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SSAT Middle Level Math : How to divide fractions

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

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Example Questions

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Example Question #4 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 5$ people are sharing a $\small 43$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 12$ and $\small 13$

$\small 10$ and $\small 11$

$\small 8$ and $\small 9$

$\small 9$ and

$\small 11$ and $\small 12$

Correct answer:

$\small 8$ and $\small 9$

Explanation:

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

$\small \frac{43}{5}=8\frac{3}{5}$

$\small 5$ can go into $\small 43$ only $\small 8$ times with $\small \frac{3}{5}$ left over.

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Example Question #5 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 9$ people are sharing a $\small 82$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 6$ and $\small 7$

$\small 9$ and $\small 10$

$\small 7$ and $\small 8$

$\small 8$ and $\small 9$

$\small 10$ and $\small 11$

Correct answer:

$\small 9$ and $\small 10$

Explanation:

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

$\small \frac{82}{9}=9\frac{1}{9}$

$\small 9$ and go into $\small 82$ only $\small 9$ times and $\small \frac{1}{9}$ will be left over.

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Example Question #6 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 8$ people are sharing a $\small 42$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 5$ and $\small 6$

$\small 9$ and $\small 10$

$\small 6$ and $\small 7$

$\small 7$ and $\small 8$

$\small 8$ and $\small 9$

Correct answer:

$\small 5$ and $\small 6$

Explanation:

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

$\small \frac{42}{8}=5\frac{2}{8}$

$\small 8$ can go into $\small 42$ only $\small 5$ times with $\small \frac{2}{8}$ left over.

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Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 3$ people are sharing a $\small 34$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 10$ and $\small 11$

$\small 8$ and $\small 9$

$\small 9$ and $\small 10$

$\small 12$ and $\small 13$

$\small 11$ and $\small 12$

Correct answer:

$\small 11$ and $\small 12$

Explanation:

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

$\small \frac{34}{3}=11\frac{1}{3}$

$\small 3$ can go into $\small 34$ only $\small 11$ times with $\small \frac{1}{3}$ left over.

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Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 4$ people are sharing a $\small 39$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 10$ and $\small 11$

$\small 11$ and $\small 12$

$\small 8$ and $\small 9$

$\small 7$ and $\small 8$

$\small 9$ and $\small 10$

Correct answer:

$\small 9$ and $\small 10$

Explanation:

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

$\small \frac{39}{4}=9\frac{3}{4}$

$\small 4$ can go into $\small 39$ only $\small 9$ times with $\small \frac{3}{4}$ left over.

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Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 5$ people are sharing a $\small 72$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 11$ and $\small 12$

$\small 14$ and $\small 15$

$\small 13$ and $\small 14$

$\small 10$ and $\small 11$

$\small 12$ and $\small 13$

Correct answer:

$\small 14$ and $\small 15$

Explanation:

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

$\small \frac{72}{5}=14\frac{2}{5}$

$\small 5$ cand go into $\small 72$ only $\small 14$ times with $\small \frac{2}{5}$ left over.

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Example Question #10 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 7$ people are sharing a $\small 40$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 3$ and $\small 4$

$\small 5$ and $\small 6$

$\small 6$ and $\small 7$

$\small 7$ and $\small 8$

$\small 4$ and $\small 5$

Correct answer:

$\small 5$ and $\small 6$

Explanation:

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

$\small \frac{40}{7}=5\frac{5}{7}$

$\small 7$ can be divided into $\small 40$ only $\small 5$ times, with $\small \frac{5}{7}$ left over.

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Example Question #31 : Number & Operations With Fractions

$\small 6$ people are sharing a $\small \small 35$ pould bag of peanuts. How much 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 $\small 9$

$\small 5$ and $\small 6$

$\small 7$ and $\small 8$

$\small 9$ and $\small 10$

Correct answer:

$\small 5$ and $\small 6$

Explanation:

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

$\small \frac{35}{6}=5\frac{5}{6}$

$\small 6$ can be divided into $\small 35$ only $\small 5$ times with $\small \frac{5}{6}$ left over.

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Example Question #51 : Fractions

$\small 3$ people are sharing a $\small 13$ -pound bag of peanuts. How much 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 $\small 5$

$\small 7$ and $\small 8$

$\small 5$ and $\small 6$

$\small 3$ and $\small 4$

Correct answer:

$\small 4$ and $\small 5$

Explanation:

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

$\small \frac{13}{3}=4\frac{1}{3}$

$\small 3$ can go into $\small 13$ only $\small 4$ times with $\small \frac{1}{3}$ left over.

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Example Question #90 : Grade 6

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$4\tfrac{2}{5}\textup{ miles}$

$4\tfrac{3}{5}\textup{ miles}$

$4\tfrac{1}{5}\textup{ miles}$

$4\tfrac{4}{5}\textup{ miles}$

$4\textup{ miles}$

Correct answer:

$4\tfrac{1}{5}\textup{ miles}$

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 $\text{Width}$ .

$\frac{3}{5}\ miles^2=\frac{1}{7}\ miles\times Width$

Divide both sides by $\frac{1}{7}\ miles$

$\frac{\frac{3}{5}\ miles^2}{\frac{1}{7}\ miles}=\frac{\frac{1}{7}\ miles \times Width}{\frac{1}{7}\ miles}$

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

Find the reciprocal of $\frac{1}{7}\ miles$

$\frac{1}{7}\ miles\rightarrow \frac{7}{1}\ miles$

Simplify and rewrite.

$Width=\frac{7}{1} \times \frac{3}{5}$

Multiply and solve.

$Width=\frac{21}{5}$

Reduce.

$Width=4\tfrac{1}{5}\ miles$

The width of the fracking site is $4\tfrac{1}{5}\ miles$

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SSAT Middle Level Math : How to divide fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #4 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #5 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #6 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #10 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #31 : Number & Operations With Fractions

Example Question #51 : Fractions

Example Question #90 : Grade 6

All SSAT Middle Level Math Resources

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