Numbers and Operations

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SSAT Middle Level: Quantitative › Numbers and Operations

Questions 1 - 10

How many of the following four numbers are elements of the set $B = \left \{ x ; | ; \frac{2}{5}< x < \frac{3}{5}\right \} ?$ ?

(A)

(B)

(C)

(D)

Two

Three

Four

None

One

Explanation

$\frac{2}{5} = 2 \div 5 = 0.4$ and $\frac{3}{5} = 3 \div 5 = 0.6$ , so we are looking for numbers that fall between 0.4 and 0.6 exclusive. Of the four choices, 0.44 and 0.55 fall between these numbers. The correct response is two.

Christine 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?

$\frac{1}{14}lb$

$\frac{14}{2}lb$

$\frac{8}{7}lb$

$\frac{2}{7}lb$

$\frac{1}{4}lb$

Explanation

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

To solve $\frac{1}{2}\div7$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{7}=\frac{1}{14}$

1 14

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

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

$\frac{2}{3}$

$\frac{1}{3}$

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

$\frac{4}{3}=1\frac{1}{3}$

$\frac{5}{3}=1\frac{2}{3}$

Explanation

$2\times\frac{1}{3}$ means the same thing as adding $\frac{1}{3}$ two times.

On our number line, we can make jumps of $\frac{1}{3}$

2 3 number line

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

$\frac{3}{7}$

$\frac{2}{7}$

$\frac{1}{7}$

$\frac{4}{7}$

$\frac{5}{7}$

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

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

$\frac{2}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

$\frac{5}{7}$

$\frac{6}{7}$

Explanation

$2\times\frac{1}{7}$ means the same thing as adding $\frac{1}{7}$ two times.

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

2 7 number line

Andrew 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 $13\div\frac{1}{3}$ we multiply by the reciprocal

$\frac{13}{1}\times\frac{3}{1}=\frac{39}{1}=39$

Select the fraction model that shows the difference of $\frac{6}{8}-\frac{3}{8}$

3 8

3 6

3 4

4 8

5 8

Explanation

$\frac{6}{8}-\frac{3}{8}=\frac{3}{8}$

The fraction model is broken up into eight pieces and three of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

A soccer team played 20 games, winning 5 of them. The ratio of wins to losses is

$1\ to\ 3$

$1\ to\ 4$

$3\ to\ 1$

$4\ to\ 1$

$1\ to\ 5$

Explanation

The ratio of wins to losses requires knowing the number of wins and losses. The question says that there are 5 wins. That means there must have been

losses.

The ratio of wins to losses is thus 5 to 15 or 1 to 3.

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?