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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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All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1303 : Ssat Middle Level Quantitative (Math)

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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Example Question #22 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Tim has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

Possible Answers:

$\frac{7}{2}lb$

$\frac{1}{28}lb$

$\frac{7}{3}lb$

$\frac{1}{7}lb$

$\frac{1}{21}lb$

Correct answer:

$\frac{1}{21}lb$

Explanation:

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div7$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{7}=\frac{1}{21}$

1 21

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Example Question #1301 : Ssat Middle Level Quantitative (Math)

David has $\frac{1}{3}lb$ of peanuts that he wants to divide evenly into bags. How much will each bag of peanuts weigh?

Possible Answers:

$\frac{1}{15}lb$

$\frac{3}{8}lb$

$\frac{8}{3}lb$

$\frac{5}{3}lb$

$\frac{1}{5}lb$

Correct answer:

$\frac{1}{15}lb$

Explanation:

We are splitting $\frac{1}{3}$ into equal groups, so we are dividing $\frac{1}{3}$ by .

To solve $\frac{1}{3}\div5$ we multiply by the reciprocal.

$\frac{1}{3}\times\frac{1}{5}=\frac{1}{15}$

1 15

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Example Question #1302 : Ssat Middle Level Quantitative (Math)

Solve the following problem.

$\frac{3}{11}\div \frac{5}{23}=$

Possible Answers:

$\frac{1}{3}$

$1 \frac{14}{55}$

$1\frac{3}{7}$

$1\frac{1}{9}$

Correct answer:

$1 \frac{14}{55}$

Explanation:

When dividing fractions, you invert the second fraction and multiply.

$\frac{3}{11}\times \frac{23}{5}=\frac{69}{55}=1\frac{14}{55}$

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Example Question #1303 : Ssat Middle Level Quantitative (Math)

How many $\frac{1}{4}\textup{ cup}$ servings are in cups of chocolate chips?

Possible Answers:

Correct answer:

Explanation:

Because we want to know how many $\frac{1}{4}\textup{ cup}$ servings are in cups, we are dividing by $\frac{1}{4}$ .

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{3}{1}\times\frac{4}{1}=\frac{12}{1}=12$

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Example Question #1304 : Ssat Middle Level Quantitative (Math)

Solve:

$\small \frac{3}{4}\div\frac{2}{3}$

Possible Answers:

$\small \frac{7}{8}$

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

$\small \frac{8}{7}$

$\small \frac{8}{9}$

$1\frac{1}{}8$

Correct answer:

$1\frac{1}{}8$

Explanation:

$\small \frac{3}{4}\div\frac{2}{3}$

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

$\small \frac{3}{4}\times\frac{3}{2}=\frac{9}{8}$

$\frac{9}{8}=1\frac{1}{8}$ because can go into one time with left over.

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Example Question #2052 : Numbers And Operations

Solve:

$\small \frac{5}{8}\div\frac{1}{2}$

Possible Answers:

$\small \frac{5}{11}$

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

$\small \frac{8}{10}$

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

$1\frac{1}{4}$

Correct answer:

$1\frac{1}{4}$

Explanation:

$\small \frac{5}{8}\div\frac{1}{2}$

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

$\small \frac{5}{8}\times\frac{2}{1}=\frac{10}{8}$

$\frac{10}{8}=1\frac{2}{8}=1\frac{1}{4}$ because can go into one time with left over.

$\frac{2}{8}\div\frac{2}{2}=\frac{1}{4}$

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Example Question #1302 : Ssat Middle Level Quantitative (Math)

Rectangle 1

The above rectangle is divided into squares of equal size. The shaded region has area 45. Give the area of the entire rectangle.

Possible Answers:

$71\frac{3}{7}$

$57 \frac{1}{7}$

$51\frac{3}{7}$

$64 \frac{2}{7}$

Correct answer:

$64 \frac{2}{7}$

Explanation:

Seven of the ten squares of the rectangle - $\frac{7}{10 }$ of it - is shaded in. If we let be the area of the rectangle, then

$A \cdot \frac{7}{10 } = 45$

$A \cdot \frac{7}{10 } \div \frac{7}{10 } = 45 \div \frac{7}{10 }$

$A = 45 \cdot \frac{10 } {7} = \frac{45 }{1}\cdot \frac{10 } {7} = \frac{450}{7}$

Divide 450 by 7 - the quotient is 64 and the remainder is 2, so the area can be written as $A = 64 \frac{2}{7}$ .

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Example Question #165 : How To Divide Fractions

Hexagon

The above hexagon is divided into triangles of equal size. The area of the shaded region is 72. Give the area of the entire hexagon.

Possible Answers:

$143 \frac{3}{7}$

$123 \frac{3}{7}$

$133 \frac{3}{7}$

$113 \frac{3}{7}$

Correct answer:

$123 \frac{3}{7}$

Explanation:

7 of the 12 triangles - that is, $\frac{7}{12}$ of the hexagon - is shaded, so, if we let be the area of the hexagon,

$\frac{7}{12} \cdot A = 72$

Solving:

$\frac{7}{12} \cdot A \div \frac{7}{12} = 72 \div \frac{7}{12}$

$A = 72 \cdot \frac{12}{7} = \frac{72 }{1}\cdot \frac{12}{7} = \frac{864}{7}$

$864 \div 7 = 123 \textrm{ R }3$ ,

so the area can be written as $123 \frac{3}{7}$ .

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Example Question #1311 : Ssat Middle Level Quantitative (Math)

These figures are NOT necessarily drawn to scale

The shaded portions Figure 1 and Figure 2 are of equal area. Figure 1 has area 36; what is the area of Figure 2?

Possible Answers:

Correct answer:

Explanation:

Figure 1 is a rectangle divided into 24 squares of equal size; 8 of the squares are shaded, which means that $\frac{8}{24} = \frac{8 \div 8 }{24 \div 8} = \frac{1}{3}$ of Figure 1 is shaded. Since Figure 1 has area 36, the shaded portion has area

$\frac{1}{3} \times 36 = \frac{36}{3} = 12$ .

Figure 2 is a triangle divided into 4 triangles of equal size; 1 is shaded, which means that $\frac{1}{4}$ of Figure 2 is shaded. Since this shaded portion has area equal to that of Figure 1, which is 12, the area of all of Figure 2 is

$12 \div \frac{1}{4} = 12 \times 4 = 48$ .

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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 #1303 : Ssat Middle Level Quantitative (Math)

Example Question #22 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #1301 : Ssat Middle Level Quantitative (Math)

Example Question #1302 : Ssat Middle Level Quantitative (Math)

Example Question #1303 : Ssat Middle Level Quantitative (Math)

Example Question #1304 : Ssat Middle Level Quantitative (Math)

Example Question #2052 : Numbers And Operations

Example Question #1302 : Ssat Middle Level Quantitative (Math)

Example Question #165 : How To Divide Fractions

Example Question #1311 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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