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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

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Example Questions

Example Question #21 : Number & Operations With Fractions

Zach cleaned $\frac{1}{8}$ of the house and Alex cleaned $\frac{1}{3}$ of the house. How much more of the house did Alex clean?

Possible Answers:

$\frac{1}{3}$

$\frac{5}{24}$

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{7}{24}$

Correct answer:

$\frac{5}{24}$

Explanation:

$\frac{1}{3}-\frac{1}{8}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{8}\times\frac{3}{3}=\frac{3}{24}$

$\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$

$\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{8}{24}-\frac{3}{24}=\frac{5}{24}$

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Example Question #161 : Numbers And Operations

Lily pulled $\frac{1}{9}$ of the weeds and Rose pulled $\frac{1}{3}$ . How much more of the weeds did Rose pull?

Possible Answers:

$\frac{3}{5}$

$\frac{2}{3}$

$\frac{5}{7}$

$\frac{1}{9}$

$\frac{2}9{}$

Correct answer:

$\frac{2}9{}$

Explanation:

$\frac{1}{3}-\frac{1}{9}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{3}\times\frac{3}{3}=\frac{3}{9}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{3}{9}-\frac{1}{9}=\frac{2}{9}$

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Example Question #23 : Number & Operations With Fractions

Sally drank $\frac{1}{12}$ of the milk and Sam drank $\frac{2}{3}$ . How much more of the milk did Sam drink?

Possible Answers:

$\frac{5}{12}$

$\frac{7}{12}$

$\frac{7}8{}$

$\frac{1}2{}$

$\frac{2}3{}$

Correct answer:

$\frac{7}{12}$

Explanation:

$\frac{2}{3}-\frac{1}{12}$

In order to solve this problem, we first need to make common denominators.

$\frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{8}{12}-\frac{1}{12}=\frac{7}{12}$

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Example Question #24 : Number & Operations With Fractions

Jake ate $\frac{1}{7}$ of the popcorn and Dave ate $\small \frac{4}{14}$ of the popcorn. How much more of the popcorn did Dave eat?

Possible Answers:

$\frac{2}7{}$

$\frac{1}7{}$

$\frac{9}{11}$

$\frac{2}3{}$

$\frac{5}6{}$

Correct answer:

$\frac{1}7{}$

Explanation:

$\frac{4}{14}-\frac{1}{7}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{7}\times\frac{2}{2}=\frac{2}{14}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{4}{14}-\frac{2}{14}=\frac{2}{14}$

$\small \frac{2}{14}$ can be reduced by dividing $\small 2$ by both sides.

$\small \frac {2}{14}\div\frac{2}{2}=\frac{1}{7}$

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Example Question #161 : Fractions

$\small \frac{3}{15}\cdot \frac{4}{5}$

Possible Answers:

$\small \frac{36}{225}$

$\small \frac{4}{25}$

$\small \frac{12}{75}$

$\small \frac{12}{225}$

$\small \frac{36}{15}$

Correct answer:

$\small \frac{4}{25}$

Explanation:

When multiplying fractions you simply multiply the numerators to find the numerator of the product, and multiply the denominators to find the denominator of the product.

$\small 3\cdot 4=12$

$\small 5\cdot 15=75$

So, our product is $\small \frac{12}{75}$ .

Since both of these numbers are divisible by three, we simplify.

$\small \frac{12}{3}=4$

$\small \frac{75}{3}= 25$

Our final answer is $\small \frac{4}{25}$ .

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Example Question #162 : Fractions

Which is the greater quantity?

(a) $3 \frac{1}{3} \times 4 \frac{1}{5}$

(b) $12 \frac{1}{15}$

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:

Rewrite the mixed numbers as improper fractions, then multiply across:

$3 \frac{1}{3} = \frac{3\times 3 + 1}{3} = \frac{10}{3}$

$4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5}$

$3 \frac{1}{3} \times 4 \frac{1}{5} = \frac{10}{3} \times \frac{21}{5} = \frac{2}{1} \times \frac{7}{1} = 14$

$14 > 12 \frac{1}{5}$

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Example Question #163 : Fractions

Which is the greater quantity?

(a) $6 \frac{5}{6} \times 6$

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) and (b) are equal

Explanation:

Rewrite the factors as improper fractions, then multiply across:

$6 \frac{5}{6} = \frac{6\times 6 + 5}{6} = \frac{36 + 5}{6} = \frac{41}{6}$

$6 = \frac{6}{1}$

$6 \frac{5}{6} \times 6 =\frac{41}{6}\times \frac{ 6}{1}=\frac{41}{1}\times \frac{ 1}{1} = 41$

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Example Question #164 : Fractions

0.75 t = 0.3

$\frac{7}{4} k = \frac{7}{10}$

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

(a) 0.75 t = 0.3

$0.75 t \div 0.75 = 0.3 \div 0.75$

$t= 0.3 \div 0.75$

Divide by moving the decimal point right two places in both numbers:

$t= 30 \div 75 = 0.4$

(b) $\frac{7}{4} k = \frac{7}{10}$

$\frac{4} {7} \cdot \frac{7}{4} k =\frac{4} {7} \cdot \frac{7}{10}$

$k =\frac{4} {7} \cdot \frac{7}{10}$

Cross-cancel:

$k =\frac{2} {1} \cdot \frac{1}{5} = \frac{2} {5}$

$0.4 = \frac{4}{10 } = \frac{4\div 2}{10\div 2 } = \frac{2}{5}$ , so k = t

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Example Question #162 : Numbers And Operations

Which is the greater quantity?

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

(B) $0.6^{2}$

Possible Answers:

(B) is greater

(A) and (B) are equal

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

(A) is greater

Correct answer:

(B) is greater

Explanation:

$\frac{3}{5} = 3 \div 5 = 0.6$ , so

$\left ( \frac{3}{5} \right )^{3} = 0.6^{3} = 0.6 \times 0.6 \times 0.6 = 0.36 \times 0.6 = 0.216$

$0.6 ^{2} = 0.6 \times 0.6 = 0.36$

0.36 > 0.216 , so $0.6^{2} > \left ( \frac{3}{5} \right )^{3}$ , making (B) greater.

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Example Question #166 : Fractions

Which is the greater quantity?

(A) 0.5

(B) $\left ( \frac{4}{5} \right )^{3}$

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

$\left ( \frac{4}{5} \right )^{3} = 0.8 ^{3} = 0.8 \times 0.8 \times 0,8 = 0.64\times 0,8 = 0.512$

Since 0.512 > 0.5 , $\left ( \frac{4}{5} \right )^{3} > 0.5$ , so (B) is greater.

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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 #21 : Number & Operations With Fractions

Example Question #161 : Numbers And Operations

Example Question #23 : Number & Operations With Fractions

Example Question #24 : Number & Operations With Fractions

Example Question #161 : Fractions

Example Question #162 : Fractions

Example Question #163 : Fractions

Example Question #164 : Fractions

Example Question #162 : Numbers And Operations

Example Question #166 : Fractions

All ISEE Middle Level Quantitative Resources

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