Numbers and Operations - ISEE Middle Level Quantitative Reasoning

Card 0 of 6205

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

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Question

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

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

(A)

(B)

(C)

(D)

Answer

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , 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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Question

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

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

(A)

(B)

(C)

(D)

Answer

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , 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".

Compare your answer with the correct one above

Question

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

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

(A)

(B)

(C)

(D)

Answer

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , 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".

Compare your answer with the correct one above

Question

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

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

(A)

(B)

(C)

(D)

Answer

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , 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".

Compare your answer with the correct one above

Question

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

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

(A)

(B)

(C)

(D)

Answer

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , 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".

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

so, in ascending order, the numbers themselves are

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

or, in their fractional equivalents,

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

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Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

so, in ascending order, the numbers themselves are

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

or, in their fractional equivalents,

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

so, in ascending order, the numbers themselves are

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

or, in their fractional equivalents,

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

so, in ascending order, the numbers themselves are

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

or, in their fractional equivalents,

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

Compare your answer with the correct one above

Question

Arrange these numbers from least to greatest:

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

Answer

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

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

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

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

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

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

so, in ascending order, the numbers themselves are

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

or, in their fractional equivalents,

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

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Question

Find the decimal equivalent of 95%.

Answer

Divide: $95\div 100=.95$

Answer:

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Question

Find the decimal equivalent of 33%.

Answer

Divide: $33\div 100=.33$

Answer: .33

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Question

Find the decimal equivalent of 58%.

Answer

Divide:

$58\div 100=.58$

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Question

Which of these is equivalent to 29%?

Answer

Divide: $29\div 100=.29$

Answer:

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Question

$\frac{3}{4}+\frac{1}{3}=$

Answer

$\frac{3}{4}+\frac{1}{3}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$

$\frac{1}{3}\times\frac{4}{4}=\frac{4}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{12}+\frac{4}{12}=\frac{13}{12}$

$\frac{13}{12}=1\frac{1}{12}$ because can go into one time, with one left over.

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