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ISEE Lower Level Quantitative : Operations with fractions and whole numbers

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #261 : Number & Operations With Fractions

Solve:

$\small \frac{4}{8}\times\frac{1}{3}$ $\displaystyle \small \frac{4}{8}\times\frac{1}{3}$

Possible Answers:

$\small \frac{2}3{}$ $\displaystyle \small \frac{2}3{}$

$\small \frac{1}{3}$ $\displaystyle \small \frac{1}{3}$

$\small \frac{1}{6}$ $\displaystyle \small \frac{1}{6}$

$\small \frac{5}{6}$ $\displaystyle \small \frac{5}{6}$

$\small \frac{6}{7}$ $\displaystyle \small \frac{6}{7}$

Correct answer:

$\small \frac{1}{6}$ $\displaystyle \small \frac{1}{6}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{4}{8}\times\frac{1}{3}=\frac{4}{24}$ $\displaystyle \small \small \frac{4}{8}\times\frac{1}{3}=\frac{4}{24}$

$\small \frac{4}{24}$ $\displaystyle \small \frac{4}{24}$ can be reduced by dividing both sides by $\small 4$ $\displaystyle \small 4$

$\small \frac{4}{24}\div\frac{4}{4}=\frac{1}{6}$ $\displaystyle \small \frac{4}{24}\div\frac{4}{4}=\frac{1}{6}$

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Example Question #253 : Fractions

Solve:

$\small \frac{4}{8}\times\frac{3}{4}$ $\displaystyle \small \frac{4}{8}\times\frac{3}{4}$

Possible Answers:

$\small \frac{2}{3}$ $\displaystyle \small \frac{2}{3}$

$\small \frac{1}{4}$ $\displaystyle \small \frac{1}{4}$

$\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$

$\small \frac{7}{9}$ $\displaystyle \small \frac{7}{9}$

$\small \frac{3}{8}$ $\displaystyle \small \frac{3}{8}$

Correct answer:

$\small \frac{3}{8}$ $\displaystyle \small \frac{3}{8}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{4}{8}\times\frac{3}{4}=\frac{12}{32}$ $\displaystyle \small \small \frac{4}{8}\times\frac{3}{4}=\frac{12}{32}$

$\small \frac{12}{32}$ $\displaystyle \small \frac{12}{32}$ can be reduced by dividing both sides by $\small 4$ $\displaystyle \small 4$

$\small \frac{12}{32}\div\frac{4}{4}=\frac{3}{8}$ $\displaystyle \small \frac{12}{32}\div\frac{4}{4}=\frac{3}{8}$

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Example Question #1893 : Numbers And Operations

Solve:

$\small \frac{7}{8}\times\frac{1}{3}$ $\displaystyle \small \frac{7}{8}\times\frac{1}{3}$

Possible Answers:

$\small \frac{9}{11}$ $\displaystyle \small \frac{9}{11}$

$\small \frac{7}{24}$ $\displaystyle \small \frac{7}{24}$

$\small \frac{5}{27}$ $\displaystyle \small \frac{5}{27}$

$\small \frac{4}{5}$ $\displaystyle \small \frac{4}{5}$

$\small \frac{7}{21}$ $\displaystyle \small \frac{7}{21}$

Correct answer:

$\small \frac{7}{24}$ $\displaystyle \small \frac{7}{24}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{7}{8}\times\frac{1}{3}=\frac{7}{24}$ $\displaystyle \small \small \frac{7}{8}\times\frac{1}{3}=\frac{7}{24}$

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Example Question #1291 : Numbers And Operations

Solve:

$\small \frac{1}{5}\times\frac{1}{8}$ $\displaystyle \small \frac{1}{5}\times\frac{1}{8}$

Possible Answers:

$\small \frac{1}{40}$ $\displaystyle \small \frac{1}{40}$

$\small \frac{5}{6}$ $\displaystyle \small \frac{5}{6}$

$\small \frac{1}{20}$ $\displaystyle \small \frac{1}{20}$

$\small \frac{2}{40}$ $\displaystyle \small \frac{2}{40}$

$\small \frac{1}{12}$ $\displaystyle \small \frac{1}{12}$

Correct answer:

$\small \frac{1}{40}$ $\displaystyle \small \frac{1}{40}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{1}{5}\times\frac{1}{8}=\frac{1}{40}$ $\displaystyle \small \small \frac{1}{5}\times\frac{1}{8}=\frac{1}{40}$

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Example Question #32 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

Solve the following:

$\small \frac{1}{3}\times\frac{1}{9}$ $\displaystyle \small \frac{1}{3}\times\frac{1}{9}$

Possible Answers:

