, Add or subtract: 9/13−4/13.Enter your answer as a reduced fraction.
5/13
Use the order of operations to simplify the given expression.
3−12⋅2+19
-2
Simplify the given expression:
5−8+3×9
24
Simplify the following expression by expanding and collecting like terms.
−(7x+6)+3(−5x−3)
Give your answer in the form ax+b.
−22x−15
Evaluate the following expression at x=1 and y=7.
5x+9y−6
62
Simplify the following expression.
(p−1q−3/r)3
=1/p3q9r3
Simplify: 10//8.
10 to the 12th power
Simplify: −7 to the 3rd power
-343
