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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 #1 : How To Subtract Fractions

Which is the greater quantity?

(a) $8 - 3 \frac{3}{7}$

(b) $5 \frac{3}{7}$

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(b) is greater

Explanation:

"Borrow" 1 from the 8 and subtract vertically:

$8 - 3 \frac{3}{7} = 7 \frac{7}{7} - 3 \frac{3}{7}$ :

$7 \frac{7}{7}$

$\underline{- 3 \frac{3}{7}}$

$4 \frac{4}{7}$

$4 \frac{4}{7} < 5 \frac{3}{7}$

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Example Question #2 : How To Subtract Fractions

Which is the greater quantity?

(a) $6 \frac{2}{7} - 2 \frac{6}{7}$

(b) $4 \frac{4}{7}$

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

"Borrow" 1 from the 6 and subtract vertically:

$6 \frac{2}{7} - 2 \frac{6}{7} = 5 \frac{9}{7} - 2 \frac{6}{7}$

$5 \frac{9}{7}$

$\underline{ - 2 \frac{6}{7}}$

$3 \frac{3}{7}$

$3 \frac{3}{7} < 4 \frac{4}{7}$

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Example Question #3 : How To Subtract Fractions

a + 3.7 = 8.2

$b + 4 \frac{2}{3} = 9$

Which is the greater quantity?

(a)

(b)

Possible Answers:

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

(b) is greater

Correct answer:

(a) is greater

Explanation:

(a) a + 3.7 =8.2

a + 3.7- 3.7 = 8.2 - 3.7

a = 4.5

(b) $b + 4 \frac{2}{3} = 9$

$b + 4 \frac{2}{3} - 4 \frac{2}{3} = 9- 4 \frac{2}{3}$

$b = 9- 4 \frac{2}{3} = 8\frac{3}{3}- 4\frac{2}{3} = 4\frac{1}{3}$

$4\frac{1}{3} = 4.333... < 4.5$ , so a>b .

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Example Question #4 : How To Subtract Fractions

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

Which is the greater quantity?

(a) x - y

(b) $-\frac{1}{2}$

Possible Answers:

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

(b) is greater

Correct answer:

(a) is greater

Explanation:

Subtract both sides of the two equations:

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

$x - y = \frac{1}{2} + \frac{1}{3}- \left ( \frac{1}{2} + \frac{2}{3} \right )$

$x - y = \frac{1}{2} + \frac{1}{3}-\frac{1}{2} - \frac{2}{3}$

$x - y = \frac{1}{2} -\frac{1}{2}+ \frac{1}{3} - \frac{2}{3}$

$x - y = - \frac{1}{3}$

Since $\frac{1}{3} < \frac{1}{2}$ , then $x-y = -\frac{1}{3} > - \frac{1}{2}$

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Example Question #4 : How To Subtract Fractions

$\frac{7}{8} - \frac{3}{4} =$

Possible Answers:

$\frac{7}{4}$

$\frac{1}{2}$

$\frac{1}{8}$

$\frac{5}{12}$

Correct answer:

$\frac{1}{8}$

Explanation:

When subtracting fractions with different denominators, first change the fractions so that they have the same denominator. Do this by finding the least common multiple of both 4 and 8. Some multiples of 4 and 8 are:

4: 4, 8, 12, 16...

8: 8, 16, 24, 32...

Since 8 is the first common multiple between 4 and 8, change the fractions accordingly so that their denominators equal 8. Since $\tfrac{7}{8}$ already has a denominator of 8, it does not need to change. Change $\tfrac{3}{4}$ , however, accordingly.

$\frac{3}{4}\times\frac{2}{2}\rightarrow\frac{6}{8}$

The problem now looks like this:

$\frac{7}{8}-\frac{6}{8}=$

Subtract the numerators. The result is your answer.

