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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 #9 : 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:

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

Explanation:

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 #10 : 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:

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #381 : Number Concepts And Operations

Order the following fractions from least to greatest:

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

Possible Answers:

$\frac{1}{8}, \frac{35}{36}, \frac{8}{9}, \frac{1}{6}$

$\frac{35}{36}, \frac{8}{9}, \frac{1}{6}, \frac{1}{8}$

$\frac{1}{8}, \frac{1}{6}, \frac{8}{9}, \frac{35}{36}$

$\frac{1}{8}, \frac{8}{9}, \frac{1}{6}, \frac{35}{36}$

Correct answer:

$\frac{1}{8}, \frac{1}{6}, \frac{8}{9}, \frac{35}{36}$

Explanation:

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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Example Question #382 : Number Concepts And Operations

Order the following fractions from greatest to least:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #381 : Number Concepts And Operations

Order the following fractions from greatest to least:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

Order the following fractions from greatest to least:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

Order the following fractions from greatest to least:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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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Example Question #12 : How To Order Fractions From Least To Greatest Or From Greatest To Least

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

Possible Answers:

$\left( \frac{6}{11},\frac{2}{3},\frac{4}{7}\right )$

$\textup{The set is already in correct order.}$

$\left( \frac{4}{7},\frac{6}{11},\frac{2}{3}\right )$

$\left( \frac{6}{11},\frac{4}{7},\frac{2}{3}\right )$

$\left(\frac{4}{7},\frac{2}{3},\frac{6}{11} \right)$

Correct answer:

$\left( \frac{6}{11},\frac{4}{7},\frac{2}{3}\right )$

Explanation:

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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Example Question #1 : Compare Two Fractions With Different Numerators And Different Denominators: Ccss.Math.Content.4.Nf.A.2

Select the symbol to correctly fill in the blank below.

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

Possible Answers:

Correct answer:

Explanation:

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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Example Question #2 : Compare Two Fractions With Different Numerators And Different Denominators: Ccss.Math.Content.4.Nf.A.2

Select the symbol to correctly fill in the blank below.

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

Possible Answers:

Correct answer:

Explanation:

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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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 #9 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #10 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #381 : Number Concepts And Operations

Example Question #382 : Number Concepts And Operations

Example Question #381 : Number Concepts And Operations

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

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

Example Question #12 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : Compare Two Fractions With Different Numerators And Different Denominators: Ccss.Math.Content.4.Nf.A.2

Example Question #2 : Compare Two Fractions With Different Numerators And Different Denominators: Ccss.Math.Content.4.Nf.A.2

All SSAT Upper Level Math Resources

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