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ISEE Middle Level Quantitative : How to find the decimal equivalent of a fraction

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

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Example Questions

Example Question #851 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Write the result as a decimal:

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

Possible Answers:

3.75 $\displaystyle 3.75$

14.25 $\displaystyle 14.25$

5.75 $\displaystyle 5.75$

56.25 $\displaystyle 56.25$

16.25 $\displaystyle 16.25$

Correct answer:

3.75 $\displaystyle 3.75$

Explanation:

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

First, evaluate the term in parenthesis:

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

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

Apply the exponent by sparing the numerator and the denominator.

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

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

To subtract, convert the terms to a common denominator.

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

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

$\frac{15}{4}$ $\displaystyle \frac{15}{4}$

Divide to convert the fraction to a decimal.

$15 \div 4 = 3.75$ $\displaystyle 15 \div 4 = 3.75$

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Example Question #191 : Numbers And Operations

$\displaystyle x$ and $\displaystyle y$ are positive.

$\frac{1}{8} x = 0 .125 y$ $\displaystyle \frac{1}{8} x = 0 .125 y$

Which is the greater quantity?

(a) $\displaystyle x$

(b) $\displaystyle y$

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

It is impossible to determine which is greater from the information given

Correct answer:

(a) and (b) are equal

Explanation:

Multiply both sides by 8, and the following is revealed:

$\frac{1}{8} x = 0 .125 y$ $\displaystyle \frac{1}{8} x = 0 .125 y$

$\frac{x }{8} = 0 .125 y$ $\displaystyle \frac{x }{8} = 0 .125 y$

$\frac{x }{8} \cdot 8 = 0 .125 y \cdot 8$ $\displaystyle \frac{x }{8} \cdot 8 = 0 .125 y \cdot 8$

On the left side, the division is cancelled by the multiplication. On the right, $0.125 \cdot 8 = 1$ $\displaystyle 0.125 \cdot 8 = 1$, so

x = y $\displaystyle x = y$

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Example Question #851 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

$\displaystyle x$ and $\displaystyle y$ are positive.

$0.66 x = \frac{2}{3} y$ $\displaystyle 0.66 x = \frac{2}{3} y$

Which is the greater quantity?

(a) $\displaystyle x$

(b) $\displaystyle y$

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

This can be solved by noting that, converting the decimal to a fraction, $0.66 = \frac{66}{100}$ $\displaystyle 0.66 = \frac{66}{100}$.

The equation can be rewritten as

$\frac{66}{100}x = \frac{2}{3} y$ $\displaystyle \frac{66}{100}x = \frac{2}{3} y$

Multiply both sides by $\frac{100}{66 }$ $\displaystyle \frac{100}{66 }$ :

$\frac{100}{66 } \cdot \frac{66}{100}x =\frac{100}{66 } \cdot \frac{2}{3} y$ $\displaystyle \frac{100}{66 } \cdot \frac{66}{100}x =\frac{100}{66 } \cdot \frac{2}{3} y$

$x =\frac{200}{198} y$ $\displaystyle x =\frac{200}{198} y$

$\frac{200}{198} > 1$ $\displaystyle \frac{200}{198} > 1$, so

$\frac{200}{198} y > 1y$ $\displaystyle \frac{200}{198} y > 1y$, and

x> y $\displaystyle x> y$.

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Example Question #191 : Fractions

Express 0.0025 $\displaystyle 0.0025$ as a fraction.

Possible Answers:

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

$\frac{1}{400}$ $\displaystyle \frac{1}{400}$

$\frac{4}{11}$ $\displaystyle \frac{4}{11}$

$\frac{1}{25}$ $\displaystyle \frac{1}{25}$

$\frac{1}{500}$ $\displaystyle \frac{1}{500}$

Correct answer:

$\frac{1}{400}$ $\displaystyle \frac{1}{400}$

Explanation:

The last nonzero digit is in the ten-thousandths place, so write the number, without decimal point or leading zeroes, over 10,000. Then reduce.

$\frac{25}{10,000} = \frac{25 \div 25}{10,000\div 25} = \frac{1}{400}$ $\displaystyle \frac{25}{10,000} = \frac{25 \div 25}{10,000\div 25} = \frac{1}{400}$

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : How to find the decimal equivalent of a fraction

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #851 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #191 : Numbers And Operations

Example Question #851 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #191 : Fractions

All ISEE Middle Level Quantitative Resources

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