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SSAT Upper Level Math : Number Concepts and Operations

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #131 : Fractions

Fill in the blank with the missing fraction.

$\frac{1}{4}\times\frac{?}{?}=\frac{4}{16}$

Possible Answers:

$\frac{2}{2}$

$\frac{6}{6}$

$\frac{3}{3}$

$\frac{5}{5}$

$\frac{4}{4}$

Correct answer:

$\frac{4}{4}$

Explanation:

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

$1\times4=4$

$4\times4=16$

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Example Question #132 : Fractions

Fill in the blank with the missing fraction.

$\frac{1}{10}\times\frac{?}{?}=\frac{3}{30}$

Possible Answers:

$\frac{2}{2}$

$\frac{3}{3}$

$\frac{5}{5}$

$\frac{1}{1}$

$\frac{4}{4}$

Correct answer:

$\frac{3}{3}$

Explanation:

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

$1\times3=3$

$10\times3=30$

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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:

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

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

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

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

Correct answer:

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

Explanation:

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:

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

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

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

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

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

Correct answer:

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

Explanation:

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:

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

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

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

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

Correct answer:

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

Explanation:

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 #2 : Ordering Fractions

Order the following fractions from least to greatest:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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 #313 : Rational Numbers

Order the following fractions from least to greatest:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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:

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

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

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

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

Correct answer:

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

Explanation:

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 #1 : 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:

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

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

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

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

Correct answer:

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

Explanation:

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 #372 : Number Concepts And Operations

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:

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

Explanation:

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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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #131 : Fractions

Example Question #132 : Fractions

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 #2 : Ordering Fractions

Example Question #313 : Rational Numbers

Example Question #6 : 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 #372 : Number Concepts And Operations

All SSAT Upper Level Math Resources

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