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SAT Math : Ordering Fractions

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Example Question #11 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #11 : Ordering Fractions

Which of the following fractions is the smallest?

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

Possible Answers:

$\frac{0.75}{2}$

$\frac{115}{276}$

$\frac{1}{3}$

$\frac{112}{350}$

$\frac{1050}{3330}$

Correct answer:

$\frac{1050}{3330}$

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).

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Example Question #472 : Arithmetic

Order from greatest to least:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

-969 > -988 > -1,105

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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Example Question #11 : Fractions

Order from least to greatest:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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.

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

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

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

96 < 98 < 105 ;

it follows that

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

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

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Example Question #12 : Ordering Fractions

Which of the following five numbers is the greatest?

Possible Answers:

$\frac{10}{13}$

$\frac{5}{7}$

$\frac{13}{17}$

$\frac{3}{4}$

$\frac{8}{11}$

Correct answer:

$\frac{10}{13}$

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.

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SAT Math : Ordering Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #11 : Ordering Fractions

Example Question #472 : Arithmetic

Example Question #11 : Fractions

Example Question #12 : Ordering Fractions

All SAT Math Resources

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