$\frac{7}{8}-\frac{6}{8}=\frac{7-6}{8}=\frac{1}{8}$

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Example Question #4 : How To Subtract Fractions

$2\tfrac{1}{2} - 1\tfrac{3}{5} =$

Possible Answers:

$1\tfrac{2}{3}$

$-1\tfrac{2}{3}$

None of these

$\frac{9}{10}$

Correct answer:

$\frac{9}{10}$

Explanation:

When dealing with fractions and mixed numbers, first convert the mixed numbers to improper fractions.

$2\tfrac{1}{2} \rightarrow\tfrac{5}{2}$

$1\tfrac{3}{5}\rightarrow\tfrac{8}{5}$

The next thing you must do is change the denominators so that they are equal. Do this by finding the least common multiple of 2 and 5. Some multiples of 2 and 5 are:

2: 2, 4, 6, 8, 10...

5: 5, 10, 15, 20...

10 is the first common multiple of both 2 and 5, so change the fractions accordingly so that their denominators both equal 10.

$\tfrac{5}{2}\times\tfrac{5}{5}\rightarrow\tfrac{25}{10}$

$\tfrac{8}{5}\times\tfrac{2}{2}\rightarrow\tfrac{16}{10}$

The problem now looks like this:

$\tfrac{25}{10}-\tfrac{16}{10}=$

Subtract the numerators of the fraction. The result is your answer.

$\tfrac{25}{10}-\tfrac{16}{10}=\tfrac{25-16}{10}=\tfrac{9}{10}$

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Example Question #471 : Fractions

This year, Samantha grew $\frac{1}{6}$ of an inch, and her brother, David, grew $\frac{2}{6}$ of an inch. How much more did David grow than Samantha?

Possible Answers:

$\frac{5}{6}$

$\frac{2}{6}$

$\frac{4}{6}$

$\frac{1}{6}$

$\frac{3}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

The phrase, "how much more" tells as that we want to find the difference in how much they've grown.

$\frac{2}{6}-\frac{1}{6}=\frac{1}{6}$

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Example Question #472 : Fractions

This year, Cassie grew $\frac{3}{9}$ of an inch, and her brother, Charlie, grew $\frac{5}{9}$ of an inch. How much more did Charlie grow than Cassie?

Possible Answers:

$\frac{6}{9}$

$\frac{5}{9}$

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{4}{9}$

Correct answer:

$\frac{2}{9}$

Explanation:

The phrase, "how much more" tells as that we want to find the difference in how much they've grown.

$\frac{5}{9}-\frac{3}{9}=\frac{2}{9}$

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Example Question #473 : Fractions

This year, Emily grew $\frac{1}{6}$ of an inch, and her brother, Dan, grew $\frac{4}{6}$ of an inch. How much more did Dan grow than Emily?

Possible Answers:

$\frac{3}{6}$

$\frac{5}{6}$

$\frac{4}{6}$

$\frac{2}{6}$

$\frac{1}{6}$

Correct answer:

$\frac{3}{6}$

Explanation:

The phrase, "how much more" tells as that we want to find the difference in how much they've grown.

$\frac{4}{6}-\frac{1}{6}=\frac{3}{6}$

Report an Error

Example Question #961 : Numbers And Operations

This year, Sally grew $\frac{3}{6}$ of an inch, and her brother, Drew, grew $\frac{5}{6}$ of an inch. How much more did Drew grow than Sally?

Possible Answers:

$\frac{4}{6}$

$\frac{5}{6}$

$\frac{3}{6}$

$\frac{2}{6}$

$\frac{1}{6}$

Correct answer:

$\frac{2}{6}$

Explanation:

The phrase, "how much more" tells as that we want to find the difference in how much they've grown.

$\frac{5}{6}-\frac{3}{6}=\frac{2}{6}$

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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 #1 : How To Subtract Fractions

Example Question #2 : How To Subtract Fractions

Example Question #3 : How To Subtract Fractions

Example Question #4 : How To Subtract Fractions

Example Question #4 : How To Subtract Fractions

Example Question #4 : How To Subtract Fractions

Example Question #471 : Fractions

Example Question #472 : Fractions

Example Question #473 : Fractions

Example Question #961 : Numbers And Operations

All ISEE Middle Level Quantitative Resources

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