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SSAT Upper Level Math : How to order fractions from least to greatest or from greatest to least

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Example Questions

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Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{4}{9}, \frac{1}{4}, \frac{7}{12}, \frac{5}{6}$

Possible Answers:

$\frac{5}{6}, \frac{7}{12}, \frac{4}{9}, \frac{1}{4}$

$\frac{5}{6}, \frac{7}{12}, \frac{1}{4}, \frac{4}{9}$

$\frac{1}{4}, \frac{4}{9}, \frac{7}{12}, \frac{5}{6}$

$\frac{4}{9}, \frac{7}{12}, \frac{1}{4}, \frac{5}{6}$

Correct answer:

$\frac{1}{4}, \frac{4}{9}, \frac{7}{12}, \frac{5}{6}$

解释:

In order to compare these fractions, they all need to have the same denominator. The least common denominator for this set of fractions is.

Now, convert these fractions so that their denominators are all.

$\frac{4}{9}=\frac{16}{36}$

$\frac{1}{4}=\frac{9}{36}$

$\frac{7}{12}=\frac{21}{36}$

$\frac{5}{6}=\frac{30}{36}$

Now, place the fractions in ascending order by looking at the numerators.

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Example Question #2 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{3}{4},\frac{1}{2}, \frac{1}{8}, \frac{2}{5}, \frac{9}{10}$

Possible Answers:

$\frac{1}{8}, \frac{2}{5}, \frac{1}{2}, \frac{3}{4}, \frac{9}{10}$

$\frac{9}{10}, \frac{3}{4}, \frac{1}{8}, \frac{2}{5}, \frac{1}{2}$

$\frac{1}{2},\frac{1}{8}, \frac{2}{5}, \frac{3}{4}, \frac{9}{10}$

$\frac{1}{8}, \frac{3}{4}, \frac{2}{5}, \frac{9}{10}, \frac{1}{2}$

$\frac{2}{5},\frac{1}{8}, \frac{1}{2}, \frac{9}{10}, \frac{3}{4}$

Correct answer:

$\frac{1}{8}, \frac{2}{5}, \frac{1}{2}, \frac{3}{4}, \frac{9}{10}$

解释:

In order to compare these fractions, we need to rewrite them so they have a common denominator. The least common denominator of these fractions is, so starting from the left:

$\frac{3}{4}=\frac{30}{40}$

$\frac{1}{2}=\frac{20}{40}$

$\frac{1}{8}=\frac{5}{40}$

$\frac{2}{5}=\frac{16}{40}$

$\frac{9}{10}=\frac{36}{40}$

Thus, the correct order from least to greatest is:

$\frac{1}{8}, \frac{2}{5}, \frac{1}{2}, \frac{3}{4}, \frac{9}{10}$

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Example Question #3 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order these fractions from least to greatest:

$\frac{7}{8}, \frac{1}{4}, \frac{5}{6}, \frac{5}{12}$

Possible Answers:

$\frac{5}{6}, \frac{1}{4}, \frac{7}{8}, \frac{5}{6}$

$\frac{7}{8}, \frac{5}{6}, \frac{5}{12}, \frac{1}{4}$

$\frac{5}{12}, \frac{1}{4}, \frac{7}{8}, \frac{5}{6}$

$\frac{1}{4}, \frac{5}{12}, \frac{5}{6}, \frac{7}{8}$

Correct answer:

$\frac{1}{4}, \frac{5}{12}, \frac{5}{6}, \frac{7}{8}$

解释:

To figure out the order of the fractions, they first all need to have the same denominator.

$\frac{7}{8}\rightarrow\frac{21}{24}$

$\frac{1}{4}\rightarrow\frac{6}{24}$

$\frac{5}{6}\rightarrow\frac{20}{24}$

$\frac{5}{12}\rightarrow\frac{10}{24}$

Now, order the fractions by looking at their numerators: $\frac{1}{4}, \frac{5}{12}, \frac{5}{6}, \frac{7}{8}$

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Example Question #4 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{1}{2}, \frac{9}{10}, \frac{3}{4}, \frac{5}{7}$

Possible Answers:

$\frac{1}{2}, \frac{5}{7}, \frac{3}{4}, \frac{9}{10}$

$\frac{1}{2}, \frac{5}{7}, \frac{9}{10}, \frac{3}{4}$

$\frac{9}{10}, \frac{1}{2}, \frac{3}{4}, \frac{5}{7}$

$\frac{3}{4}, \frac{9}{10}, \frac{1}{2}, \frac{5}{7}$

Correct answer:

$\frac{1}{2}, \frac{5}{7}, \frac{3}{4}, \frac{9}{10}$

解释:

Convert the fractions so that they all share the same denominator.

