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ISEE Middle Level Math : Numbers and Operations

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Example Questions

Example Question #321 : Numbers And Operations

How do you write $\frac{3}{100}$ $\displaystyle \frac{3}{100}$ as a decimal?

Possible Answers:

$\displaystyle .003$

$\displaystyle .30$

$\displaystyle .03$

$\displaystyle 3$

Correct answer:

$\displaystyle .03$

Explanation:

Divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction) to convert the fraction to a decimal:

$3\div 100=.03$ $\displaystyle 3\div 100=.03$

Answer: $\displaystyle .03$

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Example Question #322 : Numbers And Operations

Write $\frac{4}{160}$ $\displaystyle \frac{4}{160}$ as a decimal.

Possible Answers:

$\displaystyle .04$

$\displaystyle .025$

$\displaystyle 25$

$\displaystyle .25$

Correct answer:

$\displaystyle .025$

Explanation:

Divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction) to convert the fraction to a decimal:

$4\div 160=.025$ $\displaystyle 4\div 160=.025$

Answer: $\displaystyle .025$

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Example Question #323 : Numbers And Operations

What is the decimal equivalent to $\frac{50}{250}$ $\displaystyle \frac{50}{250}$?

Possible Answers:

$\displaystyle .50$

$\displaystyle 20$

$\displaystyle .020$

$\displaystyle .20$

Correct answer:

$\displaystyle .20$

Explanation:

Divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction) to convert the fraction to a decimal:

$50\div 250=.20$ $\displaystyle 50\div 250=.20$

Answer: $\displaystyle .20$

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Example Question #324 : Numbers And Operations

Convert $\frac{11}{110}$ $\displaystyle \frac{11}{110}$ to a decimal.

Possible Answers:

$\displaystyle .011$

$\displaystyle .11$

$\displaystyle .10$

$\displaystyle .010$

Correct answer:

$\displaystyle .10$

Explanation:

Divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction) to convert the fraction to a decimal:

$11\div 110=.10$ $\displaystyle 11\div 110=.10$

Answer: $\displaystyle .10$

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Example Question #176 : Fractions

Arrange these numbers from least to greatest:

$\left \{ \frac{1}{7}, \frac{3}{20}, \frac{7}{50} \right \}$ $\displaystyle \left \{ \frac{1}{7}, \frac{3}{20}, \frac{7}{50} \right \}$

Possible Answers:

$\left \{ \frac{1}{7} , \frac{3}{20}, \frac{7}{50} \right \}$ $\displaystyle \left \{ \frac{1}{7} , \frac{3}{20}, \frac{7}{50} \right \}$

$\left \{ \frac{7}{50}, \frac{3}{20} , \frac{1}{7} \right \}$ $\displaystyle \left \{ \frac{7}{50}, \frac{3}{20} , \frac{1}{7} \right \}$

$\left \{ \frac{3}{20} , \frac{7}{50}, \frac{1}{7} \right \}$ $\displaystyle \left \{ \frac{3}{20} , \frac{7}{50}, \frac{1}{7} \right \}$

$\left \{ \frac{3}{20}, \frac{1}{7} , \frac{7}{50}\right \}$ $\displaystyle \left \{ \frac{3}{20}, \frac{1}{7} , \frac{7}{50}\right \}$

$\left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$ $\displaystyle \left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$

Correct answer:

$\left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$ $\displaystyle \left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$

Explanation:

Rewrite all three numbers as their decimal equivalents by dividing numerator by denominator.

$\frac{1}{7} = 1 \div 7 = 0.142857 ...$ $\displaystyle \frac{1}{7} = 1 \div 7 = 0.142857 ...$

$\frac{3}{20} = 3 \div 20 = 0.15$ $\displaystyle \frac{3}{20} = 3 \div 20 = 0.15$

$\frac{7}{50} = 7 \div 50 = 0.14$ $\displaystyle \frac{7}{50} = 7 \div 50 = 0.14$

From the decimal equivalents, the fractions can be arranged as follows:

$\left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$ $\displaystyle \left \{ \frac{7}{50}, \frac{1}{7}, \frac{3}{20} \right \}$

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Example Question #325 : Numbers And Operations

Write $\frac{5 }{12}$ $\displaystyle \frac{5 }{12}$ as a decimal.

Possible Answers:

$0.41\overline{6}$ $\displaystyle 0.41\overline{6}$

$0.4 \overline{6}$ $\displaystyle 0.4 \overline{6}$

0.42 $\displaystyle 0.42$

$0.41\overline{8}$ $\displaystyle 0.41\overline{8}$

0.41 $\displaystyle 0.41$

Correct answer:

$0.41\overline{6}$ $\displaystyle 0.41\overline{6}$

Explanation:

Divide 5 by 12.

$\frac{5}{12} = 5\div 12 = 0.41666...$ $\displaystyle \frac{5}{12} = 5\div 12 = 0.41666...$

Note that the "6" repeats forever. This can be written as $0.41\overline{6}$ $\displaystyle 0.41\overline{6}$.

