Numbers and Operations

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SSAT Middle Level Quantitative › Numbers and Operations

Questions 1 - 10

Evaluate:

$8 \frac{4}{5} - 4 \frac{1}{3}$

$4 \frac{7}{15 }$

$4 \frac{1}{2 }$

$4 \frac{1}{3 }$

$4 \frac{8}{15 }$

$4 \frac{3}{5 }$

Explanation

Rewrite as the difference of improper fractions:

$8 \frac{4}{5} - 4 \frac{1}{3} = \frac{8 \times 5 + 4}{5} - \frac{4 \times 3 + 1}{3} = \frac{44}{5} - \frac{13}{3}$

Rewrite with a common denominator, then subtract numerators:

$\frac{44}{5} - \frac{13}{3} = \frac{44\times 3}{5 \times 3} - \frac{5 \times13}{5 \times3} = \frac{132}{15 } - \frac{65}{15 } = \frac{67}{15 }$

Rewrite as a mixed number:

$67\div 15 = 4 \textrm{ R } 7$

$\frac{67}{15 } = 4 \frac{7}{15 }$

$8\times\frac{1}{7}=$

$\frac{8}{7}=1\frac{1}{7}$

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

$\frac{6}{7}$

$\frac{5}{7}$

$\frac{4}{7}$

Explanation

$8\times\frac{1}{7}$ means the same thing as adding $\frac{1}{7}$ eight times.

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

8 7 number line

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

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.

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?

$\frac{1}{6}lb$

$\frac{1}{3}lb$

$\frac{1}{12}lb$

$\frac{3}{2}lb$

$\frac{1}{5}lb$

Explanation

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

To solve $\frac{1}{2}\div3$ we multiply by the reciprocal.

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

1 6

$\frac{3}{8}$ 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.

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

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

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?