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ISEE Middle Level Quantitative : Numbers and Operations

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : How To Find The Decimal Equivalent Of A Fraction

Which is the greater quantity?

(a) $\frac{1}{7}$

(b) 0.143

Possible Answers:

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

Divide 1 by 7:

$\frac{1}{7} = 1 \div 7 = 0.142857... < 0.143$

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Example Question #3 : How To Find The Decimal Equivalent Of A Fraction

Which is the greater quantity?

(a) $\frac{7}{11}$

(b) 0.63

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(a) is greater

Explanation:

Divide 7 by 11:

$\frac{7}{11} = 7 \div 11 = 0.636363... > 0.63$

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Example Question #4 : How To Find The Decimal Equivalent Of A Fraction

Which is the greater quantity?

(a) $- \frac{3}{13}$

(b) -0.23

Possible Answers:

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

Divide 3 by 13:

$\frac{3}{13} = 3 \div 13 = 0.230769... > 0.23$

$\frac{3}{13} > 0.23 \Rightarrow -\frac{3}{13} < - 0.23$

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Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Which is the greater quantity?

(a) $- \frac{7}{12}$

(b) -0.58

Possible Answers:

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

(a) is greater

Correct answer:

(b) is greater

Explanation:

Divide 7 by 12:

$7 \div 12 = 0.58333... > 0.58$

$\frac{7 }{12} > 0.58$ , so $- \frac{7 }{12} < - 0.58$

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Example Question #181 : Numbers And Operations

Column A Column B

$\frac{9}{25}$

Possible Answers:

The quantity in Column B is greater.

There is no relationship between the quantities.

The quantity in Column A is greater.

The quantites are equal.

Correct answer:

The quantity in Column A is greater.

Explanation:

There are two ways to solve this problem. You can convert both to either fractions or decimals so that you can properly compare them. If you want to compare them as decimals, convert Column B to a decimal by dividing 9 by 25, which gives you 0.36. Then, you can see that Column A is greater. If you want to look at both as fractions, put 68 over 100 to get $\frac{68}{100}.$ This can be further simplifies to $\frac{17}{25}.$ Therefore, you can see that Column A is greater.

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Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Give the answer as a decimal:

$\frac{1}{5} + \frac{1}{4} - \frac{1}{10}$

Possible Answers:

0.36

0.32

0.4

0.35

0.44

Correct answer:

0.35

Explanation:

$\frac{1}{5} = 1 \div 5 = 0.2$

$\frac{1}{4} = 1 \div 4 = 0.25$

$\frac{1}{10} = 1 \div 10 = 0.1$

$\frac{1}{5} + \frac{1}{4} - \frac{1}{10} = 0.2 + 0.25 - 0.1 = 0.45 - 0.1 = 0.35$

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Example Question #7 : How To Find The Decimal Equivalent Of A Fraction

Give the answer as a decimal:

$\left (\frac{3}{4} \right )^{2}$

Possible Answers:

0.5625

0.5125

0.5775

0.5475

0.5375

Correct answer:

0.5625

Explanation:

$\left (\frac{3}{4} \right )^{2} = \frac{3^{2}}{4^{2}} = \frac{9}{16} = 9 \div 16 = 0.5625$

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Example Question #8 : How To Find The Decimal Equivalent Of A Fraction

Give the result as a decimal:

$\frac{4}{5} + \frac{3}{4} \cdot \frac{1}{2}$

Possible Answers:

0.775

1.225

0.975

1.175

Correct answer:

1.175

Explanation:

$\frac{4}{5} + \frac{3}{4} \cdot \frac{1}{2}$

$= \frac{4}{5} + \frac{3\cdot 1}{4\cdot 2}$

$= \frac{4}{5} + \frac{3 }{8}$

$= \frac{4\cdot 8}{5 \cdot 8} + \frac{5 \cdot 3 }{5 \cdot8}$

$= \frac{32}{40} + \frac{15}{40} = \frac{32+ 15 }{40} = \frac{47 }{40}$

$\frac{47 }{40} = 47 \div 40 = 1.175$

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Example Question #9 : How To Find The Decimal Equivalent Of A Fraction

Give the result as a decimal:

$2-\left ( \frac{3}{2} \right )^{2}$

Possible Answers:

4.25

-0.25

-2.5

0.25

-4.25

Correct answer:

-0.25

Explanation:

$2-\left ( \frac{3}{2} \right )^{2}$

Square the fraction by squaring both the numerator and the denominator.

$2-\left ( \frac{3^{2}}{2^{2}} \right )$

$2- \frac{9}{4}$

To subtract, convert so that each term shares a common denominator.

$\frac{8}{4}- \frac{9}{4}$

$\frac{8-9}{4}$

$\frac{-1}{4}$

$-\frac{1}{4}$

Finally, convert to a decimal.

$- \frac{1}{4} = -1 \div 4 = -0.25$

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Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Write the result as a decimal:

$10 - \left ( 2 \frac{1}{2}\right )^{2}$

Possible Answers:

5.75

14.25

3.75

56.25

16.25

Correct answer:

3.75

Explanation:

$10 - \left ( 2 \frac{1}{2}\right )^{2}$

First, evaluate the term in parenthesis:

$10 - \left ( \frac{2 \times 2 + 1}{2}\right )^{2}$

$10 - \left ( \frac{5}{2}\right )^{2}$

Apply the exponent by sparing the numerator and the denominator.

$10 - \left ( \frac{5^{2}}{2^{2}}\right )$

$10 - \frac{25}{4}$

To subtract, convert the terms to a common denominator.

$\frac{40}{4} - \frac{25}{4}$

$\frac{40-25}{4}$

$\frac{15}{4}$

Divide to convert the fraction to a decimal.

$15 \div 4 = 3.75$

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Numbers and Operations

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #2 : How To Find The Decimal Equivalent Of A Fraction

Example Question #3 : How To Find The Decimal Equivalent Of A Fraction

Example Question #4 : How To Find The Decimal Equivalent Of A Fraction

Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Example Question #181 : Numbers And Operations

Example Question #5 : How To Find The Decimal Equivalent Of A Fraction

Example Question #7 : How To Find The Decimal Equivalent Of A Fraction

Example Question #8 : How To Find The Decimal Equivalent Of A Fraction

Example Question #9 : How To Find The Decimal Equivalent Of A Fraction

Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

All ISEE Middle Level Quantitative Resources

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