$\frac{1}{2}\cdot \frac{70}{70}=\frac{70}{140}$

$\frac{3}{4}\cdot \frac{35}{35}=\frac{105}{140}$

$\frac{5}{7}\cdot \frac{20}{20}=\frac{100}{140}$

$\frac{9}{10}\cdot \frac{14}{14}=\frac{126}{140}$

Now, look at the numerators and order them from the least to the greatest:

$\frac{1}{2}, \frac{5}{7}, \frac{3}{4}, \frac{9}{10}$

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Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{1}{8}, \frac{9}{24}, \frac{3}{4}, \frac{5}{12}$

Possible Answers:

$\frac{9}{24}, \frac{1}{8}, \frac{5}{12}, \frac{3}{4}$

$\frac{3}{4}, \frac{5}{12}, \frac{9}{24}, \frac{1}{8}$

$\frac{1}{8}, \frac{9}{24}, \frac{5}{12}, \frac{3}{4}$

$\frac{9}{24}, \frac{5}{12}, \frac{1}{8}, \frac{3}{4}$

Correct answer:

$\frac{1}{8}, \frac{9}{24}, \frac{5}{12}, \frac{3}{4}$

解释:

Convert all the fractions so that they share the same denominator, then order the numerators from least to greatest.

$\frac{1}{8}\cdot \frac{3}{3}=\frac{3}{24}$

$\frac{9}{24}$ stays the same.

$\frac{3}{4}\cdot \frac{6}{6}=\frac{18}{24}$

$\frac{5}{12}\cdot \frac{2}{2}=\frac{10}{24}$

$\frac{1}{8}, \frac{9}{24}, \frac{5}{12}, \frac{3}{4}$ is the order of the fractions from least to greatest.

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Example Question #6 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{1}{5}, \frac{5}{8}, \frac{3}{10}, \frac{1}{4}$

Possible Answers:

$\frac{1}{5}, \frac{3}{10}, \frac{1}{4}, \frac{5}{8}$

$\frac{1}{5}, \frac{5}{8}, \frac{3}{10}, \frac{1}{4}$

$\frac{1}{5}, \frac{1}{4}, \frac{3}{10}, \frac{5}{8}$

$\frac{5}{8}, \frac{1}{4}, \frac{3}{10}, \frac{1}{5}$

Correct answer:

$\frac{1}{5}, \frac{1}{4}, \frac{3}{10}, \frac{5}{8}$

解释:

Convert the fractions so they all share the same denominator. Then, compare the numerators to order from least to greatest.

$\frac{1}{5}\cdot \frac{8}{8}=\frac{8}{40}$

$\frac{5}{8}\cdot \frac{5}{5}=\frac{25}{40}$

$\frac{3}{10}\cdot \frac{4}{4}=\frac{12}{40}$

$\frac{1}{4}\cdot \frac{10}{10}=\frac{10}{40}$

$\frac{1}{5}, \frac{1}{4}, \frac{3}{10}, \frac{5}{8}$ is the order of the fractions from least to greatest.

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Example Question #7 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{1}{4}, \frac{3}{4}, \frac{3}{20}, \frac{2}{5}$

Possible Answers:

$\frac{3}{20}, \frac{2}{5}, \frac{1}{4}, \frac{3}{4}$

$\frac{3}{20}, \frac{3}{4}, \frac{2}{5}, \frac{1}{4}$

$\frac{3}{20}, \frac{1}{4}, \frac{2}{5}, \frac{3}{4}$

$\frac{3}{4}, \frac{2}{5}, \frac{1}{4}, \frac{3}{20}$

Correct answer:

$\frac{3}{20}, \frac{1}{4}, \frac{2}{5}, \frac{3}{4}$

解释:

Convert the fractions so that they all share the same denominator. Then, order the fractions from least to greatest by comparing their numerators.

$\frac{1}{4}\cdot \frac{5}{5}=\frac{5}{20}$

$\frac{3}{20}$ stays the same.

