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ISEE Middle Level Math : How to divide fractions

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Example Questions

Example Question #326 : Concepts

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

Possible Answers:

$\frac{2}{94}$

196

$1\frac{3}{4}$

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 #31 : Fractions

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

Possible Answers:

$3\frac{1}{3}$

$2\frac{7}{9}$

$2\frac{20}{27}$

$1\frac{2}{3}$

$2\frac{22}{27}$

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 #21 : How To Divide Fractions

Divide:

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

Possible Answers:

$\frac{1}{}3$

$\frac{4}{}9$

$\frac{2}{3}$

$\frac{7}{}9$

$\frac{3}{4}$

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 #22 : How To Divide Fractions

What is the below expression equal to?

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

Possible Answers:

$\frac{21}{10}$

$\frac{10}{21}$

$\frac{1}{2}$

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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Example Question #328 : Concepts

What is the value of in this equation?

$\frac{9}{5}\div \frac{5}{7}=x$

Possible Answers:

$\frac{7}{9}$

$\frac{63}{25}$

$\frac{9}{7}$

$\frac{25}{63}$

Correct answer:

$\frac{63}{25}$

Explanation:

In order to solve $\frac{9}{5}\div \frac{5}{7}$ , the latter fraction must be inverted and then multiplied by the first fraction, as shown below:

$\frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$

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Example Question #23 : How To Divide Fractions

One euro is worth approximately $1.27. For how many euros (nearest whole) can an American tourist expect to exchange $1,000?

Possible Answers:

1,270

7,874

787

127

Correct answer:

787

Explanation:

One Euro is equivalent to $1.27, so divide the number of dollars by this conversion factor. $1,000 is equivalent to

$1,000 \div 1.27\approx 787$ euros

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Example Question #24 : How To Divide Fractions

One Mexican peso is equal to about 7.4 cents. To the nearest whole number, for how many pesos can a tourist to Mexico expect to exchange $500?

Possible Answers:

676

6,757

3,700

37,000

370

Correct answer:

6,757

Explanation:

One peso is equivalent to 7.4 cents, or $0.074, so divide $500 dollars by this conversion factor. $500 is equivalent to

$500 \div 0.074 \approx 6,757$ pesos.

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Example Question #25 : How To Divide Fractions

What is the solution to the expression below?

$\frac{1}{4}\div \frac{9}{17}$

Possible Answers:

$\frac{1}{3}$

$\frac{17}{36}$

$\frac{36}{17}$

$\frac{3}{12}$

Correct answer:

$\frac{17}{36}$

Explanation:

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

$\frac{1}{4}\div \frac{9}{17}$

$\frac{1}{4}\div \frac{17}{9}$

$\frac{17}{36}$

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Example Question #26 : How To Divide Fractions

Divide.

$\frac{21}{56}\div \frac{3}{4}$

Possible Answers:

$\frac{1}{3}$

$\frac{3}{4}$

$\frac{7}{8}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Multiply the first fraction by the reciprocal of the second fraction.

$\frac{21}{56}\times \frac{4}{3}$

$21\times4=84$

$56\times3=168$

$\frac{84}{168}=\frac{1}{2}$

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Example Question #24 : How To Divide Fractions

Simplify the following expression:

$\frac{4}{5}\div\frac{64}{625}$

Possible Answers:

$\frac{16}{125}$

$\frac{ 5}{4}$

$\frac{125}{16}$

$\frac{25}{16}$

Correct answer:

$\frac{125}{16}$

Explanation:

Simplify the following expression:

$\frac{4}{5}\div\frac{64}{625}$

To divide fractions, we must multiply by the reciprocal.

That means that we should first flip our second fraction. (This is called taking the reciprocal

$\frac{4}{5}\div\frac{64}{625}=\frac{4}{5}\ast\frac{625}{64}$

Next, we can simplify by dividing the smaller numbers on the left out of the bigger numbers on the right.

$\frac{4}{5}\ast\frac{625}{64}=\frac{{\color{Red} 4}}{{\color{Blue} 5}}\ast\frac{{\color{Blue} 5}*125}{{\color{Red} 4}*16}=\frac{125}{16}$

So our answer is:

$\frac{125}{16}$

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ISEE Middle Level Math : How to divide fractions

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #326 : Concepts

Example Question #31 : Fractions

Example Question #21 : How To Divide Fractions

Example Question #22 : How To Divide Fractions

Example Question #328 : Concepts

Example Question #23 : How To Divide Fractions

Example Question #24 : How To Divide Fractions

Example Question #25 : How To Divide Fractions

Example Question #26 : How To Divide Fractions

Example Question #24 : How To Divide Fractions

All ISEE Middle Level Math Resources

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