working with Percent
Exponents
Order of Operations
Solve
Percents/ Ratios
GCF/LCM
100
What is 40% of 80?
32
100
When you see the following expression, what is the big number called and what is the little number on top of it called? Then solve it.
24
What is base? What is exponent? 16
100
Simplify the following expression:
100
x - 5x = 64
x = -16
We can solve the equation x - 5x = 64 for x by combining the terms with x and then isolating x.
Here's how to solve it:
Combine terms with x: We can combine the terms with x on the left side of the equation. Since they have the same coefficient (1), simply subtract them: 1x - 5x = 64 becomes -4x = 64
Isolate x: To isolate x, we need to get it by itself. Divide both sides of the equation by -4. -4x = 64 becomes x = 64 / (-4)
100
What is 10% of 86?
8.6
100
Find the GCF of 18 and 9
9
Listing the factors:
- Find the factors of 18: 1, 2, 3, 6, 9, 18
- Find the factors of 9: 1, 3, 9
- The greatest common factor that both numbers share is 9.
Prime factorization:
- Prime factorize 18: 18 = 2 * 3 * 3
- Prime factorize 9: 9 = 3 * 3
- The greatest common factors (considering only the factors that appear in both numbers raised to the lowest power) is 3 * 3, which equals 9.
200
What is 75% of 92?
69
200
How can you rewrite 92 in expanded form?
9x9
200
Simplify the following expression:
200
Solve for m
-0.3m = -12
m=40
Divide both sides by -0.3
Since multiplication is the inverse of division, to undo the effect of multiplying m by -0.3, we can divide both sides of the equation by -0.3.
Important Note: Dividing by a negative number flips the sign of the result.
Therefore:
-0.3m = -12
becomes:
m = -12 / (-0.3)
Simplify
m = 40
200
If 12 pencils cost $15. How much do 24 pencils cost?
$30
- Calculate the cost per pencil:
- Divide the total cost (price of 12 pencils) by the number of pencils (12).
- Cost per pencil = $15 (total cost) / 12 (number of pencils)
- Cost per pencil = $1.25
- Calculate the cost of 24 pencils:
- Multiply the cost per pencil by the number of pencils (24).
- Cost of 24 pencils = $1.25 (cost per pencil) * 24 (number of pencils)
- Cost of 24 pencils = $30.00
Therefore, 24 pencils cost $30.00.
200
Find the LCM of 6 and 5
30
Listing multiples:
- List the multiples of 6: 6, 12, 18, 24, 30, ...
- List the multiples of 5: 5, 10, 15, 20, 25, 30, ...
- The least common multiple that appears in both lists is 30.
Prime factorization:
- Prime factorize 6: 6 = 2 * 3
- Prime factorize 5: 5 (5 is already prime)
- Find the highest power of each prime factor that appears in either number: LCM = 2^1 * 3^1 * 5^1 = 30
300
How can you rewrite the following in exponential form?
7 x 7 x 7 x 7 x 7
What is 7^5?
300
Free points!!
Niceeeee!
300
Solve for x
2.5x = -60
x= -24
To solve for x in the equation 2.5x = -60, we need to isolate x on one side of the equation. Here's how:
Divide both sides by 2.5
Since multiplication is the inverse of division, to undo the effect of multiplying x by 2.5, we can divide both sides of the equation by 2.5.
Important Note: When dividing both sides of an equation by a number, the number itself doesn't change its sign.
Therefore:
2.5x = -60
becomes:
x = -60 / 2.5
Simplify
x = -24
300
What is 34% of 78?
26.52
Method 1: Using multiplication
- Convert the percentage into a decimal dividing by 100: 34% = 34 / 100 = 0.34
- Multiply the decimal by the whole number: 0.34 * 78 = 26.52
Method 2: Proportions
- Set up a proportion: part / whole = percent / 100
- In this case, part represents the unknown amount (what 34% of 78 is), whole is 78 (the total amount), and percent is 34.
