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ISEE Middle Level Math : Algebraic Concepts

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 #663 : Concepts

Simplify the expression:

78k*2k

Possible Answers:

156k

$74k^{2}$

$80k^{2}$

$156k^{2}$

76k^2

Correct answer:

$156k^{2}$

Explanation:

The commutative property lets us reorganize the expression.

78k*2k=78*k*2*k=78*2*k*k

By separating the whole numbers and the variables, we can easily multiply.

78*2=156

k*k=k^2

72*2*k*k=156*k^2=156k^2

$78k*2k=156k^{2}$

Answer: $156k^{2}$

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Example Question #664 : Concepts

Simplify the expression:

$25m*15m^{2}$

Possible Answers:

$375m^{3}$

375m

None of these

375

$375m^{2}$

Correct answer:

$375m^{3}$

Explanation:

Multiply the whole numbers and add the variables:

$25m*15m^{2}=375m^{3}$

Answer: $375m^{3}$

The commutative property lets us reorganize the expression.

25m*15m^2=25*m*15*m^2=25*15*m*m^2

By separating the whole numbers and the variables, we can easily multiply.

25*15=375

m*m^2=m^3

25*15*m*m^2=375*m^3=375m^3

$25m*15m^{2}=375m^{3}$

Answer: $375m^{3}$

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Example Question #665 : Concepts

Mulitply:

x(-2-x)

Possible Answers:

$-2x+2x^{2}$

-2x-2x

-2x+2x

-2x-x^2

-2x+x^2

Correct answer:

-2x-x^2

Explanation:

x(-2-x)=(x)(-2)+(x)(-x)=-2x+(-x^2)=-2x-x^2

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Example Question #666 : Concepts

$7n\cdot 3n=$

Possible Answers:

10n

$10n^{2}$

$7n^{3}$

$21n^{2}$

Correct answer:

$21n^{2}$

Explanation:

Multiply the numbers and multiply the variables:

$7n\cdot 3n=21n^{2}$

Answer: $21n^{2}$

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Example Question #667 : Concepts

$25f*20f^{3}=$

Possible Answers:

$500f^{4}$

$500f^{6}$

$500f^{3}$

$45f^{3}$

$45f^{4}$

Correct answer:

$500f^{4}$

Explanation:

Multiply the constants and add an exponent to the variable totaling the number of variables in the equation:

$25f*20f^{3}=500f^{4}$

Answer: $500f^{4}$

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Example Question #56 : Algebra

Simplify:

$(4v^{3})(xy^{2}v)(2x^{3}v)$

Possible Answers:

$8x^{2}y^{2}v^{3}$

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

$9x^{2}y^{2}v^{3}$

$x^{6}y^{2}v^{14}$

$8x^{4}y^{2}v^{5}$

Correct answer:

$8x^{4}y^{2}v^{5}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(4 * 2) (v^{3}*v*v)(x*x^{3})(y^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(8)(v^{3+1+1})(x^{1+3})(y^2)$

$(8) (v^{5})(x^{4})(y^{2})$

This is the same as:

$8x^{4}y^{2}v^{5}$

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Example Question #57 : Algebra

Simplify:

$e * t * f^{4} * t^{2} * 10 * f$

Possible Answers:

$ef^{21}t^{3}$

$e^{10}f^{5}t^{3}$

$ef^{14}t^{3}$

$10ef^{4}t^{2}$

$10ef^{5}t^{3}$

Correct answer:

$10ef^{5}t^{3}$

Explanation:

$(10)(e)(f^{4} *f)(t * t^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(10)(e)(f^{4+1})(t^{1+2})$

$(10)(e)(f^{5})(t^{3})$

This is the same as:

$10ef^{5}t^{3}$

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Example Question #668 : Concepts

Simplify:

4e*f*e*e*f*f*f*e*3*e*e*e*f*f

Possible Answers:

18ef

$7e^{7}f^{6}$

$12e^{7}f^{6}$

20ef

$4e^{9}f^{6}$

Correct answer:

$12e^{7}f^{6}$

Explanation:

(4 *3)(e*e*e *e*e*e*e) (f*f*f*f**f*f)

When multiplying variables of the same type, you add their exponents together. (All of these variables have exponents of 1.) This gets you:

$(12)(e^{1+1+1+1+1+1+1})(f^{1+1+1+1+1+1})$

$(12)(e^{7}) (f^{6})$

This is the same as:

$12e^{7}f^{6}$

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Example Question #671 : Concepts

Simplify:

$2(f^{6})(u^{7})(e^{2}f^{2})(eu)$

Possible Answers:

$2e^{2}f^{12}u^{7}$

$2e^{3}f^{8}u^{6}$

$2e^{3}f^{8}u^{8}$

$2e^{2}f^{24}u^{7}$

$e^{3}f^{14}u^{8}$

Correct answer:

$2e^{3}f^{8}u^{8}$

Explanation:

$(2)(e * e^{2})(f^{6}*f^{2})(u*u^{7})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(2)(e^{1+2})(f^{6+2})(u^{1+7})$

$(2)(e^{3})(f^{8})(u^{8})$

This is the same as:

$2e^{3}f^{8}u^{8}$

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Example Question #672 : Concepts

Simplify:

$(4g)(2r^{2})(r^{3})(g^{2})$

Possible Answers:

$4g^{5}r^{5}$

$8g^{3}r^{5}$

$8g^{2}r^{6}$

$8g^{2}r^{5}$

$6g^{3}r^{5}$

Correct answer:

$8g^{3}r^{5}$

Explanation:

$(2*4)(g*g^{2})(r^{2}*r^{3})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(8)(g^{1+2})(r^{2+3})$

$(8)(g^{3})(r^{5})$

This is the same as:

$8g^{3}r^{5}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #663 : Concepts

Example Question #664 : Concepts

Example Question #665 : Concepts

Example Question #666 : Concepts

Example Question #667 : Concepts

Example Question #56 : Algebra

Example Question #57 : Algebra

Example Question #668 : Concepts

Example Question #671 : Concepts

Example Question #672 : Concepts

All ISEE Middle Level Math Resources

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