### All SAT Math Resources

## Example Questions

### Example Question #1 : Fractions And Percentage

Write as a fraction: 22%

**Possible Answers:**

2/3

4/9

4/7

11/50

11/100

**Correct answer:**

11/50

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

### Example Question #2 : Percentage

When *y* is decreased by ten percent, the result is equal to fifteen percent of *x*. Assuming both *x* and *y* are nonzero, what is the ratio of *x* to *y*?

**Possible Answers:**

3

1/6

18

1/3

6

**Correct answer:**

6

The problem states that decreasing *y* by ten percent gives us the same thing as taking fifteen percent of *x*. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of *x*, and then set these two things equal.

If we were to decrease *y* by ten percent, we would be left with ninety percent of *y* (because the percentages must add to one hundred percent). We could write ninety percent of *y* as 0.90*y* = (90/100)*y* = (9/10)*y*. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of *x* as 0.15*x* = (15/100)*x* = (3/20)*x*.

Now, we set these two expressions equal to one another.

(9/10)*y* = (3/20)*x*

Multiply both sides by 20 to eliminate fractions.

18*y* = 3*x*

The question asks us to find the ratio of *x* to *y*, which is equal to *x*/*y*. Thus, we must rearrange the equation above until we have *x*/*y* by itself on one side.

18*y* = 3*x*

Divide both sides by 3.

6*y* = *x*

Divide both sides by *y*.

6 = *x*/*y*

Thus, the ratio of *x* to *y* is 6.

The answer is 6.

### Example Question #1 : Percentage

Write 7.5% as a fraction.

**Possible Answers:**

**Correct answer:**

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

### Example Question #4 : Percentage

25% of 64 is equal to 5% of what number?

**Possible Answers:**

90

320

94

108

112

**Correct answer:**

320

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

### Example Question #5 : Percentage

Turn the following percentage into a fraction:

**Possible Answers:**

**Correct answer:**

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

From here, simplify the fraction as necessary:

### Example Question #6 : Percentage

Turn the following percentage into a fraction:

**Possible Answers:**

**Correct answer:**

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

From here, simplify the fraction as necessary:

### Example Question #7 : Percentage

Turn the following percentage into a decimal:

**Possible Answers:**

**Correct answer:**

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

From here, simplify the fraction as necessary:

### Example Question #8 : Percentage

Turn the following percentage into a fraction:

**Possible Answers:**

**Correct answer:**

From here, simplify the fraction as necessary:

### Example Question #9 : Percentage

Turn the following percentage into a fraction:

**Possible Answers:**

**Correct answer:**

From here, simplify the fraction as necessary:

### Example Question #10 : Percentage

Turn the following percentage into a fraction:

**Possible Answers:**

**Correct answer:**

From here, simplify the fraction as necessary: