Fractions

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SSAT Upper Level Quantitative › Fractions

Questions 1 - 10

$\frac{\frac{2}{3}}{\frac{4}{5}}=?$

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{8}{15}$

$\frac{4}{5}$

Explanation

Keep in mind that the main fraction line just means "divide."

So then,

$\frac{\frac{2}{3}}{\frac{4}{5}}=\frac{2}{3}\div\frac{4}{5}$

Now, divide this like any other fraction.

$\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$

$\frac{\frac{2}{3}}{\frac{4}{5}}=?$

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{8}{15}$

$\frac{4}{5}$

Explanation

Keep in mind that the main fraction line just means "divide."

So then,

$\frac{\frac{2}{3}}{\frac{4}{5}}=\frac{2}{3}\div\frac{4}{5}$

Now, divide this like any other fraction.

$\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$

Order the following fractions from least to greatest:

$\frac{1}{2}, \frac{9}{10}, \frac{3}{4}, \frac{5}{7}$

$\frac{1}{2}, \frac{5}{7}, \frac{3}{4}, \frac{9}{10}$

$\frac{9}{10}, \frac{1}{2}, \frac{3}{4}, \frac{5}{7}$

$\frac{1}{2}, \frac{5}{7}, \frac{9}{10}, \frac{3}{4}$

$\frac{3}{4}, \frac{9}{10}, \frac{1}{2}, \frac{5}{7}$

Explanation

Convert the fractions so that they all share the same denominator.

$\frac{1}{2}\cdot \frac{70}{70}=\frac{70}{140}$

$\frac{3}{4}\cdot \frac{35}{35}=\frac{105}{140}$

$\frac{5}{7}\cdot \frac{20}{20}=\frac{100}{140}$

$\frac{9}{10}\cdot \frac{14}{14}=\frac{126}{140}$

Now, look at the numerators and order them from the least to the greatest:

$\frac{1}{2}, \frac{5}{7}, \frac{3}{4}, \frac{9}{10}$

Simplify.

$\frac{5}{x}\cdot\frac{x^2}{10}$

$\frac{x}{2}$

$\frac{2}{x}$

$\frac{x^2}{2}$

$\frac{5x^2}{10x}$

$\frac{1}{2}$

Explanation

When multiplying fractions, find a way to reduce any of the fractions before multplying them out.

For example, since is a multiple of , you would cancel out the and that becomes a and the becomes a .

The same goes for and . The becomes and the goes to .

Overall, the fractions to multiply becomes

$\frac{1}{1}\cdot \frac{x}{2}$ . Answer should be $\frac{x}{2}$ .

$\frac{5x^2}{10x}$ is not correct because it's not reduced.

Solve,

$\frac{2}{13}+\frac{4}{13}=?$

$\frac{6}{13}$

$\frac{6}{26}$

$\frac{3}{13}$

$\frac{2}{13}$

Explanation

Since the denominators for the fractions are the same, keep the denominator and add the numerators.

$\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}$

After a discount, a car costs $\$6,000$ . How much did the car cost before the discount?

$\$8,000$

$\$4,500$

$\$7,000$

$\$6,000$

Explanation

Let be the cost of the car before the discount. Since we know that the car at a discount costs $\$6,000$ , we can write the following equation:

Now, solve for to find the cost of the car before the discount.

$x=\frac{6000}{0.75}$

The car originally cost $\$8,000$ before the discount was applied.

$\frac{5}{6}\div \frac{1}{12}=?$

$\frac{5}{72}$

$\frac{1}{2}$

Explanation

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

$\frac{5}{6}\div \frac{1}{12}=\frac{5}{6}\times\frac{12}{1}=\frac{60}{6}=10$