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:

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

Possible Answers:

\(\displaystyle 3.75\)

\(\displaystyle 14.25\)

\(\displaystyle 5.75\)

\(\displaystyle 56.25\)

\(\displaystyle 16.25\)

Correct answer:

\(\displaystyle 3.75\)

Explanation:

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

First, evaluate the term in parenthesis:

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

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

Apply the exponent by sparing the numerator and the denominator.

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

\(\displaystyle 10 - \frac{25}{4}\)

To subtract, convert the terms to a common denominator.

\(\displaystyle \frac{40}{4} - \frac{25}{4}\)

\(\displaystyle \frac{40-25}{4}\)

\(\displaystyle \frac{15}{4}\)

Divide to convert the fraction to a decimal.

\(\displaystyle 15 \div 4 = 3.75\)

Example Question #191 : Numbers And Operations

\(\displaystyle x\) and \(\displaystyle y\) are positive.

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

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:

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

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

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

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

\(\displaystyle x = y\)

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

\(\displaystyle x\) and \(\displaystyle y\) are positive.

\(\displaystyle 0.66 x = \frac{2}{3} y\)

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, \(\displaystyle 0.66 = \frac{66}{100}\).

The equation can be rewritten as

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

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

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

\(\displaystyle x =\frac{200}{198} y\)

\(\displaystyle \frac{200}{198} > 1\), so

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

\(\displaystyle x> y\).

Example Question #191 : Fractions

Express \(\displaystyle 0.0025\) as a fraction.

Possible Answers:

\(\displaystyle \frac{2}{27}\)

\(\displaystyle \frac{1}{400}\)

\(\displaystyle \frac{4}{11}\)

\(\displaystyle \frac{1}{25}\)

\(\displaystyle \frac{1}{500}\)

Correct answer:

\(\displaystyle \frac{1}{400}\)

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.

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

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