SSAT Middle Level Quantitative - How to find the decimal equivalent of a fraction

What fractions equals ?

$\frac{8}{16}$

$\frac{8}{12}$

$\frac{8}{4}$

$\frac{8}{2}$

$\frac{8}{32}$

Explanation

is equal to $\frac{1}{2}$ .

Thus we are looking for a fraction that reduces to $\frac{1}{2}$ .

$\frac{8}{12}$ reduces to $\frac{2}{3}$ (divide numerator and denominator by 4).

$\frac{8}{4}$ reduces to 2 (divide numerator and denominator by 4).

$\frac{8}{2}$ reduces to 4 (divide numerator and denominator by 2).

$\frac{8}{32}$ reduces $\frac{1}{4}$ (divide numerator and denominator by 4).

$\frac{8}{16}$ is the only one that reduces to $\frac{1}{2}$ (divide numerator and denominator by 8).

Which of the following is NOT equal to $0.5 \bullet 20$ ?

$\frac{3}{4} \bullet 16$

$\frac{1}{5} \bullet 50$

$2 \bullet 5$

$\frac{2}{3} \bullet 15$

$\frac{1}{4} \bullet 40$

Explanation

All of the answer choices multiply to give you 10 except

$\frac{3}{4} \bullet 16$

so that is the correct answer.

How many of the following four numbers are elements of the set $B = \left { x ; | ; \frac{2}{5}< x < \frac{3}{5}\right } ?$ ?

(A)

(B)

(C)

(D)

Two

Three

Four

None

One

Explanation

$\frac{2}{5} = 2 \div 5 = 0.4$ and $\frac{3}{5} = 3 \div 5 = 0.6$ , so we are looking for numbers that fall between 0.4 and 0.6 exclusive. Of the four choices, 0.44 and 0.55 fall between these numbers. The correct response is two.

What is the decimal equivalent to the following fraction?

$\frac{21}{25}$

Explanation

When solving for a decimal from a fraction, you have two options. You can either do long division, and divide it out. How many times does 25 go into 21? Or the second option is setting the denominator as 100.

In this case, 25 goes into 100 evenly.

$\frac{21}{24}\times \frac{4}{4}=\frac{84}{100}$ .

If the denominator is 100, then the numerator is the number after the decimal point.

$\frac{84}{100}=0.84$ .

$10 +\tfrac{3}{20}$

Explanation

The question is asking you to add the two numbers and find its equivalent in decimal form. Naturally,

$10 + \tfrac{3}{20} = 10 \tfrac{3}{20}$

We must find out how to represent $\tfrac{3}{20}$ as a decimal in order to solve the problem. To find the decimal form, divide 1.00 by 20.

$1.00 \div 20 = 0.05$

You divide by 1.00 because decimals are based off of this number (fractions are based on 1 and percents on 100%). The answer is exactly $\tfrac{1}{20}$ . In order to figure out what the equivalent of $\tfrac{3}{20}$ is, simply multiply your answer by the numerator, 3.

$3 \times 0.05 = 0.15$

Your answer is

Rewrite as a decimal:

$\frac{7}{12}$

$0.58\overline{3}$

$0.5\overline{3}$

$0.\overline{53}$

Explanation

$7 \div 12 = 0.583333...$

That is, after 5 and 8, the digit 3 will repeat infinitely. This can be rewritten as $0.58\overline{3}$ .

Arrange these numbers from least to greatest:

$\left { -0.44404, -0.44044, -0.40444, \right }$

$\left { -0.44404, -0.44044, -0.40444 \right }$

$\left { -0.44404,-0.40444, -0.44044 \right }$

$\left { -0.40444,-0.44404, -0.44044 \right }$

$\left { -0.40444,-0.44044, -0.44404 \right }$

$\left { -0.40444 , -0.44404, -0.44044\right }$

Explanation

To arrange negative numbers from least to greatest, we must arrange them so that their absolute values (values without the negative symbol) go from greatest to least.

$\left { 0.44404, 0.44044, 0.40444 \right }$

This can be done by going from right to left starting with the units digit. The units and tenths digits are the same, but the hundredths digit of 0.40444 is the least, so this number is less than the other two. The thousandths digit of 0.44044 is less than that of 0.44404, so it is the lesser of the two that remain. Therefore, in descending order, the absolute values are

$\left { 0.44404, 0.44044, 0.40444 \right }$ ,