How to order fractions from least to greatest or from greatest to least - SAT Math

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Question

Which of the following is greater than 1/2 ?

Answer

There are two ways to deal with fractions. One way is to convert them all to decimals. (By using your calculator, divide the numerator by the denominator). Using this method all you would need to do is to see which is greater than 0.5. Otherwise to see which is greater than 1/2, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 12, which is bigger than 11.

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Question

Which of the following has the greatest value?

Answer

If all are converted to decimals, 0.65 is the biggest.

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Question

Which fraction falls between ½ and 3/4?

Answer

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.

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Question

If Ben is taller than Jaime, Mary is taller than Ben, and Chris is taller than Mary. Who is the second tallest?

Answer

Using math symbols to dictate height we find that Ben>Jaime, Mary>Ben, Chris>Mary. Putting these in order we have Chris>Mary, Mary>Ben, Ben>Jaime. This shows that Mary is the second tallest.

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Question

Order the following fractions in descending order.

1/2, 2/3, 2/5, 3/4, 4/7

Answer

Method 1:

Find the common denominator (420) and convert each fraction to this denominator:

1/2 = 210/420

2/3 = 280/420

2/5 = 168/420

3/4 = 315/420

4/7 = 240/420

Now sort by numerator, largest to smallest.

Method 2:

Divide each fraction to obtain a decimal. Sort the decimals, largest to smallest.

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Question

Answer

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Question

Which of the following fractions is between 0.2 and 0.3?

Answer

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

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

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

The other three choices are larger than 0.3.

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Question

Which of the following fractions is the greatest?

Answer

The trick to this problem is to see that three of the choices have the numerator and denominator 3 units apart. The other two choices can be made three units apart as well- multiply both $\frac{3}{4}$ and $\frac{2}{3}$ by $\frac{3}{3}$ to get them to be $\frac{9}{12}$ and $\frac{6}{9}$ , respectively.

The trick is that once all fractions are the same units apart in denominator and numerator, the biggest number is the largest fraction.

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Question

Order the following from least to greatest: three-fifths, seven-eighths, 0.5, sixteen-eighteenths, 97%, 17-fifths.

Answer

We need to order: three fifths, seven eights, 0.5, sixteen eighteenths, 97%, seventeen fifths.

Let us re-write each as a fraction: $\frac{3}{5}$ , $\frac{7}{8}$ , $\frac{1}{2}$ , $\frac{16}{18}=\frac{8}{9}$ , $\frac{97}{100}$ , and $\frac{17}{5}$ . We can now easily order these:

$\frac{1}{2},\frac{3}{5},\frac{7}{8},\frac{8}{9},\frac{97}{100},\frac{17}{5}$

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Question

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

Answer

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 .

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Question

Order the following fractions from least to greatest:

$\frac{1}{6}, \frac{5}{7}, \frac{1}{3}, \frac{5}{6}$

Answer

To solve this problem, let's find the least common denominator for our fractions.

$7\cdot6 = 42$

is the lowest number that each of our current denominators are factors of.

Now, let's rewrite each fraction so that its denominator is .

$\frac{1 \cdot 7}{6 \cdot7}, \frac{5\cdot6}{7\cdot6}, \frac{1\cdot14}{3 \cdot 14}, \frac{5\cdot7}{6\cdot7} = \frac{7}{42}, \frac{30}{42}, \frac{14}{42}, \frac{35}{42}$

Then we can rearrange these new fractions from least to greatest, keeping in mind what they're reduced forms were.

$\frac{7}{42}, \frac{14}{42}, \frac{30}{42}, \frac{35}{42}$

Then, by either simplifying these fractions or by remembering their original forms, we can see that the order of our fractions from least to greatest is:

$\frac{1}{6}, \frac{1}{3}, \frac{5}{7}, \frac{5}{6}$

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Question

Which of the following fractions is the smallest?

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

Answer

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).

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Question

Order from least to greatest:

$\frac{4}{7} , \frac{5}{8}, \frac{7}{12}$

Answer

Express all three fractions in terms of their least common denominator - the least common multiple of denominators 7, 8, and 12, which is 168. Do this by multiplying the numerator and denominator in each fraction by whatever number yields a product of 168 in the denominator.

$\frac{4 }{7} = \frac{4 \cdot 24 }{7 \cdot 24 } = \frac{96}{168}$

$\frac{5}{8} = \frac{5 \cdot 21 }{8 \cdot 21 } = \frac{105}{168 }$

$\frac{7}{12} = \frac{7 \cdot 14 }{12 \cdot 14 } = \frac{98}{168}$

;

it follows that

$\frac{96}{168}< \frac{98}{168} < \frac{105}{168 }$ ,

so

$\frac{4 }{7} < \frac{7}{12} <\frac{5}{8}$

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Question

Which of the following five numbers is the greatest?

Answer

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

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

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Question

Order from greatest to least:

$- \frac{3}{13}, - \frac{4}{17}, - \frac{5}{19}$

Answer

Rewrite the numbers $- \frac{3}{13}, - \frac{4}{17}, - \frac{5}{19}$ in terms of the least common denominator, which is $13 \times 17 \times 19 = 4,199$ :

$- \frac{3}{13} = - \frac{3 \times 17 \times 19 }{13 \times 17 \times 19 } = - \frac{969}{4,199} = \frac{-969}{4,199}$

$- \frac{4}{17} = - \frac{4 \times 13 \times 19}{17 \times 13 \times 19 } = -\frac{988}{4,199} = \frac{-988}{4,199}$

$- \frac{5}{19} = - \frac{5 \times 13 \times 17 }{19 \times 13 \times 17} = -\frac{1,105}{4,199}= \frac{-1,105}{4,199}$

Comparing numerators, we see that

It follows that

$\frac{-969}{4,199} >\frac{ -988}{4,199} >\frac{ -1,105}{4,199}$

and

$- \frac{3}{13}> - \frac{4}{17}>- \frac{5}{19}$ ,

making this the correct order.

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