SSAT Middle Level Quantitative - SSAT Middle Level Quantitative (Math)

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

$\frac{3}{8}$ is equal to which of the options below?

$\frac{2}{8}+\frac{1}{8}$

$\frac{4}{8}+\frac{1}{8}$

$\frac{1}{8}+\frac{1}{8}$

$\frac{3}{8}+\frac{2}{8}$

$\frac{3}{8}+\frac{1}{8}$

Explanation

When we add fractions, we have to have common denominators and we only add the numerators.

$\frac{2}{8}+\frac{1}{8}=\frac{3}{8}$

What number is eight hundred sixty-two and four tenths?

Explanation

In number form, eight hundred sixty-two and four tenths is . The "and" signifies the decimal, and " tenths" signifies the place value of the last decimal number.

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

$3\tfrac{3}{4}\textup{ miles}$

$3\tfrac{1}{3}\textup{ miles}$

$4\tfrac{1}{4}\textup{ miles}$

$3\tfrac{5}{7}\textup{ miles}$

$5\tfrac{3}{4}\textup{ miles}$

Explanation

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

Andy is having a party. If each person at a party will eat $\frac{2}{7}$ of a pound of peanuts, and there will be people at the party, how many pounds of peanuts will Andy need? Select the choice with the whole numbers that your answer will be between.

and

Explanation

$\frac{5}{1}\times\frac{2}{7}=\frac{10}{7}$

$\frac{10}{7}=1\frac{3}{7}$ because can go into one time, with left over.

$1\frac{3}{7}$ is between the whole numbers and .

Melissa has $\frac{1}{2}lb$ of gummy candies that she wants to divide evenly into bags. How much will each bag of gummy candies weigh?

$\frac{1}{16}lb$

$\frac{16}{2}lb$

$\frac{1}{7}lb$

$\frac{1}{6}lb$

$\frac{1}{9}lb$

Explanation

We are splitting $\frac{1}{2}$ into equal groups, so we are dividing $\frac{1}{2}$ by .

To solve $\frac{1}{2}\div8$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}$

1 16

On Thursday it snowed $\frac{2}{12}$ of an inch in the afternoon and $\frac{1}{12}$ of an inch in the evening. What was the total amount of snowfall on Thursday?

$\frac{3}{12}$

$\frac{4}{12}$

$\frac{5}{12}$

$\frac{6}{12}$

$\frac{7}{12}$

Explanation

To solve this problem, we are putting the amount of snowfall from the afternoon and the evening together, so we add the fractions.

$\frac{2}{12}+\frac{1}{12}=\frac{3}{12}$

3 12

Which of the following is NOT equal to $0.5 \bullet 20$ ?

$\frac{3}{4} \bullet 16$

$\frac{1}{5} \bullet 50$

$2 \bullet 5$

$\frac{2}{3} \bullet 15$

$\frac{1}{4} \bullet 40$

Explanation

All of the answer choices multiply to give you 10 except

$\frac{3}{4} \bullet 16$

so that is the correct answer.

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

Solve for :