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Example Question #326 : Numbers And Operations

How many of the following four numbers are elements of the set

$A = \left \{ x \; | \; \frac{1}{2}< x < \frac{2}{3}\right \} ?$ $\displaystyle A = \left \{ x \; | \; \frac{1}{2}< x < \frac{2}{3}\right \} ?$

(A) 0.52 $\displaystyle 0.52$

(B) 0.57 $\displaystyle 0.57$

(D) 0.67 $\displaystyle 0.67$

Possible Answers:

One

Three

Two

Four

None

Correct answer:

Three

Explanation:

$\frac{1}{2} = 1\div 2 = 0.5$ $\displaystyle \frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ $\displaystyle \frac{2}{3} = 2 \div 3= 0.666...$, so we choose the numbers that fall between these two. Of the four choices, only 0.67 is not between these two numbers. The correct response is "three".

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Example Question #327 : Numbers And Operations

Add the fractions:

$\frac{8}{26}+\frac{11}{26}=$ $\displaystyle \frac{8}{26}+\frac{11}{26}=$

Possible Answers:

$\frac{20}{26}$ $\displaystyle \frac{20}{26}$

$\frac{2}{26}$ $\displaystyle \frac{2}{26}$

$\frac{19}{26}$ $\displaystyle \frac{19}{26}$

$\frac{3}{26}$ $\displaystyle \frac{3}{26}$

Correct answer:

$\frac{19}{26}$ $\displaystyle \frac{19}{26}$

Explanation:

Add the numerators and keep the denominator the same:

$\frac{8}{26}+\frac{11}{26}=\frac{19}{26}$ $\displaystyle \frac{8}{26}+\frac{11}{26}=\frac{19}{26}$

Answer: $\frac{19}{26}$ $\displaystyle \frac{19}{26}$

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Example Question #328 : Numbers And Operations

Arrange these numbers from least to greatest:

$\left \{- \frac{3}{4}, -\frac{7}{9},-\frac{8}{11} \right \}$ $\displaystyle \left \{- \frac{3}{4}, -\frac{7}{9},-\frac{8}{11} \right \}$

Possible Answers:

$\left \{- \frac{3}{4}, -\frac{7}{9},-\frac{8}{11} \right \}$ $\displaystyle \left \{- \frac{3}{4}, -\frac{7}{9},-\frac{8}{11} \right \}$

$\left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$ $\displaystyle \left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$

$\left \{ -\frac{8}{11}, -\frac{7}{9} , - \frac{3}{4}\right \}$ $\displaystyle \left \{ -\frac{8}{11}, -\frac{7}{9} , - \frac{3}{4}\right \}$

$\left \{-\frac{7}{9}, -\frac{8}{11} , - \frac{3}{4}\right \}$ $\displaystyle \left \{-\frac{7}{9}, -\frac{8}{11} , - \frac{3}{4}\right \}$

$\left \{ -\frac{8}{11} , - \frac{3}{4}, -\frac{7}{9}\right \}$ $\displaystyle \left \{ -\frac{8}{11} , - \frac{3}{4}, -\frac{7}{9}\right \}$

Correct answer:

$\left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$ $\displaystyle \left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$

Explanation:

Rewrite all three numbers as their decimal equivalents by dividing numerator by denominator.

$- \frac{3}{4} = -3 \div 4 = -0.75$ $\displaystyle - \frac{3}{4} = -3 \div 4 = -0.75$

$-\frac{7}{9} = -7 \div 9 = -0.777...$ $\displaystyle -\frac{7}{9} = -7 \div 9 = -0.777...$

$-\frac{8}{11} = -8 \div 11 = -0.7272...$ $\displaystyle -\frac{8}{11} = -8 \div 11 = -0.7272...$

To arrange negative numbers from least to greatest, we must arrange them so that their absolute values (values without the negative symbol) go from greatest to least. In descending order, the absolute values are

$\left \{ 0.777..., 0.75, 0.7272... \right \}$ $\displaystyle \left \{ 0.777..., 0.75, 0.7272... \right \}$,

so, in ascending order, the numbers themselves are

$\left \{ - 0.777..., -0.75, -0.7272... \right \}$ $\displaystyle \left \{ - 0.777..., -0.75, -0.7272... \right \}$,

or, in their fractional equivalents,

$\left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$ $\displaystyle \left \{-\frac{7}{9}, - \frac{3}{4}, -\frac{8}{11} \right \}$.

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Example Question #329 : Numbers And Operations

What is the decimal equivalent to $\frac{52}{130}$ $\displaystyle \frac{52}{130}$?

Possible Answers:

$\displaystyle 52$

$\displaystyle .40$

$\displaystyle 40$

$\displaystyle .52$

$\displaystyle .130$

Correct answer:

$\displaystyle .40$

Explanation:

To solve, divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction):

$52\div 130=.40$ $\displaystyle 52\div 130=.40$

Answer: $\displaystyle .40$

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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 #321 : Numbers And Operations

Example Question #322 : Numbers And Operations

Example Question #323 : Numbers And Operations

Example Question #324 : Numbers And Operations

Example Question #176 : Fractions

Example Question #325 : Numbers And Operations

Example Question #326 : Numbers And Operations

Example Question #327 : Numbers And Operations

Example Question #328 : Numbers And Operations

Example Question #329 : Numbers And Operations

All ISEE Middle Level Math Resources

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