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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 #171 : Fractions

Which is the greater quantity?

(A) $\left (\frac{3}{5} \right )^{2}$

(B) $1 - \left ( \frac{2}{5} \right )^{2}$

Possible Answers:

(B) is greater

(A) is greater

(A) and (B) are equal

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

Correct answer:

(B) is greater

Explanation:

$\left (\frac{3}{5} \right )^{2} = \frac{3^{2}}{5^{2}} = \frac{9}{25}$

$1 - \left ( \frac{2}{5} \right )^{2} = 1- \frac{2^{2}}{5^{2}} = 1- \frac{4}{25} = \frac{25}{25}- \frac{4}{25} = \frac{25-4}{25}= \frac{21}{25}$

$\frac{21}{25} > \frac{9}{25}$ , so (B) is greater

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Example Question #2 : How To Multiply Fractions

Which is the greater quantity?

(A) $\left ( \frac{7}{25} \right )^{2}+ \left ( \frac{24}{25} \right )^{2}$

(B) $0.8^{2} + 0.6^{2}$

Possible Answers:

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

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

$\left ( \frac{7}{25} \right )^{2}+ \left ( \frac{24}{25} \right )^{2}$

$=\frac{7^{2}}{25^{2}} + \frac{24^{2}}{25^{2}}$

$=\frac{49}{625 } + \frac{576}{625 } = \frac{49+576}{625 } = \frac{625}{625 } = 1$

$0.8 ^{2} + 0.6^{2}$

$=0.8 \times 0.8 + 0.6 \times 0.6$

=0.64 + 0.36 = 1

The expressions are equal.

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Example Question #172 : Fractions

$a=1.5,\ b = 4.5$

Which is the greater quantity?

(A)

(B) a + b

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

(A) is greater

Explanation:

Solve for (A):

$ab = 1.5 \cdot 4.5 = 6.75$

Solve for (B):

a + b = 1.5 + 4.5 = 6

Since 6.75>6 , ab > a+b and (A) is greater.

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Example Question #173 : Fractions

$\tfrac{3}{4} \times 12 =$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{12}$

Correct answer:

Explanation:

When dealing with problems that involve fractions and whole numbers, first convert your whole number into a fraction. You can easily do this by putting the whole number over 1.

$12 \rightarrow\tfrac{12}{1}$

$\tfrac{3}{4}\times12=\tfrac{3}{4}\times\tfrac{12}{1}$

When multiplying, multiply the numerators by each other and the denominators by each other.

$\tfrac{3}{4} \times\tfrac{12}{1} = \tfrac{3\times12}{4\times1}=\tfrac{36}{4}$

Always reduce a fraction when possible. In this case, the numerator and denominator of $\tfrac{36}{4}$ are both divisible by 4. So, it reduces to 9.

$\tfrac{36}{4}=\tfrac{36\div4}{4\div4}=\tfrac{9}{1}=9$

$\tfrac{36}{4} \rightarrow\tfrac{9}{1}\rightarrow9$

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Example Question #173 : Numbers And Operations

$\frac{1}{2} \times \frac{2}{3} =$

Possible Answers:

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{1}{6}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

When multiplying fractions, simply multiply the numerators by each other and the denominators by each other.

$\frac{1}{2} \times \frac{2}{3} = \frac{1\times2}{2\times3}=\frac{2}{6}$

Always reduce fractions when possible. In this case, both the numerator and denominator are divisible by 2.

$\frac{2}{6}=\frac{2\div2}{6\div2}=\frac{1}{3}$

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Example Question #174 : Numbers And Operations

$\frac{4}{7} \times \frac{1}{2} =$

Possible Answers:

$\frac{2}{7}$

$\frac{3}{7}$

$\frac{8}{7}$

$\frac{2}{14}$

$\frac{4}{7}$

Correct answer:

$\frac{2}{7}$

Explanation:

When multiplying fractions, multiply the numerators and denominators.

$\frac{4}{7} \times \frac{1}{2} =\frac{4\times1}{7\times2}=\frac{4}{14}$

When possible, always reduce your fraction. In this case, both 4 and 14 are divisible by 2.

$\frac{4}{14}\rightarrow\frac{2}{7}$

The result is your answer.

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Example Question #175 : Numbers And Operations

$3 \times \tfrac{1}{3} =$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

Explanation:

When dealing with fractions and whole numbers, first convert the whole number into a fraction. This is easily done by putting the whole number over 1.

$3\rightarrow\tfrac{3}{1}$

When multiplying fractions, multiply both the numerators and denominators.

$\frac{3}{1}\times\frac{1}{3} =\frac{3\times1}{1\times3}=\frac{3}{3}$

When possible, always reduce your fraction. In this case, since the numerator and denominator is the same, the result is 1.

$\tfrac{3}{3}\rightarrow1$

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Example Question #173 : Fractions

Pentagon

The above pentagon has area 100. Which is the greater quantity?

(a) The area of the white region

(b) 25

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

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

Correct answer:

(b) is the greater quantity

Explanation:

Of the five triangles of equal area, one of them is white - this is $\frac{1}{5 }$ of the pentagon. The pentagon has area 100, so the area of the white triangle is

$\frac{1}{5 } \cdot 100 = \frac{100}{5 } = 20$ ,

which is less than 25.

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Example Question #174 : Fractions

Assorted 2

Note: figure NOT drawn to scale

Above are a rectangle and a triangle, each of which is divided equally into smaller shapes. Which is the greater quantity?

(a) The area of the shaded portion of the rectangle

(b) The area of the shaded portion of the triangle

Possible Answers:

(a) is the greater quantity

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

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

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

Explanation:

It cannot be determined which of the figures has the greater shaded area, because nothing is given about the areas, or even the comparative areas, of the rectangle and the triangle.

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Example Question #1 : How To Find The Decimal Equivalent Of A Fraction

Express 0.0025 as a fraction.

Possible Answers:

$\frac{1}{2,000}$

$\frac{1}{5,000}$

$\frac{1}{400}$

$\frac{1}{4,000}$

$\frac{1}{500}$

Correct answer:

$\frac{1}{400}$

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.

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

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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 #171 : Fractions

Example Question #2 : How To Multiply Fractions

Example Question #172 : Fractions

Example Question #173 : Fractions

Example Question #173 : Numbers And Operations

Example Question #174 : Numbers And Operations

Example Question #175 : Numbers And Operations

Example Question #173 : Fractions

Example Question #174 : Fractions

Example Question #1 : How To Find The Decimal Equivalent Of A Fraction

All ISEE Middle Level Quantitative Resources

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