How to order fractions from least to greatest or from greatest to least - SSAT Upper Level Quantitative (Math)

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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order these fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from least to greatest:

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

Answer

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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Question

Order the following fractions from greatest to least:

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

Answer

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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Question

Order the following fractions from least to greatest:

$\frac{1}{8}, \frac{8}{9}, \frac{1}{6}, \frac{35}{26}$

Answer

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

$\frac{1}{8}\cdot \frac{9}{9}=\frac{9}{72}$

$\frac{1}{6}\cdot \frac{12}{12}=\frac{12}{72}$

$\frac{8}{9}\cdot \frac{8}{8}=\frac{64}{72}$

$\frac{35}{36}\cdot \frac{2}{2}=\frac{70}{72}$

$\frac{1}{8}, \frac{1}{6}, \frac{8}{9}, \frac{35}{36}$ is in order from least to greatest.

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Question

Order the following fractions from greatest to least:

$\frac{3}{4}, \frac{7}{8}, \frac{3}{20}, \frac{13}{20}$

Answer

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

$\frac{7}{8}\cdot \frac{10}{10}=\frac{70}{80}$

$\frac{3}{4}\cdot \frac{20}{20}=\frac{60}{80}$

$\frac{13}{20}\cdot \frac{4}{4}=\frac{52}{80}$

$\frac{3}{20}\cdot \frac{4}{4}=\frac{12}{80}$

$\frac{7}{8}, \frac{3}{4}, \frac{13}{20}, \frac{3}{20}$ is in order from greatest to least.

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Question

Order the following fractions from greatest to least:

$\frac{3}{10}, \frac{1}{5}, \frac{1}{25}, \frac{13}{25}$

Answer

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

$\frac{13}{25}\cdot \frac{2}{2}=\frac{26}{50}$

$\frac{3}{10}\cdot \frac{5}{5}=\frac{15}{50}$

$\frac{1}{5}\cdot \frac{10}{10}=\frac{10}{50}$

$\frac{1}{25}\cdot \frac{2}{2}=\frac{2}{50}$

$\frac{13}{25}, \frac{3}{10}, \frac{1}{5}, \frac{1}{25}$ is in order from greatest to least.

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Question

Order the following fractions from greatest to least:

$\frac{3}{4}, \frac{1}{12}, \frac{5}{24}, \frac{5}{6}$

Answer

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

$\frac{5}{6}\cdot \frac{4}{4}=\frac{20}{24}$

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

$\frac{5}{24}$ stays the same.

$\frac{1}{12}\cdot \frac{2}{2}=\frac{2}{24}$

$\frac{5}{6}, \frac{3}{4}, \frac{5}{24}, \frac{1}{12}$ is in order from greatest to least.

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Question

Order the following fractions from greatest to least:

$\frac{3}{5}, \frac{3}{10}, \frac{1}{6}, \frac{2}{3}$

Answer

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

$\frac{2}{3}\cdot \frac{10}{10}=\frac{20}{30}$

$\frac{3}{5}\cdot \frac{6}{6}=\frac{18}{30}$

$\frac{3}{10}\cdot \frac{3}{3}=\frac{9}{30}$

$\frac{1}{6}\cdot \frac{5}{5}=\frac{5}{30}$

$\frac{2}{3}, \frac{3}{5}, \frac{3}{10}, \frac{1}{6}$ is in order from greatest to least.

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Question

Order the following fractions from least to greatest: $\left(\frac{2}{3}. \frac{6}{11},\frac{4}{7}\right)$

Answer

To determine the correct order from least to greatest, convert all three fractions to a common denominator.

The least common denominator, LCD, can be determined by multiplying the three denominators together.

$3\times11\times7 = 231$

Convert the set by multiplying to the numerator by what was multiplied to the denominator to achieve the LCD.

$\left(\frac{2}{3}. \frac{6}{11},\frac{4}{7} \right )= \left( \frac{154}{231},\frac{126}{231},\frac{132}{231}\right )$

Reorder the set. The correct order from least to greatest is:

$\left( \frac{126}{231},\frac{132}{231},\frac{154}{231}\right ) =\left( \frac{6}{11},\frac{4}{7},\frac{2}{3}\right )$

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Question

Select the symbol to correctly fill in the blank below.

$\frac{1}{2}$ __________ $\frac{1}{8}$

Answer

To compare fractions, we need to first make common denominators.

$\frac{1}{2}\times\frac{4}{4}=\frac{4}{8}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{4}{8}>\frac{1}{8}$

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Question

Select the symbol to correctly fill in the blank below.

$\frac{3}{4}$ __________ $\frac{7}{8}$

Answer

To compare fractions, we need to first make common denominators.

$\frac{3}{4}\times\frac{2}{2}=\frac{6}{8}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{6}{8}<\frac{7}{8}$

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Question

Select the symbol to correctly fill in the blank below.

$\frac{1}{2}$ __________ $\frac{6}{12}$

Answer

To compare fractions, we need to first make common denominators.

$\frac{1}{2}\times\frac{6}{6}=\frac{6}{12}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{6}{12}=\frac{6}{12}$

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Question

Select the symbol to correctly fill in the blank below.

$\frac{5}{7}$ __________ $\frac{1}{3}$

Answer

To compare fractions, we need to first make common denominators.

$\frac{5}{7}\times\frac{3}{3}=\frac{15}{21}$

$\frac{1}{3}\times\frac{7}{7}=\frac{7}{21}$

Now that we have common denominators, we can compare numerators. The fraction with the bigger numerator has the greater value.

$\frac{15}{21}>\frac{7}{21}$

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