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ISEE Middle Level Math : Numbers and Operations

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #891 : Numbers And Operations

What is the decimal equivalent to $\frac{30}{120}$ $\displaystyle \frac{30}{120}$?

Possible Answers:

$\displaystyle .30$

$\displaystyle 25$

$\displaystyle .25$

$\displaystyle .120$

Correct answer:

$\displaystyle .25$

Explanation:

Divide the numerator (top number) by the denominator (bottom number):

$30\div 120=.25$ $\displaystyle 30\div 120=.25$

Answer: $\displaystyle .25$

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Example Question #212 : Percentage

What is $\frac{240}{600}$ $\displaystyle \frac{240}{600}$ written as a decimal?

Possible Answers:

$\displaystyle .60$

$\displaystyle .40$

4.0 $\displaystyle 4.0$

$\displaystyle .24$

Correct answer:

$\displaystyle .40$

Explanation:

Divide the numerator (top number) by the denominator (bottom number):

$240\div 600=.40$ $\displaystyle 240\div 600=.40$

Answer: $\displaystyle .40$

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Example Question #21 : Percentages

What is the decimal equivalent of $\frac{12}{96}$ $\displaystyle \frac{12}{96}$?

Possible Answers:

$\displaystyle .125$

125 $\displaystyle 125$

12.5 $\displaystyle 12.5$

1.25 $\displaystyle 1.25$

Correct answer:

$\displaystyle .125$

Explanation:

Divide the numerator (top number) by the denominator (bottom number):

$12\div 96=.125$ $\displaystyle 12\div 96=.125$

Answer: $\displaystyle .125$

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Example Question #22 : Percentages

Write $\frac{42}{70}$ $\displaystyle \frac{42}{70}$ as a decimal.

Possible Answers:

$\displaystyle 60$

6.0 $\displaystyle 6.0$

$\displaystyle .60$

$\displaystyle .06$

Correct answer:

$\displaystyle .60$

Explanation:

Divide the numerator (top number) by the denominator (bottom number):

$42\div 70=.60$ $\displaystyle 42\div 70=.60$

Answer: $\displaystyle .60$

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Example Question #23 : Percentages

Write $42\%$ $\displaystyle 42\%$ as a decimal.

Possible Answers:

$\displaystyle 42$

$\displaystyle .042$

$\displaystyle .42$

4.2 $\displaystyle 4.2$

Correct answer:

$\displaystyle .42$

Explanation:

To convert a percentage into a decimal, divide the number by 100.

Here's a trick: Simply pretend there is a decimal point at the end of the number, and then move the decimal point two places to the left.

You can think of 42 as 42.0 (or 42. - the zero doesn't matter). Now move the decimal point two places to the left.

Answer: $\displaystyle .42$

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Example Question #892 : Numbers And Operations

What is 0.06% of 0.07?

Possible Answers:

0.00042 $\displaystyle 0.00042$

$\displaystyle 42$

$\displaystyle 0.000042$

4,200 $\displaystyle 4,200$

0.0042 $\displaystyle 0.0042$

Correct answer:

$\displaystyle 0.000042$

Explanation:

0.06%, as a decimal, is equal to $0.06 \div 100 = 0.0006$ $\displaystyle 0.06 \div 100 = 0.0006$, so 0.06% of 0.07 is equal to

$0.0006 \times 0.07 = 0.000042$ $\displaystyle 0.0006 \times 0.07 = 0.000042$

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Example Question #897 : Numbers And Operations

What is $5 \frac{1}{3} \%$ $\displaystyle 5 \frac{1}{3} \%$ of $333\frac{1}{3}$ $\displaystyle 333\frac{1}{3}$ ?

Possible Answers:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

$1 \frac{7}{9}$ $\displaystyle 1 \frac{7}{9}$

$17 \frac{7}{9}$ $\displaystyle 17 \frac{7}{9}$

$62 \frac{1}{2 }$ $\displaystyle 62 \frac{1}{2 }$

$6 \frac{1}{4}$ $\displaystyle 6 \frac{1}{4}$

Correct answer:

$17 \frac{7}{9}$ $\displaystyle 17 \frac{7}{9}$

Explanation:

$5 \frac{1}{3} \%$ $\displaystyle 5 \frac{1}{3} \%$ of $333\frac{1}{3}$ $\displaystyle 333\frac{1}{3}$ is equal to:

