Rational Numbers

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SSAT Upper Level Quantitative › Rational Numbers

Questions 1 - 10

Which of the following operations is equivalent to taking of a number?

Dividing the number by

Moving the decimal point one place to the left, then doubling the result

Moving the decimal point one place to the left, then tripling the result

Explanation

Let's just pick a number at random, for example .

of this number is , which is divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

In a high school, the ratio of freshmen to seniors is . If there are seniors, how many freshmen are there?

Explanation

Set up the following proportion, with being the number of freshmen.

$\frac{4}{5}=\frac{x}{150}$

Now, cross-multiply and solve for .

Which of the following operations is equivalent to taking of a number?

Dividing the number by

Moving the decimal point one place to the left, then doubling the result

Moving the decimal point one place to the left, then tripling the result

Explanation

Let's just pick a number at random, for example .

of this number is , which is divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

Convert into a fraction in simplest form.

$\frac{19}{50}$

$\frac{19}{25}$

$\frac{38}{50}$

$\frac{5}{19}$

Explanation

Think of the decimal as the fraction $\frac{0.38}{1}$ .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by .

$\frac{0.38}{1}\times 100=\frac{38}{100}$

Now, simplify this fraction.

$\frac{38}{100}=\frac{19}{50}$

Put the fraction in simplest form.

$\frac{224}{400}$

$\frac{14}{25}$

$\frac{28}{50}$

$\frac{25}{14}$

$\frac{56}{100}$

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{224\div4}{400\div4}=\frac{56\div2}{100\div2}=\frac{28\div2}{50\div2}=\frac{14}{25}$

What is the least common denominator for the fractions $\frac{1}{5}$ and $\frac{5}{6}$ ?

Explanation

To find the least common denominator, list out the multiples for each denominator then choose the lowest one that is in both sets.

Convert into a fraction.

$\frac{9}{25}$

$\frac{18}{25}$

$\frac{36}{7}$

$\frac{25}{9}$

Explanation

Write the decimal divided by .

$0.36=\frac{0.36}{1}$

Multiply the numerator and denominator by to get rid of the decimal, then simplify.

$\frac{0.36\times100}{1\times100}=\frac{36}{100}=\frac{9}{25}$

$\frac{\frac{2}{3}}{\frac{4}{5}}=?$

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{8}{15}$

$\frac{4}{5}$

Explanation

Keep in mind that the main fraction line just means "divide."

So then,

$\frac{\frac{2}{3}}{\frac{4}{5}}=\frac{2}{3}\div\frac{4}{5}$

Now, divide this like any other fraction.

$\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$

Put the fraction in simplest form.

$\frac{224}{400}$

$\frac{14}{25}$

$\frac{28}{50}$

$\frac{25}{14}$

$\frac{56}{100}$

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{224\div4}{400\div4}=\frac{56\div2}{100\div2}=\frac{28\div2}{50\div2}=\frac{14}{25}$

Multiply these fractions:

$\frac{1}{4}\cdot \frac{2}{5}$