- Set up the proportion: part / 78 = 34 / 100
- Cross-multiply: part * 100 = 78 * 34
- Solve for part : part = (78 * 34) / 100 = 26.52
300
Find the GCF of 21 and 14
7
Listing the factors:
- Find the factors of 21: 1, 3, 7, 21
- Find the factors of 14: 1, 2, 7, 14
- The greatest common factor that both numbers share is 7.
Prime factorization:
- Prime factorize 21: 21 = 3 * 7
- Prime factorize 14: 14 = 2 * 7
- The greatest common factors (considering only the factors that appear in both numbers raised to the lowest power) is 7.
400
Terry bought a game for $60. He sold it at a markup price of 50% profit. How much did he sell it for?
$90.00
400
What is the value of:
84
400
What is 45?
400
Solve for x
x - (-3) = 5
x=2
Simplify the right side:
x - (-3) = 5 becomes x + 3 = 5
Isolate x:
We want x by itself. Subtract 3 from both sides of the equation:
x + 3 - 3 = 5 - 3
Combine like terms: Simplifying the equation: x = 2
400
If I can walk 1.5 miles in 45 minutes, how many miles can I walk in an hour?
2 miles
Convert minutes to hours: There are 60 minutes in 1 hour. So, 45 minutes is equal to 45 minutes / 60 minutes/hour = 0.75 hours.
Calculate the walking rate: We know you can walk 1.5 miles in 0.75 hours. To find your walking rate in miles per hour, divide the distance by the time: Walking rate = Distance / Time = 1.5 miles / 0.75 hours.
Simplify: Walking rate = 2 miles per hour.
400
Find the LCM of 10 and 12
60
Listing multiples:
- List the multiples of 10: 10, 20, 30, 40, 50, 60, ...
- List the multiples of 12: 12, 24, 36, 48, 60, ...
- The least common multiple that appears in both lists is 60.
Prime factorization:
- Prime factorize 10: 10 = 2 * 5
- Prime factorize 12: 12 = 2 * 2 * 3
- Find the highest power of each prime factor that appears in either number: LCM = 2^2 * 3^1 * 5^1 = 60
500
The original price for a book is $30. It is on sale for 20% off. What is the sale price?
$24.00
500
What is the value of:
23 + 32 - 42
500
What is 30?
500
Solve for x
x - 0.9x = 7
x=70
Combine like terms: We can combine the terms with x on the left side of the equation. Since they have the same variable (x), simply subtract the coefficients: x - 0.9x becomes 0.1x = 7
Isolate x: To isolate x, divide both sides of the equation by 0.1. 0.1x = 7 becomes x = 7 / 0.1
Important Note: Dividing by a decimal is the same as dividing by a whole number with a trailing zero, but the decimal point moves one position to the right.
Therefore:
x = 7 / 0.1 becomes x = 70
500
What is 97% of 728?
706.16
Method 1: Using multiplication
- Convert the percentage into a decimal dividing by 100: 97% = 97 / 100 = 0.97
- Multiply the decimal by the whole number: 0.97 * 728 = 706.16
Method 2: Proportions
- Set up a proportion: part / whole = percent / 100
- In this case, part represents the unknown amount (what 97% of 728 is), whole is 728 (the total amount), and percent is 97.
- Set up the proportion: part / 728 = 97 / 100
- Cross-multiply: part * 100 = 728 * 97
- Solve for part : part = (728 * 97) / 100 = 706.16
500
Find the GCF and LCM of:
36 and 24
GCF = 12
LCM = 72
There are a couple of ways to find the GCF:
Listing the factors:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- The greatest common factor that both numbers share is 12.
Prime factorization:
- Prime factorize 36: 36 = 2 * 2 * 3 * 3
- Prime factorize 24: 24 = 2 * 2 * 2 * 3
- The greatest common factors (considering only the factors that appear in both numbers raised to the lowest power) is 2 * 2 * 3 = 12.
- LCM (Least Common Multiple): 72
There are two methods to find the LCM:
Listing multiples:
- List the multiples of 36: 36, 72, 108, ...
- List the multiples of 24: 24, 48, 72, ...
- The least common multiple that appears in both lists is 72.
Prime factorization: (same prime factors as above)
- Find the highest power of each prime factor that appears in either number: LCM = 2^2 * 3^2 = 72.