SAT Math - Ordering Fractions

Which of the following fractions is less than $\frac{3}{8}$ ?

$\frac{1}{3}$

$\frac{6}{16}$

$\frac{4}{7}$

$\frac{1}{2}$

$\frac{5}{13}$

Explanation

The purpose of this question is to find understandable values of fractions, which must be done using a common scale. Since looking at the denominators in the answers shows that there are many different numbers, decimal values would be easier to use.

The decimal equivalencies are as follows:

$\frac{6}{16}=0.375$

$\frac{4}{7}=0.571$

$\frac{1}{2}=0.5$

$\frac{5}{13}=0.385$

$\frac{1}{3}=0.333$

Therefore, we know that $\frac{3}{8}$ is equal to and find that the fraction that is less than that is $\frac{1}{3}$ , which is equal to .

Which of the following fractions is less than $\frac{3}{8}$ ?

$\frac{1}{3}$

$\frac{6}{16}$

$\frac{4}{7}$

$\frac{1}{2}$

$\frac{5}{13}$

Explanation

The decimal equivalencies are as follows:

$\frac{6}{16}=0.375$

$\frac{4}{7}=0.571$

$\frac{1}{2}=0.5$

$\frac{5}{13}=0.385$

$\frac{1}{3}=0.333$

Therefore, we know that $\frac{3}{8}$ is equal to and find that the fraction that is less than that is $\frac{1}{3}$ , which is equal to .

Which of the following fractions is between 0.2 and 0.3?

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{2}{3}$

Explanation

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

Which of the following fractions is between 0.2 and 0.3?

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{2}{3}$

Explanation

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

Which of the following fractions is the smallest?

1/3, 115/276, 112/350, 1050/3330, 0.75/2

$\frac{1050}{3330}$

$\frac{0.75}{2}$

$\frac{112}{350}$

$\frac{1}{3}$

$\frac{115}{276}$

Explanation

1/3, 115/276, 112/350, 1050/3330, 0.75/2

First you need to put the fractions in ascending order:

1050/3330, 112/350, 1/3, 0.75/2, 115/276

Then choose the fraction with the smallest value (1050/3330).

Which of the following fractions is the smallest?

1/3, 115/276, 112/350, 1050/3330, 0.75/2

$\frac{1050}{3330}$

$\frac{0.75}{2}$

$\frac{112}{350}$

$\frac{1}{3}$

$\frac{115}{276}$

Explanation

1/3, 115/276, 112/350, 1050/3330, 0.75/2

First you need to put the fractions in ascending order:

1050/3330, 112/350, 1/3, 0.75/2, 115/276

Then choose the fraction with the smallest value (1050/3330).

Which of the following five numbers is the greatest?

$\frac{10}{13}$

$\frac{5}{7}$

$\frac{3}{4}$

$\frac{13}{17}$

$\frac{8}{11}$

Explanation

For each fraction, divide the numerator by the denominator. This is shown below for each fraction to three decimal places:

Division

From the decimal representations, $\frac{10}{13}$ can be seen to be the greatest of the five choices.

Which of the following five numbers is the greatest?

$\frac{10}{13}$

$\frac{5}{7}$

$\frac{3}{4}$

$\frac{13}{17}$

$\frac{8}{11}$

Explanation

For each fraction, divide the numerator by the denominator. This is shown below for each fraction to three decimal places:

Division

From the decimal representations, $\frac{10}{13}$ can be seen to be the greatest of the five choices.

Which fraction falls between ½ and 3/4?

4/5

3/6

5/8

6/8

1/3

Explanation

The easiest method is to put each of these fractions into a calculator, and then place them in order on a number line to see which value falls in between 1/2 = 0.5 and ¾ = 0.75. Without a calculator you must do long division to find the value of the numerator (top number) divided by the denominator (bottom number) for each fraction. You can actually eliminate answers b. and d. because they are equal to 1/2 and ¾ respectively. 4/5= 0.80, 3/6 = 0.5, 5/8= 0.625, 6/8 = 0.75.

Which fraction falls between ½ and 3/4?

4/5

3/6

5/8

6/8

1/3

Ordering Fractions

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