$\frac{5 \frac{1}{3} }{100} \times 333 \frac{1}{3}$ $\displaystyle \frac{5 \frac{1}{3} }{100} \times 333 \frac{1}{3}$

$= \frac{ \frac{16}{3} }{100} \times \frac{1,000}{3}$ $\displaystyle = \frac{ \frac{16}{3} }{100} \times \frac{1,000}{3}$

$= \frac{16}{3} \times \frac{1 }{100} \times \frac{1,000}{3}$ $\displaystyle = \frac{16}{3} \times \frac{1 }{100} \times \frac{1,000}{3}$

Cross-cancel:

$\frac{16}{3} \times \frac{1 }{1} \times \frac{10}{3}$ $\displaystyle \frac{16}{3} \times \frac{1 }{1} \times \frac{10}{3}$

$= \frac{160}{9} = 17 \frac{7}{9}$ $\displaystyle = \frac{160}{9} = 17 \frac{7}{9}$

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Example Question #893 : Numbers And Operations

What is $17 \frac{1}{2} \%$ $\displaystyle 17 \frac{1}{2} \%$ of $17 \frac{1}{2}$ $\displaystyle 17 \frac{1}{2}$ ?

Possible Answers:

$30 \frac{5}{8}$ $\displaystyle 30 \frac{5}{8}$

$306 \frac{1}{4}$ $\displaystyle 306 \frac{1}{4}$

100 $\displaystyle 100$

$\displaystyle 1$

$3\frac{1}{16}$ $\displaystyle 3\frac{1}{16}$

Correct answer:

$3\frac{1}{16}$ $\displaystyle 3\frac{1}{16}$

Explanation:

$17 \frac{1}{2} \%$ $\displaystyle 17 \frac{1}{2} \%$ of $17 \frac{1}{2}$ $\displaystyle 17 \frac{1}{2}$ can be rewritten as

$\frac{17 \frac{1}{2} }{100} \times 17 \frac{1}{2}$ $\displaystyle \frac{17 \frac{1}{2} }{100} \times 17 \frac{1}{2}$

$= \frac{35}{2} \times \frac{1}{100} \times \frac{35}{2}$ $\displaystyle = \frac{35}{2} \times \frac{1}{100} \times \frac{35}{2}$

$= \frac{35 \times 1 \times 35}{2 \times 100 \times 2}$ $\displaystyle = \frac{35 \times 1 \times 35}{2 \times 100 \times 2}$

$= \frac{1,225}{400} = \frac{1,225 \div 25}{400\div 25} = \frac{49}{16} = 3 \frac{1}{16}$ $\displaystyle = \frac{1,225}{400} = \frac{1,225 \div 25}{400\div 25} = \frac{49}{16} = 3 \frac{1}{16}$

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Example Question #225 : Percentage

What is 1,800% of 0.00018?

Possible Answers:

$\displaystyle 1,000,000$

0.00324 $\displaystyle 0.00324$

0.0001 $\displaystyle 0.0001$

10,000 $\displaystyle 10,000$

0.324 $\displaystyle 0.324$

Correct answer:

0.00324 $\displaystyle 0.00324$

Explanation:

1,800% of 0.00018 is equal to

$\frac{1,800}{100} \times 0.00018 = 18 \times 0.00018 = 0.00324$ $\displaystyle \frac{1,800}{100} \times 0.00018 = 18 \times 0.00018 = 0.00324$.

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Example Question #226 : Percentage

What is 1.11% percent of 1.11?

Possible Answers:

$\displaystyle 0.012321$

100 $\displaystyle 100$

$\displaystyle 0.0012321$

0.12321 $\displaystyle 0.12321$

$\displaystyle 1$

Correct answer:

$\displaystyle 0.012321$

Explanation:

Taking 1.11% percent of a number is the same as multiplying it by 0.0111, so

1.11% percent of 1.11 is equal to

$0.0111 \times 1.11 = 0.012321$ $\displaystyle 0.0111 \times 1.11 = 0.012321$.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Numbers and Operations

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #891 : Numbers And Operations

Example Question #212 : Percentage

Example Question #21 : Percentages

Example Question #22 : Percentages

Example Question #23 : Percentages

Example Question #892 : Numbers And Operations

Example Question #897 : Numbers And Operations

Example Question #893 : Numbers And Operations

Example Question #225 : Percentage

Example Question #226 : Percentage

All ISEE Middle Level Math Resources

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