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SSAT Middle Level Math : How to divide fractions

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

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:

$\frac{7}{3}lb$

$\frac{1}{7}lb$

$\frac{1}{21}lb$

$\frac{1}{28}lb$

$\frac{7}{2}lb$

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 #161 : How To Divide Fractions

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:

$\frac{1}{15}lb$

$\frac{5}{3}lb$

$\frac{3}{8}lb$

$\frac{1}{5}lb$

$\frac{8}{3}lb$

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 #161 : How To Divide Fractions

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 #164 : How To Divide Fractions

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 #545 : Number & Operations With Fractions

Solve:

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

Possible Answers:

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

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

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

$1\frac{1}{}8$

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

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 #546 : Number & Operations With Fractions

Solve:

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

Possible Answers:

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

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

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

$1\frac{1}{4}$

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

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 #167 : How To Divide Fractions

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:

$71\frac{3}{7}$

$51\frac{3}{7}$

$57 \frac{1}{7}$

$64 \frac{2}{7}$

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 #161 : 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:

$143 \frac{3}{7}$

$123 \frac{3}{7}$

$113 \frac{3}{7}$

$133 \frac{3}{7}$

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 #161 : Fractions

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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Example Question #162 : How To Divide Fractions

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:

$3\frac{1}{3}$

$2\frac{2}{3}$

$2\frac{1}{2}$

$2\frac{1}{3}$

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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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 #1301 : Ssat Middle Level Quantitative (Math)

Example Question #161 : How To Divide Fractions

Example Question #161 : How To Divide Fractions

Example Question #164 : How To Divide Fractions

Example Question #545 : Number & Operations With Fractions

Example Question #546 : Number & Operations With Fractions

Example Question #167 : How To Divide Fractions

Example Question #161 : How To Divide Fractions

Example Question #161 : Fractions

Example Question #162 : How To Divide Fractions

All SSAT Middle Level Math Resources

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