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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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 #93 : Algebraic Concepts

Reduce the expression:

$\frac{4x^{3}y^{2}}{2x}$

Possible Answers:

$2y^{2}$

$2x^{2}y^{2}$

Cannot be reduced

$y^{5}$

Correct answer:

$2x^{2}y^{2}$

Explanation:

For this division problem, you must deal with the like terms.

You will divide the constants and then divide the variables.

$4\div2=2$

and then

$x^{3}\div x=x^{2}$

because when dividing exponents with common bases, you just subtract the exponents.

The variable remains unchanged and your answer is,

$2x^{2}y^{2}$ .

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Example Question #94 : Algebraic Concepts

$7^{4} \div (18-11) =$

Possible Answers:

343

Correct answer:

343

Explanation:

To solve

$7^{4} \div (18-11) =$

First, use the order of operations.

$7^{4} \div 7 =$

When dividing with variables and the coefficients are the same, subtract the exponents.

$7^{4} \div 7^{1} = 7^{4-1}$

$7^{4-1} = 7^{3}$ $7^{3} = 7\times 7\times 7 = 343$

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Example Question #2211 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\frac{x^{8}}{x^{2}}$

Possible Answers:

$x^{4}$

$x^{6}$

$x^{10}$

$x^{\frac{1}{4}}$

Correct answer:

$x^{6}$

Explanation:

To solve, subtract the exponents

$\frac{x^{8}}{x^{2}} = x^{8-2}$

$x^{6}$

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Example Question #2212 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\frac{n^{3}}{n^{6}}$

Possible Answers:

$n^{\frac{1}{2}}$

$n^{9}$

$n^{3}$

$\frac{1}{n^{3}}$

Correct answer:

$\frac{1}{n^{3}}$

Explanation:

To solve $\frac{n^{3}}{n^{6}}$ subtract the exponents

$n^{3-6} = n^{-3}$

$n^{-3} = n\div -3 =$

$\frac{1}{n^{3}}$

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Example Question #97 : Algebraic Concepts

The area (A) of a rectangle is $36ab^{3}$ square units. The length is 6ab units. What is the width of this rectangle?

Possible Answers:

$6b^{2$ units

$216ab^{2}$ units

$6a^{2}b^{2}$ units

$216a^{2}b^{4}$ units

Correct answer:

$6b^{2$ units

Explanation:

The formula for the Area of a rectangle is:

A - length x width

Is this problem, you are given the amount of total area or A, which is $36ab^{3}$ square units, and you are given the measurement of the length, which is 6ab . In order to solve for the measurement of the width, divide. When dividing, exponents are subtracted.

$36\div6 =6$

$\frac{a^{1}}{a^{1}} = a^{1-1} = a^{0} = 1$

$\frac{b^{3}}{b^{1}} = b^{3-1} = b^{2}$

$6 (1) \times b^{2} = 6b^{2}$ units

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Example Question #95 : Algebraic Concepts

$\frac{9x^{4}y^{6}}{3x^{2}y^{2}} =$

Possible Answers:

$6x^{2}y^{4}$ $3x^{2}y^{3}$

$6x^{8}y^{12}$

$3x^{2}y^{4}$

Correct answer:

$3x^{2}y^{4}$

Explanation:

To solve $\frac{9x^{4}y^{6}}{3x^{2}y^{2}}$ separate each part of the terms and divide. When dividing variables with exponents, subtract the exponents.

$9\div 3 = 3$

$\frac{x^{4}}{x^{2}}=x^{4-2} =x^{2}$

$\frac{y^{6}}{y^{2}}=y^{6-2} =y^{4}$

$3x^{2}y^{4}$

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Example Question #101 : Algebraic Concepts

$\frac{9x^{5}y^{4}}{3x^{3}y^{9}}$

Possible Answers:

$\frac{y^{5}}{3x^{2}}$

$3x^{8}y^{13}$

$\frac{3x^{2}}{y^5}$

$3x^{2}y^{5}$

Correct answer:

$\frac{3x^{2}}{y^5}$

Explanation:

Separate each part of the division problem. When dividing, exponents are subtracted.

$9 \div3 =3$

$\frac{x^{5}}{x^{3}} = x^{5-3} = x^{2}$

$\frac{y^{4}}{y^{9}} = y^{4-9} = y^{-5}$

$3x^{2}y^{-5} =$

$\frac{3x^{2}}{y^{5}}$

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Example Question #101 : Algebraic Concepts

Simplify the following statement.

$\frac{14x^6}{7x^3}$

Possible Answers:

3x^2

7x^3

2x^2

2x^3

Correct answer:

2x^3

Explanation:

Simplify the following statement.

$\frac{14x^6}{7x^3}$

TO divide variables, we need to subtract the exponents. The coefficients (numbers out in front) can be divided as you would normally divide.

$\frac{14x^6}{7x^3}=\frac{14}{7}*x^{6-3}=2x^3$

So we get our answer of two x cubed.

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Example Question #1 : Expressions & Equations

Simplify:

14x - 5 (x + 8)

Possible Answers:

9x + 8

9x+ 40

9x - 8

9x -40

Correct answer:

9x -40

Explanation:

14x - 5 (x + 8)

$= 14x - 5 \cdot x - 5 \cdot 8$

= 14x - 5x - 40

= (14- 5) x - 40

= 9x - 40

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Example Question #2 : Expressions & Equations

Simplify:

8 (x - 7) - 3(x + 2)

Possible Answers:

11x - 62

11x-9

5 x - 50

5 x - 62

5x-9

Correct answer:

5 x - 62

Explanation:

8 (x - 7) - 3(x + 2)

$= 8 \cdot x -8 \cdot 7 - 3 \cdot x + (-3) \cdot 2$

= 8x -56 - 3 x -6

= 8x - 3 x -56 -6

=( 8 - 3 ) x - (56 + 6)

=5 x - 62

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #93 : Algebraic Concepts

Example Question #94 : Algebraic Concepts

Example Question #2211 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2212 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #97 : Algebraic Concepts

Example Question #95 : Algebraic Concepts

Example Question #101 : Algebraic Concepts

Example Question #101 : Algebraic Concepts

Example Question #1 : Expressions & Equations

Example Question #2 : Expressions & Equations

All ISEE Middle Level Math Resources

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