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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #1953 : Ssat Middle Level Quantitative (Math)

Rectangle 1

The above rectangle, which is divided into squares of equal size, has area $33 \frac{3}{5}$ . Give the area of the shaded portion of the rectangle.

Possible Answers:

Correct answer:

Explanation:

The area of the rectangle can be rewritten as

$33 \frac{3}{5} = \frac{33 \times 5+ 3}{5} = \frac{165+3}{5} = \frac{168}{5}$

5 out of the 12 segments, or $\frac{5}{12}$ , of the rectangle, is shaded, so the area of the shaded region is

$\frac{5}{12} \times \frac{168}{5}$

Cross-cancelling:

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

= 14

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Example Question #1954 : Ssat Middle Level Quantitative (Math)

Stars

Each of the stars in the above diagram is divided into parts with the size and shape, and each star has area 14. Give the area of the shaded region.

Possible Answers:

$64\frac{2}{5}$

$58 \frac{3}{5}$

$66 \frac{4}{5}$

$62 \frac{2}{5}$

Correct answer:

$64\frac{2}{5}$

Explanation:

Four whole stars and three out of five parts of a fifth are shaded - this is $4 \frac{3}{5 }$ stars. Each star has area 14, so the shaded region has area

$4 \frac{3}{5 } \times 14 = \frac{23}{5 } \times \frac{14 }{1} = \frac{322}{5 } = 64 \frac{2}{5}$ .

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Example Question #1955 : Ssat Middle Level Quantitative (Math)

Pentagon

The above pentagon, which is divided into triangles of equal size and shape, has area $47 \frac{1}{2 }$ .

Give the area of the shaded region.

Possible Answers:

Correct answer:

Explanation:

4 out of 5 triangles, or $\frac{4}{5}$ , of the pentagon is shaded in, so the shaded area is

$\frac{4}{5} \times 47 \frac{1}{2 }$

$= \frac{4}{5} \times \frac{47 \times 2 + 1}{2 }$

$= \frac{4}{5} \times \frac{95}{2 }$

Cross-cancelling:

$= \frac{2}{1} \times \frac{19}{1 }$

$= 2 \times 19 = 38$

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Example Question #261 : Number & Operations With Fractions

Solve:

$\small \frac{7}{8}\times\frac{1}{3}$

Possible Answers:

$\small \frac{7}{24}$

$\small \frac{4}{5}$

$\small \frac{9}{11}$

$\small \frac{7}{21}$

$\small \frac{5}{27}$

Correct answer:

$\small \frac{7}{24}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{7}{8}\times\frac{1}{3}=\frac{7}{24}$

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Example Question #262 : Number & Operations With Fractions

Solve:

$\small \frac{1}{5}\times\frac{1}{8}$

Possible Answers:

$\small \frac{1}{40}$

$\small \frac{1}{20}$

$\small \frac{2}{40}$

$\small \frac{1}{12}$

$\small \frac{5}{6}$

Correct answer:

$\small \frac{1}{40}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{1}{5}\times\frac{1}{8}=\frac{1}{40}$

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Example Question #1951 : Ssat Middle Level Quantitative (Math)

Dan collected $\small \frac{1}{4}$ of a bag of leaves. Sean collected $\small 6$ times as many bags as Dan. How many bags did Sean collect?

Possible Answers:

$\small 3$

$\small 1\frac{1}{2}$

$\small 1$

$\small 2\frac{2}{4}$

Correct answer:

$\small 1\frac{1}{2}$

Explanation:

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{6}{1}\times\frac{1}{4}=\frac{6}{4}$

$\small \frac{6}{4}=1\frac{2}{4}$ Because can go into $\small 6$ only $\small 1$ time and $\small \frac{2}{4}$ is left over.

Sean collected $\small 1\frac{2}{4}$ bags of leaves.

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

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Example Question #1956 : Ssat Middle Level Quantitative (Math)

Solve the following:

$\frac{1}{8} \cdot \frac{3}{5}$

Possible Answers:

$\frac{29}{40}$

$\frac{4}{40}$

$\frac{3}{13}$

$\frac{3}{40}$

$\frac{4}{13}$

Correct answer:

$\frac{3}{40}$

Explanation:

To multiply fractions, we will multiply the numerator together, then we will multiply the denominators together. So, we get

$\frac{1}{8} \cdot \frac{3}{5}$

$\frac{1 \cdot 3}{8 \cdot 5}$

$\frac{3}{40}$

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Example Question #1291 : Numbers And Operations

Evaluate:

1.2 + 0.6 (0.5 + 2.3)

Possible Answers:

3.8

2.88

3.08

1.98

5.04

Correct answer:

2.88

Explanation:

By order of operations, perform the rightmost addition (the one within the parentheses) first, the multiplication second. and the leftmost addition last.

$1.2 + 0.6 (0.5 + 2.3) = 1.2 + 0.6 \cdot 2.8 = 1.2 + 1.68 = 2.88$

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Example Question #1 : Multiply A Fraction And A Whole Number By Understanding A Multiple Of A/B As A Multiple Of 1/B: Ccss.Math.Content.4.Nf.B.4b

Select the answer choice that is equal to the following:

$3\times\frac{2}{5}$

Possible Answers:

$5\times\frac{2}{5}$

$5\times\frac{1}{5}$

$3\times\frac{1}{5}$

$6\times\frac{1}{5}$

$4\times\frac{2}{5}$

Correct answer:

$6\times\frac{1}{5}$

Explanation:

When we multiply a whole number by a fraction, we multiply the whole number by the numerator, and the denominator stays the same.

$\frac{3}{1}\times\frac{2}{5}=\frac{6}{5}$

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

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Example Question #244 : Fractions

Solve the following:

$\small \frac{3}{4}\times3$

Possible Answers:

$\small \frac{9}{4}$

$\small \frac{1}{3}$

$\small \frac{3}{4}$

$\small \frac{1}{2}$

$\small \frac{4}{9}$

Correct answer:

$\small \frac{9}{4}$

Explanation:

$\small \frac{3}{4}\times3$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal.

$\small \small \frac{3}{4}\times\frac{3}{1}=\frac{9}{4}$

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1953 : Ssat Middle Level Quantitative (Math)

Example Question #1954 : Ssat Middle Level Quantitative (Math)

Example Question #1955 : Ssat Middle Level Quantitative (Math)

Example Question #261 : Number & Operations With Fractions

Example Question #262 : Number & Operations With Fractions

Example Question #1951 : Ssat Middle Level Quantitative (Math)

Example Question #1956 : Ssat Middle Level Quantitative (Math)

Example Question #1291 : Numbers And Operations

Example Question #1 : Multiply A Fraction And A Whole Number By Understanding A Multiple Of A/B As A Multiple Of 1/B: Ccss.Math.Content.4.Nf.B.4b

Example Question #244 : Fractions

All SSAT Middle Level Math Resources

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