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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 #202 : Fractions

Evaluate:

$20 - 7.5 \times 3 - 1.2$

Possible Answers:

6.5

22.5

- 3.7

-1.3

36.3

Correct answer:

- 3.7

Explanation:

By the order of operations, carry out the multiplication first, then the leftmost subtraction, then the rightmost subtraction:

$20 - 7.5 \times 3 - 1.2$

= 20 - 22.5 - 1.2

= - 2.5 - 1.2

$= - 2.5 + \left ( - 1.2 \right )$

= - 3.7

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Example Question #351 : Numbers And Operations

Raise to the fifth power.

Possible Answers:

-1,024

1,024

625

cannot be raised to the fifth power.

Correct answer:

-1,024

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative:

$\left ( -4 \right ) ^{5 } = - \left ( 4^{5}\right ) = - \left ( 4 \times 4 \times 4 \times 4 \times 4\right ) = -1,024$

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Example Question #352 : Numbers And Operations

Raise to the fourth power.

Possible Answers:

-4,096

1,296

4,096

-1,296

Correct answer:

1,296

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power:

$\left ( -6 \right )^{4} = 6 ^{4} = 6 \times 6 \times 6 \times 6 = 1,296$

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Example Question #353 : Numbers And Operations

Evaluate:

$15 - \left ( \frac{2}{3} \times 3 + \frac{4}{3}\right )$

Possible Answers:

$12\frac{1}{9}$

$44\frac{1}{3}$

$11 \frac{2}{3}$

$13\frac{1}{3}$

$18\frac{1}{3}$

Correct answer:

$11 \frac{2}{3}$

Explanation:

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and an addition present, carry them out in that order. Finally, carry out the subtraction:

$15 - \left ( \frac{2}{3} \times 3 + \frac{4}{3}\right )$

$= 15 - \left ( 2+ \frac{4}{3}\right )$

$= 15 - \frac{10}{3}$

$= 11 \frac{2}{3}$

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Example Question #18 : How To Multiply Fractions

Raise $- \frac{2}{3}$ to the fourth power.

Possible Answers:

$\frac{81}{16}$

$\frac{16}{81}$

$- \frac{8}{3}$

$- \frac{16}{81}$

$\frac{16} {81}$

Correct answer:

$\frac{16}{81}$

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{2}{3} \right )^{4} = \left( \frac{2}{3} \right )^{4} = \frac{2^{4} }{3^{4} } = \frac{ 2 \times 2 \times 2 \times 2 }{ 3 \times 3\times 3 \times 3 } \right ) = \frac{16}{81}$

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Example Question #353 : Numbers And Operations

Raise $- \frac{3}{2}$ to the fifth power.

Possible Answers:

$\frac{243} {32}$

$-\frac{243} {32}$

$\frac{32}{243}$

$- \frac{3}{2}$ cannot be raised to the fifth power.

$-\frac{32}{243}$

Correct answer:

$-\frac{243} {32}$

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{3}{2} \right )^{5} = - \left ( \frac{3}{2}\right )^{5} = - \left ( \frac{3^{5}} {2^{5}} \right ) = - \left ( \frac{3 \times 3 \times 3\times 3 \times 3 }{2\times 2 \times 2 \times 2 \times 2 } \right ) = -\frac{243}{32}$

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Example Question #21 : How To Multiply Fractions

Solve for in this equation:

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

Possible Answers:

$\frac{1}{3}$

$\frac{27}{10}$

$\frac{5}{27}$

$\frac{10}{29}$

$\frac{10}{27}$

Correct answer:

$\frac{10}{27}$

Explanation:

To solve for , we need to cross multiply.

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

$2\times5=9\times3x$

10=27x

Divide both sides by 27 to isolate the variable.

$\frac{10}{27}=x$

The fraction cannot be reduced, making this our final answer.

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Example Question #1241 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Which of the answer choices is equal to $\frac{63}{9}\cdot\frac{3}{2}$ ?

Possible Answers:

$11\frac{1}{2}$

$10\frac{1}{2}$

Correct answer:

$10\frac{1}{2}$

Explanation:

The expression, $\frac{63}{9}\cdot\frac{3}{2}$ is equal to:

$(63\div9)\cdot\frac{3}{2}$

This is equal to:

$7\cdot \frac{3}{2}$

This equals:

$\frac{21}{2}=10\frac{1}{2}$

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Example Question #22 : How To Multiply Fractions

Find the product.

$\frac{2}{7}\times \frac{5}{9}$

Possible Answers:

$\frac{10}{42}$

$\frac{7}{16}$

$\frac{10}{63}$

$\frac{18}{35}$

Correct answer:

$\frac{10}{63}$

Explanation:

To multiply fractions, simply multiply the first numerator by the second numerator and the first denominator by the second denominator. Simply when necessary.

$2\times5=10$

$7\times9=63$

$\frac{2}{7}\times \frac{5}{9}=\frac{10}{63}$

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Example Question #21 : How To Multiply Fractions

What is $\frac{1}{5}$ of $\frac{7}{6}$ ?

Possible Answers:

$\frac{7}{5}$

$\frac{7}{30}$

$\frac{6}{30}$

$\frac{8}{11}$

$\frac{7}{6}$

Correct answer:

$\frac{7}{30}$

Explanation:

To find the answer, you must multiple the fractions together.

When multiplying fractions, all you have to do is multiple the numerators together and the denominators together.

1*7=7

and

5*6=30

giving us

$\frac{7}{30}$ .

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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 #202 : Fractions

Example Question #351 : Numbers And Operations

Example Question #352 : Numbers And Operations

Example Question #353 : Numbers And Operations

Example Question #18 : How To Multiply Fractions

Example Question #353 : Numbers And Operations

Example Question #21 : How To Multiply Fractions

Example Question #1241 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #22 : How To Multiply Fractions

Example Question #21 : How To Multiply Fractions

All ISEE Middle Level Math Resources

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