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SSAT Middle Level Math : Fractions

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

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All SSAT Middle Level Math Resources

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Example Questions

Example Question #543 : Number & Operations With Fractions

Solve:

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

Possible Answers:

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

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

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

$\frac{3}{4}$

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

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 #181 : Operations With Fractions And Whole Numbers

Solve:

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

Possible Answers:

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

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

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

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

$3\frac{1}{2}$

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 #1081 : Common Core Math: Grade 5

$\small 10$ 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 $\small 7$

$\small 4$ and $\small 5$

$\small 5$ and $\small 6$

$\small 8$ and $\small 9$

$\small 7$ 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 #174 : How To Divide 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 #1 : Divide Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7

Solve the following:

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

Possible Answers:

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

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

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

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

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

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 #5 : 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:

$\frac{1}{14}lb$

$\frac{8}{7}lb$

$\frac{1}{4}lb$

$\frac{14}{2}lb$

$\frac{2}{7}lb$

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 #402 : Fractions

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

Possible Answers:

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

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

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

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

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

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 #2 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

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:

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

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

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

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

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

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 #1491 : Common Core Math: Grade 5

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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Example Question #476 : Concepts

$1 \frac{1}{2} + 2 \frac{3}{4} =$

Possible Answers:

4.7

3.25

4.5

3.75

4.25

Correct answer:

4.25

Explanation:

I think the easiest way to do this problem is to make a common denominator. 4 is the smallest common denominator.

$2 \frac{3}{4}$ is equivalent to $\frac{11}{4}$ .

When you add $\frac{6}{4}$ and $\frac{11}{4}$ you get $\frac{17}{4}$ .

$\frac{17}{4}$ reduces to $4 \frac{1}{4}}$ and is equivalent to 4.25 .

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SSAT Middle Level Math : Fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #543 : Number & Operations With Fractions

Example Question #181 : Operations With Fractions And Whole Numbers

Example Question #1081 : Common Core Math: Grade 5

Example Question #174 : How To Divide Fractions

Example Question #1 : Divide Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7

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

Example Question #402 : Fractions

Example Question #2 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #1491 : Common Core Math: Grade 5

Example Question #476 : Concepts

All SSAT Middle Level Math Resources

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