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ISEE Middle Level Quantitative : How to multiply fractions

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Example Questions

Example Question #1 : How To Multiply Fractions

$\small \frac{3}{15}\cdot \frac{4}{5}$

Possible Answers:

$\small \frac{4}{25}$

$\small \frac{36}{15}$

$\small \frac{36}{225}$

$\small \frac{12}{225}$

$\small \frac{12}{75}$

Correct answer:

$\small \frac{4}{25}$

Explanation:

When multiplying fractions you simply multiply the numerators to find the numerator of the product, and multiply the denominators to find the denominator of the product.

$\small 3\cdot 4=12$

$\small 5\cdot 15=75$

So, our product is $\small \frac{12}{75}$ .

Since both of these numbers are divisible by three, we simplify.

$\small \frac{12}{3}=4$

$\small \frac{75}{3}= 25$

Our final answer is $\small \frac{4}{25}$ .

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Example Question #2 : How To Multiply Fractions

Which is the greater quantity?

(a) $3 \frac{1}{3} \times 4 \frac{1}{5}$

(b) $12 \frac{1}{15}$

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

Rewrite the mixed numbers as improper fractions, then multiply across:

$3 \frac{1}{3} = \frac{3\times 3 + 1}{3} = \frac{10}{3}$

$4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5}$

$3 \frac{1}{3} \times 4 \frac{1}{5} = \frac{10}{3} \times \frac{21}{5} = \frac{2}{1} \times \frac{7}{1} = 14$

$14 > 12 \frac{1}{5}$

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Example Question #3 : How To Multiply Fractions

Which is the greater quantity?

(a) $6 \frac{5}{6} \times 6$

(b)

Possible Answers:

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

Rewrite the factors as improper fractions, then multiply across:

$6 \frac{5}{6} = \frac{6\times 6 + 5}{6} = \frac{36 + 5}{6} = \frac{41}{6}$

$6 = \frac{6}{1}$

$6 \frac{5}{6} \times 6 =\frac{41}{6}\times \frac{ 6}{1}=\frac{41}{1}\times \frac{ 1}{1} = 41$

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Example Question #3 : How To Multiply Fractions

0.75 t = 0.3

$\frac{7}{4} k = \frac{7}{10}$

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

Correct answer:

(a) and (b) are equal

Explanation:

(a) 0.75 t = 0.3

$0.75 t \div 0.75 = 0.3 \div 0.75$

$t= 0.3 \div 0.75$

Divide by moving the decimal point right two places in both numbers:

$t= 30 \div 75 = 0.4$

(b) $\frac{7}{4} k = \frac{7}{10}$

$\frac{4} {7} \cdot \frac{7}{4} k =\frac{4} {7} \cdot \frac{7}{10}$

$k =\frac{4} {7} \cdot \frac{7}{10}$

Cross-cancel:

$k =\frac{2} {1} \cdot \frac{1}{5} = \frac{2} {5}$

$0.4 = \frac{4}{10 } = \frac{4\div 2}{10\div 2 } = \frac{2}{5}$ , so k = t

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Example Question #4 : How To Multiply Fractions

Which is the greater quantity?

(A) $\left ( \frac{3}{5} \right )^{3}$

(B) $0.6^{2}$

Possible Answers:

It is impossible to determine which is greater from the information given

(A) is greater

(A) and (B) are equal

(B) is greater

Correct answer:

(B) is greater

Explanation:

$\frac{3}{5} = 3 \div 5 = 0.6$ , so

$\left ( \frac{3}{5} \right )^{3} = 0.6^{3} = 0.6 \times 0.6 \times 0.6 = 0.36 \times 0.6 = 0.216$

$0.6 ^{2} = 0.6 \times 0.6 = 0.36$

0.36 > 0.216 , so $0.6^{2} > \left ( \frac{3}{5} \right )^{3}$ , making (B) greater.

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Example Question #5 : How To Multiply Fractions

Which is the greater quantity?

(A) 0.5

(B) $\left ( \frac{4}{5} \right )^{3}$

Possible Answers:

(A) is greater

(B) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

$\left ( \frac{4}{5} \right )^{3} = 0.8 ^{3} = 0.8 \times 0.8 \times 0,8 = 0.64\times 0,8 = 0.512$

Since 0.512 > 0.5 , $\left ( \frac{4}{5} \right )^{3} > 0.5$ , so (B) is greater.

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Example Question #6 : How To Multiply Fractions

Which is the greater quantity?

(A) $\left (\frac{3}{5} \right )^{2}$

(B) $1 - \left ( \frac{2}{5} \right )^{2}$

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(B) is greater

Explanation:

$\left (\frac{3}{5} \right )^{2} = \frac{3^{2}}{5^{2}} = \frac{9}{25}$

$1 - \left ( \frac{2}{5} \right )^{2} = 1- \frac{2^{2}}{5^{2}} = 1- \frac{4}{25} = \frac{25}{25}- \frac{4}{25} = \frac{25-4}{25}= \frac{21}{25}$

$\frac{21}{25} > \frac{9}{25}$ , so (B) is greater

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Example Question #2 : How To Multiply Fractions

Which is the greater quantity?

(A) $\left ( \frac{7}{25} \right )^{2}+ \left ( \frac{24}{25} \right )^{2}$

(B) $0.8^{2} + 0.6^{2}$

Possible Answers:

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

$\left ( \frac{7}{25} \right )^{2}+ \left ( \frac{24}{25} \right )^{2}$

$=\frac{7^{2}}{25^{2}} + \frac{24^{2}}{25^{2}}$

$=\frac{49}{625 } + \frac{576}{625 } = \frac{49+576}{625 } = \frac{625}{625 } = 1$

$0.8 ^{2} + 0.6^{2}$

$=0.8 \times 0.8 + 0.6 \times 0.6$

=0.64 + 0.36 = 1

The expressions are equal.

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Example Question #7 : How To Multiply Fractions

$a=1.5,\ b = 4.5$

Which is the greater quantity?

(A)

(B) a + b

Possible Answers:

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

Correct answer:

(A) is greater

Explanation:

Solve for (A):

$ab = 1.5 \cdot 4.5 = 6.75$

Solve for (B):

a + b = 1.5 + 4.5 = 6

Since 6.75>6 , ab > a+b and (A) is greater.

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Example Question #173 : Fractions

$\tfrac{3}{4} \times 12 =$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{12}$

Correct answer:

Explanation:

When dealing with problems that involve fractions and whole numbers, first convert your whole number into a fraction. You can easily do this by putting the whole number over 1.

$12 \rightarrow\tfrac{12}{1}$

$\tfrac{3}{4}\times12=\tfrac{3}{4}\times\tfrac{12}{1}$

When multiplying, multiply the numerators by each other and the denominators by each other.

$\tfrac{3}{4} \times\tfrac{12}{1} = \tfrac{3\times12}{4\times1}=\tfrac{36}{4}$

Always reduce a fraction when possible. In this case, the numerator and denominator of $\tfrac{36}{4}$ are both divisible by 4. So, it reduces to 9.

$\tfrac{36}{4}=\tfrac{36\div4}{4\div4}=\tfrac{9}{1}=9$

$\tfrac{36}{4} \rightarrow\tfrac{9}{1}\rightarrow9$

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : How to multiply fractions

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #4 : How To Multiply Fractions

Example Question #5 : How To Multiply Fractions

Example Question #6 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #7 : How To Multiply Fractions

Example Question #173 : Fractions

All ISEE Middle Level Quantitative Resources

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