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ISEE Middle Level Math : Fractions

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Example Questions

Example Question #381 : Fractions

Simplify:

$\frac{\frac{4}{x}}{(\frac{1}{x}-4x)}$

Possible Answers:

$\frac{4}{(1+4x^2)}$

$\frac{1}{(1-x^2)}$

$\frac{4}{(1-4x^2)}$

$\frac{1}{(1-4x^2)}$

$\frac{1}{(1+4x^2)}$

Correct answer:

$\frac{4}{(1-4x^2)}$

Explanation:

We can first find a common denominator for the expression in the numerator, which is . This gives us:

$\frac{\frac{4}{x}}{\left(\frac{1}{x}-\frac{4x^2}{x}\right)}=\frac{\frac{4}{x}}{\left(\frac{1-4x^2}{x}\right)}$

$=\frac{4}{x}\times \left(\frac{x}{1-4x^2}\right)$

$=\frac{4}{(1-4x^2)}$

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Example Question #382 : Fractions

Which of the following is the reciprocal of $-1 \frac {4}{5}$ ?

Possible Answers:

$-5 \frac {1}{4}$

$1 \frac {4}{5}$

$\frac {5}{9}$

$-\frac {5}{9}$

Correct answer:

$-\frac {5}{9}$

Explanation:

First, rewrite this as an improper fraction:

$-1 \frac {4}{5} =-\frac {5 \times 1+ 4}{5}= -\frac {9}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, retaining the negative sign, so the reciprocal is $-\frac {5}{9}$ .

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Example Question #383 : Fractions

Which of the following is the reciprocal of 2.8?

Possible Answers:

$\frac{5}{14}$

$\frac{2}{7}$

$-2 \frac{4}{5}$

$2 \frac{4}{5}$

Correct answer:

$\frac{5}{14}$

Explanation:

First, rewrite this as an improper fraction:

$2.8 = \frac{28}{10} = \frac{28\div 2}{10\div 2} = \frac{14}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, so the reciprocal is $\frac{5}{14}$ .

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Example Question #384 : Fractions

Solve:

$\frac{3}{7}\div \frac{1}{5}$

Possible Answers:

$\frac{3}{35}$

$\frac{3}{2}$

$\frac{15}{7}$

$\frac{1}{2}$

Correct answer:

$\frac{15}{7}$

Explanation:

$\frac{3}{7}\div \frac{1}{5}=\frac{3}{7}\times \frac{5}{1}=\frac{15}{7}$

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Example Question #385 : Fractions

Which of the following is the reciprocal of 31.25?

Possible Answers:

0.032

0.024

0.036

0.028

Correct answer:

0.032

Explanation:

Rewrite 31.25 as a fraction:

$31.25 = \frac{3,125}{100} = \frac{3,125\div 25}{100\div 25} = \frac{125}{4}$

Exchange the positions of the numerator and the denominator to get $\frac{4}{125}$ . Now divide 4 by 125:

$\frac{4}{125} = 4 \div 125 = 0.032$

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Example Question #386 : Fractions

Solve:

$\frac{9}{10}\div \frac{3}{5}=$

Possible Answers:

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

$\frac{2}{3}$

$\frac{5}{6}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

$\small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$

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Example Question #21 : How To Divide Fractions

$\frac{7}{49}\div \frac{2}{14}=$

Possible Answers:

196

$1\frac{3}{4}$

$\frac{2}{94}$

Correct answer:

Explanation:

Change division to multiplication by flipping the second fraction. Then, simplify and perform the multiplication.

$\frac{7}{49}\div \frac{2}{14}=$

$\frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$

The answer is 1.

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Example Question #21 : How To Divide Fractions

$12 \frac{4}{6} \div 4\frac{2}{4}=$

Possible Answers:

$2\frac{7}{9}$

$2\frac{20}{27}$

$2\frac{22}{27}$

$1\frac{2}{3}$

$3\frac{1}{3}$

Correct answer:

$2\frac{22}{27}$

Explanation:

First convert each fraction into an improper fraction.

$\frac{76}{6}\div \frac{18}{4}=$

Then flip the second fraction, reduce and multiply:

$\frac{76}{6}\ast \frac{4}{18}=$

The answer is $2\frac{22}{27}$ .

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Example Question #22 : How To Divide Fractions

Divide:

$\frac{4}{9}\div \frac{2}{3}$

Possible Answers:

$\frac{4}{}9$

$\frac{7}{}9$

$\frac{2}{3}$

$\frac{1}{}3$

$\frac{3}{4}$

Correct answer:

$\frac{2}{3}$

Explanation:

The first step in dividing fractions is to make the second fraction a reciprocal (flip it) and then rewrite the problem as a multiplication problem: $\left(\frac{4}{9}\times \frac{3}{2}\right)$ .

You can cross-reduce so that the problem now becomes $\left(\frac{2}{3}\times \frac{1}{1}\right)$ . Then, mulitply straight across so that your answer is $\frac{2}{3}$ .

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Example Question #21 : How To Divide Fractions

What is the below expression equal to?

$\frac{3}{5}\div \frac{2}{7}$

Possible Answers:

$\frac{21}{10}$

$\frac{1}{2}$

$\frac{10}{21}$

Correct answer:

$\frac{21}{10}$

Explanation:

When one fraction is being divided by another, the latter fraction must be inverted. The numerators are then multiplied by each other, and the denominators are also multiplied by each other.

$\frac{3}{5}\div \frac{2}{7}$

$\frac{3}{5}\cdot \frac{7}{2}=\frac{21}{10}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Fractions

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #381 : Fractions

Example Question #382 : Fractions

Example Question #383 : Fractions

Example Question #384 : Fractions

Example Question #385 : Fractions

Example Question #386 : Fractions

Example Question #21 : How To Divide Fractions

Example Question #21 : How To Divide Fractions

Example Question #22 : How To Divide Fractions

Example Question #21 : How To Divide Fractions

All ISEE Middle Level Math Resources

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