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SSAT Middle Level Math : Numbers and Operations

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Example Questions

Example Question #651 : Numbers And Operations

Rectangles

Each of the rectangles in the above diagram has the same area, and is divided into squares of the same size and shape; the area of the shaded region is 10. Give the area of one of the four rectangles.

Possible Answers:

$2\frac{1}{2}$

$3\frac{1}{3}$

$2\frac{1}{3}$

$2\frac{2}{3}$

Correct answer:

$2\frac{2}{3}$

Explanation:

Each rectangle is divided into fourths, and fifteen fourths are shaded. If we let be the area of one rectangle, then, since the shaded region has area 10,

$\frac{15}{4} A = 10$

$\frac{4} {15}\cdot \frac{15}{4} A = \frac{4} {15}\cdot 10$

$A = \frac{4} {15}\cdot 10 = \frac{4} {15}\cdot \frac{10}{1} = \frac{40}{15} = \frac{8}{3} = 2\frac{2}{3}$

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Example Question #541 : Number & Operations With Fractions

Solve:

$\small \frac{3}{12}\div\frac{1}{3}$

Possible Answers:

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

$\small \frac{3}{36}$

$\frac{3}{4}$

$\small \frac{12}9{}$

$\small \frac{36}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

$\small \frac{3}{12}\div\frac{1}{3}$

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.

$\small \small \frac{3}{12}\times\frac{3}{1}=\frac{9}{12}$

$\frac{9}{12}$ can be reduced because both and are divisible by

$\frac{9}{12}\div\frac{3}{3}=\frac{3}{4}$

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Example Question #542 : Number & Operations With Fractions

Solve:

$\small \frac{7}{8}\div\frac{1}{4}$

Possible Answers:

$\small \frac{7}{32}$

$\small \frac{8}{28}$

$3\frac{1}{2}$

$\small \frac{9}{15}$

$\small \frac{32}{7}$

Correct answer:

$3\frac{1}{2}$

Explanation:

$\small \frac{7}{8}\div\frac{1}{4}$

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.

$\small \frac{7}{8}\times\frac{4}{1}=\frac{28}{8}$

$\frac{28}{8}=3\frac{4}{8}=3\frac{1}{2}$ because can go into three times, with left over.

$\frac{4}{8}$ can be reduced because both and are divisible by .

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

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Example Question #651 : Numbers And Operations

$\small 10$ people are sharing a $\small 73$ -pound bag of peanuts. If the peanuts are distributed evenly, how many pounds of peanuts will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 6$ and $\small 7$

$\small 8$ and $\small 9$

$\small 4$ and $\small 5$

$\small 5$ and $\small 6$

$\small 7$ and $\small 8$

Correct answer:

$\small 7$ and $\small 8$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{73}{10}=7\frac{3}{10}$

$\small 10$ can go into $\small 73$ only $\small 7$ times with $\small \frac{3}{10}$ left over.

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Example Question #633 : Number & Operations With Fractions

How many $\frac{1}{2}$ cup servings are in cups of chocolate chips?

Possible Answers:

Correct answer:

Explanation:

Because we want to know how many $\frac{1}{2}\ cup$ servings are in cups, we are dividing by $\frac{1}{2}$ .

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

$\frac{6}{1}\times\frac{2}{1}=\frac{12}{1}=12$

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Example Question #652 : Numbers And Operations

Solve the following:

$\small \frac{1}{2}\div\frac{2}{3}$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

$\small \frac{1}{2}\div\frac{2}{3}$

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.

$\small \frac{1}{2}\times\frac{3}{2}=\frac{3}{4}$

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Example Question #2 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

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?

Possible Answers:

$\frac{8}{7}lb$

$\frac{1}{4}lb$

$\frac{1}{14}lb$

$\frac{2}{7}lb$

$\frac{14}{2}lb$

Correct answer:

$\frac{1}{14}lb$

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

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Example Question #5 : Divide Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7

$\small \frac{12}{13}\div\frac{2}{1}$

Possible Answers:

$\small \frac{9}{28}$

$\small \frac{12}{26}$

$\small \frac{10}{22}$

$\small \frac{14}{32}$

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

Correct answer:

$\small \frac{12}{26}$

Explanation:

$\small \frac{12}{13}\div\frac{2}{1}$

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.

$\small \frac{12}{13}\times\frac{1}{2}=\frac{12}{26}$

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Example Question #1321 : Ssat Middle Level Quantitative (Math)

Hydraulic fracturing is a process used by gas companies to rupture and collect pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{3}{4}\textup{ miles}$ in length and occupies an area of $\frac{1}{2}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{3}{5}\textup{ miles}$

$\frac{6}{7}\textup{ miles}$

$\frac{1}{3}\textup{ miles}$

$\frac{2}{5}\textup{ miles}$

$\frac{2}{3}\textup{ miles}$

Correct answer:

$\frac{2}{3}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{1}{2}\ miles^2=\frac{3}{4}\ miles\times Width$

Divide both sides by $\frac{3}{4}\ miles$

$\frac{\frac{1}{2}\ miles^2}{\frac{3}{4}\ miles}=\frac{\frac{3}{4}\ miles \times Width}{\frac{3}{4}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{3}{4}\ miles$

$\frac{3}{4}\ miles\rightarrow \frac{4}{3}\ miles$

Simplify and rewrite.

$Width=\frac{4}{3} \times \frac{1}{2}$

Multiply and solve.

$Width=\frac{4}{6}$

Reduce.

$Width=\frac{2}{3}\ miles$

The width of the fracking site is $\frac{2}{3}\ miles$

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Example Question #1321 : Ssat Middle Level Quantitative (Math)

How many $\frac{1}{3}\textup{ cup}$ servings are in five cups of chocolate chips?

Possible Answers:

Correct answer:

Explanation:

Because we want to know how many $\frac{1}{3}\textup{ cup}$ servings are in cups, we are dividing by $\frac{1}{3}$ .

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

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

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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 #651 : Numbers And Operations

Example Question #541 : Number & Operations With Fractions

Example Question #542 : Number & Operations With Fractions

Example Question #651 : Numbers And Operations

Example Question #633 : Number & Operations With Fractions

Example Question #652 : Numbers And Operations

Example Question #2 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #5 : Divide Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7

Example Question #1321 : Ssat Middle Level Quantitative (Math)

Example Question #1321 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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