### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find A Fraction From A Percentage

We asked 1000 people their preferences of movie genres. 7.5% of those asked preferred horror movies, 35% preferred romantic films, 20% preferred dramas and 37.5% preferred comedies. How many people liked horror films?

**Possible Answers:**

7.5

75

37.5

35

750

**Correct answer:**

75

People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people

### Example Question #1 : How To Find A Fraction From A Percentage

There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?

**Possible Answers:**

**Correct answer:**

There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.

girls in the class.

### Example Question #3 : Percentage

Which of the following represents as a fraction?

**Possible Answers:**

**Correct answer:**

To represent a percentage as a fraction, keep the percentage in the numerator and put in the denominator.

Therefore:

### Example Question #4 : Percentage

Which of the following fractions is equivalent to

**Possible Answers:**

**Correct answer:**

To convert an integer percentage into an improper fraction, set the percentage as a fraction over and simplify as far as you can. At that point, simply convert the improper fraction into a mixed fraction.

### Example Question #5 : Percentage

A politician promises to spend up to of his budget on improving roads. Which of the following is closest to the fraction of their budget the politician must devote to road improvement?

**Possible Answers:**

**Correct answer:**

To convert a decimal percentage into a fraction, first convert it to a decimal:

Now, set ths as a fraction with as the denominator (expanding to as many significant digits as you need to line the fraction up):

Now just reduce your fraction!

### Example Question #6 : Percentage

Convert to a fraction:

**Possible Answers:**

**Correct answer:**

To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.

### Example Question #7 : Percentage

Luke went to the grocery store. It took him 15 minutes to drive to the store from his house, 30 minutes to shop, 5 minutes to put groceries in his car, and 20 minutes to drive home due to traffic.

What percentage of the trip did Luke spend inside his car?

**Possible Answers:**

35%

75%

50%

45%

15%

**Correct answer:**

50%

You take 15 + 20 = 35 minutes as total time spent in the car.

Then, you take 15 + 20 + 5 + 30 = 70 minutes as total trip time.

We take (35/70) x 100% = 50%

### Example Question #8 : Percentage

There are 300 sandwiches at a company-wide picnic. If half of the sandwiches are tuna, and the provider mistakenly uses expired tuna in three-fifths of those sandwiches, what percentage of total sandwiches still remain edible?

**Possible Answers:**

**Correct answer:**

This multi-part question makes use of both fractions and percentages, as well as some tricky language if you are not paying close attention.

First off, determine what three-fifths of the 150 tuna sandwiches is:

Now, refer back to the question, which asks how many **TOTAL** sandwiches (tuna and non-tuna) still remain edible. This is simple arithmetic.

Finally, find what percentage this equals:

### Example Question #9 : Percentage

Express the fraction as a percentage.

**Possible Answers:**

**Correct answer:**

Converting a fraction to a percentage can be done in two ways. The first way involves recalling that a percent is just a fraction of 100 (per cent). Therefore, the percent equivalent to is the numerator of the equivalent fraction whose denominator is 100. In order to convert to a fraction over 100, I need to multiply the numerator and denominator each by 4.

Therefore, our answer is 28%.

The other approach is to convert the fraction to a decimal first by dividing 7 by 25.

To convert a decimal to a percent, just shift the decimal point two places to the right.

With this method, our answer is again 28%.

### Example Question #10 : Percentage

Convert to a percentage:

**Possible Answers:**

**Correct answer:**

Despite the presence of a variable, the rule remains the same: To convert a fraction to a percentage, multiply the numerator by 100 and solve the fraction.

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