$\frac{2}{5}\cdot \frac{4}{4}=\frac{8}{20}$

$\frac{3}{4}\cdot \frac{5}{5}=\frac{15}{20}$

$\frac{3}{20}, \frac{1}{4}, \frac{2}{5}, \frac{3}{4}$ is in order from least to greatest.

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Example Question #1 :Ordering Fractions

Order the following fractions from least to greatest:

$\frac{3}{16}, \frac{11}{16}, \frac{1}{4}, \frac{11}{32}$

Possible Answers:

$\frac{3}{16}, \frac{1}{4}, \frac{11}{32}, \frac{11}{16}$

$\frac{11}{32}, \frac{1}{4}, \frac{3}{16}, \frac{11}{16}$

$\frac{11}{16}, \frac{11}{32}, \frac{1}{4}, \frac{3}{16}$

$\frac{1}{4}, \frac{3}{16}, \frac{11}{32}, \frac{11}{16}$

Correct answer:

$\frac{3}{16}, \frac{1}{4}, \frac{11}{32}, \frac{11}{16}$

解释:

Convert the fractions so that they all share the same denominators. Then, compare their numerators to put them in order from least to greatest.

$\frac{3}{16} \cdot \frac{2}{2}=\frac{6}{32}$

$\frac{1}{4}\cdot \frac{8}{8}=\frac{8}{32}$

$\frac{11}{32}$ stays the same.

$\frac{11}{16}\cdot \frac{2}{2}=\frac{22}{32}$

$\frac{3}{16}, \frac{1}{4}, \frac{11}{32}, \frac{11}{16}$ is in order from least to greatest.

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Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from least to greatest:

$\frac{2}{9}, \frac{1}{3}, \frac{1}{18}, \frac{1}{6}$

Possible Answers:

$\frac{1}{3}, \frac{2}{9}, \frac{1}{6}, \frac{1}{18}$

$\frac{1}{3}, \frac{1}{6}, \frac{2}{9}, \frac{1}{18}$

$\frac{1}{6}, \frac{1}{18}, \frac{1}{3}, \frac{2}{9}$

$\frac{1}{18}, \frac{1}{6}, \frac{2}{9}, \frac{1}{3}$

Correct answer:

$\frac{1}{18}, \frac{1}{6}, \frac{2}{9}, \frac{1}{3}$

解释:

Convert the fractions so that they share the same denominator. Then, compare their numerators to put them in order from least to greatest.

$\frac{1}{18}\cdot \frac{2}{2}=\frac{2}{36}$

$\frac{1}{6}\cdot \frac{6}{6}=\frac{6}{36}$

$\frac{2}{9}\cdot \frac{4}{4}=\frac{8}{36}$

$\frac{1}{3}\cdot \frac{12}{12}=\frac{12}{36}$

$\frac{1}{18}, \frac{1}{6}, \frac{2}{9}, \frac{1}{3}$ is in order from least to greatest.

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Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following fractions from greatest to least:

$\frac{9}{10}, \frac{1}{5}, \frac{18}{25}, \frac{7}{20}$

Possible Answers:

$\frac{9}{10}, \frac{18}{25}, \frac{7}{20}, \frac{1}{5}$

$\frac{18}{25}, \frac{9}{10}, \frac{7}{20}, \frac{1}{5}$

$\frac{9}{10}, \frac{7}{20}, \frac{18}{25}, \frac{1}{5}$

$\frac{1}{5}, \frac{7}{20}, \frac{8}{25}, \frac{9}{10}$

Correct answer:

$\frac{9}{10}, \frac{18}{25}, \frac{7}{20}, \frac{1}{5}$

解释:

Convert the fractions so that they all share the same denominator. Then, compare their numerators to put them in order from greatest to least.

$\frac{9}{10}\cdot \frac{10}{10}=\frac{90}{100}$

$\frac{18}{25}\cdot \frac{4}{4}=\frac{72}{100}$

$\frac{7}{20}\cdot \frac{5}{5}=\frac{35}{100}$

$\frac{1}{5}\cdot \frac{20}{20}=\frac{20}{100}$

$\frac{9}{10}, \frac{18}{25}, \frac{7}{20}, \frac{1}{5}$ is in order from greatest to least.

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SSAT Upper Level Math : How to order fractions from least to greatest or from greatest to least

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #2 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #3 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #4 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #6 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #7 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 :Ordering Fractions

Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 :How To Order Fractions From Least To Greatest Or From Greatest To Least

All SSAT Upper Level Math Resources

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