ACT Math - How to find percentage from a fraction

Convert to a percentage: $\frac{3a}{2a^2}$

$150a^{-1} %$

$a^{1.5} %$

$\frac{3^a}{2^a} %$

$300a^{2} %$

Explanation

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.

$\frac{3a}{2a^2} = (\frac{300a}{2a^2}) = 150a^{-1} %$

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?

45%

50%

75%

15%

35%

Explanation

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%

Express the fraction $\frac{7}{25}$ as a percentage.

Explanation

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 $\frac{7}{25}$ is the numerator of the equivalent fraction whose denominator is 100. In order to convert $\frac{7}{25}$ to a fraction over 100, I need to multiply the numerator and denominator each by 4.

$\frac{7}{25}\cdot \frac{4}{4}=\frac{28}{100}$

Therefore, our answer is 28%.

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

$7\div25=0.28$

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%.

A politician promises to spend a minimum of $\frac{3}{8}$ of his budget on improving roads. What is the minimum percent of the budget that must be spent on roads to keep this promise?

Explanation

To find a percentage from a fraction, multiply the numerator by , then solve the fraction.

$\frac{3}{8} = (\frac{3 \cdot 100}{8}) % = \frac{300}{8} % = 37.5 %$

Thus, the politician must spend at least of the budget on roads.

Convert to a percentage: $\frac{2}{5} + \frac{13}{15}$

Round to the nearest integer.

Explanation

We can solve this problem either by adding the two fractions and then converting to a percentage, or by converting each fraction to a percentage before adding them. We'll use the first method in this case:

$\frac{2}{5} + \frac{13}{15} = \frac{6}{15} + \frac{13}{15} = \frac{19}{15}$

Now, just as before, multiply our numerator by and solve the fraction:

$\frac{19}{15} = \left (\frac{1900}{15} \right ) % \approx 127 %$

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?