$\small \frac{1}{28}$ $\displaystyle \small \frac{1}{28}$

$\small \frac{1}{27}$ $\displaystyle \small \frac{1}{27}$

$\small \frac{2}{27}$ $\displaystyle \small \frac{2}{27}$

$\small \frac{5}{27}$ $\displaystyle \small \frac{5}{27}$

$\small \frac{1}{6}$ $\displaystyle \small \frac{1}{6}$

Correct answer:

$\small \frac{1}{27}$ $\displaystyle \small \frac{1}{27}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{1}{3}\times\frac{1}{9}=\frac{1}{27}$ $\displaystyle \small \small \frac{1}{3}\times\frac{1}{9}=\frac{1}{27}$

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Example Question #33 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

Solve:

$\small \frac{2}{5}\times\frac{1}{7}$ $\displaystyle \small \frac{2}{5}\times\frac{1}{7}$

Possible Answers:

$\small \frac{7}{8}$ $\displaystyle \small \frac{7}{8}$

$\small \frac{1}{15}$ $\displaystyle \small \frac{1}{15}$

$\small \frac{2}{7}$ $\displaystyle \small \frac{2}{7}$

$\small \frac{2}{35}$ $\displaystyle \small \frac{2}{35}$

$\small \frac{1}{5}$ $\displaystyle \small \frac{1}{5}$

Correct answer:

$\small \frac{2}{35}$ $\displaystyle \small \frac{2}{35}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\small \small \frac{2}{5}\times\frac{1}{7}=\frac{2}{35}$ $\displaystyle \small \small \frac{2}{5}\times\frac{1}{7}=\frac{2}{35}$

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Example Question #31 : Operations With Fractions And Whole Numbers

Jessica made $\displaystyle 2$ gallons of punch. $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch was water. How many gallons of water did she use to make the punch?

Possible Answers:

$\displaystyle 2$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\displaystyle 1$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

Correct answer:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch is water.

We know that we have $\displaystyle 2$ gallons of punch so we can set up our multiplication problem.

$\frac{1}{5}\times2$ $\displaystyle \frac{1}{5}\times2$

2 5

$\frac{1}{5}\times2$ $\displaystyle \frac{1}{5}\times2$ which means $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of each group of $2=\frac{2}{5}$ $\displaystyle 2=\frac{2}{5}$

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Example Question #1 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Ronda made $\displaystyle 3$ gallons of punch. $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch was water. How much water did she use to make the punch?

Possible Answers:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\displaystyle 1$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\displaystyle 3$

Correct answer:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch is water.

We know that we have $\displaystyle 3$ gallons of punch so we can set up our multiplication problem.

$\frac{1}{5}\times3$ $\displaystyle \frac{1}{5}\times3$

3 5

$\frac{1}{5}\times3$ $\displaystyle \frac{1}{5}\times3$ which means $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of each group of $3=\frac{3}{5}$ $\displaystyle 3=\frac{3}{5}$

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Example Question #2 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Mary-Beth made $\displaystyle 4$ gallons of punch. $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch was water. How much water did she use to make the punch?

Possible Answers:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\displaystyle 4$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\displaystyle 2$

Correct answer:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the punch is water.

We know that we have $\displaystyle 4$ gallons of punch so we can set up our multiplication problem.

$\frac{1}{5}\times4$ $\displaystyle \frac{1}{5}\times4$

4 5

$\frac{1}{5}\times4$ $\displaystyle \frac{1}{5}\times4$ which means $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of each group of $4=\frac{4}{5}$ $\displaystyle 4=\frac{4}{5}$

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Example Question #1 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Alison made $\displaystyle 2$ gallons of punch. $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the punch was water. How much water did she use to make the punch?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{3}{3}$ $\displaystyle \frac{3}{3}$

$\displaystyle 2$

$\displaystyle 3$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the punch is water.

We know that we have $\displaystyle 2$ gallons of punch so we can set up our multiplication problem.

$\frac{1}{3}\times2$ $\displaystyle \frac{1}{3}\times2$

2 3

$\frac{1}{3}\times2$ $\displaystyle \frac{1}{3}\times2$ which means $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of each group of $2=\frac{2}{3}$ $\displaystyle 2=\frac{2}{3}$

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Lower Level Quantitative : Operations with fractions and whole numbers

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #261 : Number & Operations With Fractions

Example Question #253 : Fractions

Example Question #1893 : Numbers And Operations

Example Question #1291 : Numbers And Operations

Example Question #32 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

Example Question #33 : Multiply A Fraction Or Whole Number By A Fraction: Ccss.Math.Content.5.Nf.B.4

Example Question #31 : Operations With Fractions And Whole Numbers

Example Question #1 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Example Question #2 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Example Question #1 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

All ISEE Lower Level Quantitative Resources

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