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ISEE Middle Level Math : Fractions

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

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Example Questions

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Example Question #24 : How To Divide Fractions

What is the value of in this equation?

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

Possible Answers:

$\frac{7}{9}$

$\frac{9}{7}$

$\frac{25}{63}$

$\frac{63}{25}$

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 #391 : 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:

127

7,874

787

1,270

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 #392 : 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:

370

3,700

6,757

676

37,000

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 #22 : How To Divide Fractions

What is the solution to the expression below?

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

Possible Answers:

$\frac{1}{3}$

$\frac{36}{17}$

$\frac{3}{12}$

$\frac{17}{36}$

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 #29 : How To Divide Fractions

Divide.

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

Possible Answers:

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{7}{8}$

$\frac{1}{3}$

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 #30 : How To Divide Fractions

Simplify the following expression:

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

Possible Answers:

$\frac{25}{16}$

$\frac{125}{16}$

$\frac{ 5}{4}$

$\frac{16}{125}$

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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Example Question #391 : Fractions

Simplify the following expression:

$\frac{12}{35}\div\frac{5}{42}$

Possible Answers:

$\frac{95}{6}$

19.6

195

$\frac{72}{25}$

Correct answer:

$\frac{72}{25}$

Explanation:

Simplify the following expression:

$\frac{12}{35}\div\frac{5}{42}$

To divide fractions, we need to multiply by the reciprocal. This means that we flip the second fraction and then multiply:

$\frac{12}{35}\div\frac{5}{42}=\frac{12}{35}\ast\frac{42}{5}$

Before multiplying, simplify the two fractions by factoring out a seven from the 42 and the 35. We can do this, because they are on opposite sides of the fraction.

$\frac{12}{35}\ast\frac{42}{5}=\frac{12}{5}*\frac{6}{5}=\frac{72}{25}$

So we get an answer of:

$\frac{72}{25}$

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Example Question #392 : Fractions

Simplify the following:

$\frac{5}{6} \div \frac{1}{3}$

Possible Answers:

$\frac{5}{2}$

$\frac{1}{2}$

$\frac{3}{6}$

$\frac{4}{3}$

$\frac{5}{18}$

Correct answer:

$\frac{5}{2}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction.

(Reciprocal simply means we will take the fraction and flip it. The numerator will become the denominator and the denominator will become the numerator.)

So,

$\frac{5}{6} \div \frac{1}{3}$

will become

$\frac{5}{6} \cdot \frac{3}{1}$

Now, we multiply.

$\frac{5 \cdot 3}{6 \cdot 1}$

$\frac{15}{6}$

Now, we can simplify. We can divide the numerator and the denominator by 3. We get

$\frac{5}{2}$

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Example Question #31 : How To Divide Fractions

The reciprocal of is $\frac{3}{4}$ . What is the reciprocal of X - 1 ?

Possible Answers:

$\frac{1}{3}$

$\frac{4}{7}$

Correct answer:

Explanation:

The reciprocal of is $\frac{3}{4}$ , so is the reciprocal of $\frac{3}{4}$ , or

$X = \frac{4}{3} = 1 \frac{1}{3}$

$X -1 = 1 \frac{1}{3} - 1 = \frac{1}{3}$

The reciprocal of this is 3.

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Example Question #394 : Fractions

Divide the following:

$\frac{5}{6} \div \frac{1}{6}$

Possible Answers:

$\frac{5}{36}$

$\frac{5}{6}$

$\frac{1}{5}$

Correct answer:

Explanation:

To divide fractions, we will simply turn it into multiplication. We will leave the first fraction alone. We will take the second fraction, and write the reciprocal. Then, we will multiply the two fractions together. We have

$\frac{5}{6} \div \frac{1}{6}$

we will leave $\frac{5}{6}$ alone. We will take $\frac{1}{6}$ and write the reciprocal (flip the fraction, the numerator and denominator switch places). The reciprocal is $\frac{6}{1}$ . Now, we multiply.

$\frac{5}{6} \cdot \frac{6}{1}$

$\frac{5 \cdot 6}{6 \cdot 1}$

$\frac{30}{6}$

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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 #24 : How To Divide Fractions

Example Question #391 : Fractions

Example Question #392 : Fractions

Example Question #22 : How To Divide Fractions

Example Question #29 : How To Divide Fractions

Example Question #30 : How To Divide Fractions

Example Question #391 : Fractions

Example Question #392 : Fractions

Example Question #31 : How To Divide Fractions

Example Question #394 : Fractions

All ISEE Middle Level Math Resources

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