Numbers and Operations

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SSAT Middle Level Quantitative › Numbers and Operations

Questions 1 - 10

Which of the following statements demonstrates the associative property of addition?

None of the examples in the other responses demonstrates the associative property of addition.

Explanation

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

demonstrates this property, so it is the correct choice.

$3\times\frac{1}{7}=$

$\frac{3}{7}$

$\frac{2}{7}$

$\frac{1}{7}$

$\frac{4}{7}$

$\frac{5}{7}$

Explanation

$3\times\frac{1}{7}$ means the same thing as adding $\frac{1}{7}$ three times.

On our number line, we can make jumps of $\frac{1}{7}$

3 7 number line

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

A baker used $\frac{4}{8}$ of a package of sprinkles and $\frac{6}{8}$ of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

$\frac{2}{8}$

$\frac{3}{8}$

$\frac{4}{8}$

$\frac{5}{8}$

$\frac{6}{8}$

Explanation

The phrase, "how much more" tells as that we want to find the difference, so we subtract.

$\frac{6}{8}-\frac{4}{8}=\frac{2}{8}$

2 8

Aubtin has gallons of soda. Each glass holds $\frac{1}{3}$ of a gallon. How many glasses can he fill?

Explanation

Think: How many $\frac{1}{3}$ s are in wholes?

To solve $2\div\frac{1}{3}$ we multiply by the reciprocal

$\frac{2}{1}\times\frac{3}{1}=\frac{6}{1}=6$

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.