SSAT Middle Level Quantitative - Numbers and Operations

$29\frac{5}{13}-8\frac{2}{13}$

$21\frac{3}{13}$

$22\frac{3}{13}$

$23\frac{3}{13}$

$21\frac{7}{13}$

$22\frac{7}{13}$

Explanation

When we subtract mixed numbers, we subtract whole numbers by whole numbers and fractions by fractions.

$\frac{5}{13}-\frac{2}{13}=\frac{3}{13}$

Remember, when we are subtracting fractions we must have common denominators and we only subtract the numerators.

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 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.

Multiply:

$0.58 \times 8.3$

Explanation

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

In March, there were 10 sunny days, 10 cloudy days, and 11 rainy days. How many days did it rain in March?

Explanation

Identify the number of rainy days in March: days

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

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

$\frac{13}{7}=1\frac{6}{7}$

$\frac{12}{7}=1\frac{5}{7}$

$\frac{11}{7}=1\frac{4}{7}$

$\frac{10}{7}=1\frac{3}{7}$

Explanation

$14\times\frac{1}{7}$ means the same thing as adding $\frac{1}{7}$ fourteen times.

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

14 7 number line

Add:

$\frac{6}{61}+\frac{11}{61}=$

$\frac{17}{61}$

$\frac{5}{61}$

$\frac{66}{61}$

$\frac{61}{17}$

Explanation

Add the numerators and leave the denominators the same:

$\frac{6}{61}+\frac{11}{61}=\frac{17}{61}$

Answer:

$\frac{17}{61}$

Kailynn has gallons of water. Each water bottle holds $\frac{1}{2}$ of a gallon. How many water bottles can she fill?

Explanation

Think: How many $\frac{1}{2}$ s are in wholes?

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

$\frac{2}{1}\times\frac{2}{1}=\frac{4}{1}=4$

Tom has gallons of soda. Each glass holds $\frac{1}{6}$ of a gallon. How many glasses can he fill?

Explanation

Think: How many $\frac{1}{6}$ s are in wholes?

To solve $8\div\frac{1}{6}$ we multiply by the reciprocal

$\frac{8}{1}\times\frac{6}{1}=\frac{48}{1}=48$

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?