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ISEE Lower Level Math : Distributive Property

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Example Questions

Example Question #1 : Numbers And Operations

Solve the following equation.

$\dpi{100} 3(2-5)=$ $\displaystyle \dpi{100} 3(2-5)=$ ?

Possible Answers:

$\dpi{100} 6$ $\displaystyle \dpi{100} 6$

$\dpi{100} 9$ $\displaystyle \dpi{100} 9$

$\dpi{100} -9$ $\displaystyle \dpi{100} -9$

$\dpi{100} -6$ $\displaystyle \dpi{100} -6$

Correct answer:

$\dpi{100} -9$ $\displaystyle \dpi{100} -9$

Explanation:

$\dpi{100} 2-5=-3$ $\displaystyle \dpi{100} 2-5=-3$ .

$\dpi{100} 3\times -3=9$ $\displaystyle \dpi{100} 3\times -3=9$

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Example Question #1 : Distributive Property

Solve

$\displaystyle 4(6+3) - 9 =$

Possible Answers:

$\displaystyle 19$

$\displaystyle 26$

$\displaystyle 28$

$\displaystyle 45$

$\displaystyle 27$

Correct answer:

$\displaystyle 27$

Explanation:

Use the distributive property to solve:

$\displaystyle 4(6) + 4(3)= 36 - 9 = 27$

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Example Question #3 : Numbers And Operations

Expand the expression.

$\displaystyle (x+2)(3x-5)$

Possible Answers:

$3x^{2}-x-10$ $\displaystyle 3x^{2}-x-10$

$3x^{2}-11x-10$ $\displaystyle 3x^{2}-11x-10$

$3x^{2}+x-10$ $\displaystyle 3x^{2}+x-10$

$3x^{2}+x-3$ $\displaystyle 3x^{2}+x-3$

$3x^{2}+11x+10$ $\displaystyle 3x^{2}+11x+10$

Correct answer:

$3x^{2}+x-10$ $\displaystyle 3x^{2}+x-10$

Explanation:

Use FOIL (first, outer, inner, last) to expand.

First: $(x)(3x)= 3x^{2}$ $\displaystyle (x)(3x)= 3x^{2}$

Outside: $\displaystyle (x)(-5) = -5x$

Inside: $\displaystyle (2)(3x)=6x$

Last: $\displaystyle (2)(-5) =-10$

Sum the four terms into one expression.

$3x^{2}-5x+6x-10$ $\displaystyle 3x^{2}-5x+6x-10$

Simplify by combining like terms.

$\displaystyle 3x^2+x-10$

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Example Question #1 : Numbers And Operations

Simplify the expression:

$\displaystyle 14x + 28 - 7x + 19$

Possible Answers:

7x - 9 $\displaystyle 7x - 9$

7x + 47 $\displaystyle 7x + 47$

7x + 9 $\displaystyle 7x + 9$

54x $\displaystyle 54x$

7x - 47 $\displaystyle 7x - 47$

Correct answer:

7x + 47 $\displaystyle 7x + 47$

Explanation:

$\displaystyle 14x + 28 - 7x + 19$

$\displaystyle =14x- 7x + 28 + 19$

$=\left (14- 7 \right )x + 28 + 19$ $\displaystyle =\left (14- 7 \right )x + 28 + 19$

$\displaystyle =7x + 47$

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Example Question #1 : How To Find The Distributive Property

Simplify the expression:

$\displaystyle 17x + 38 - 7x - 13$

Possible Answers:

$\displaystyle 10x + 51$

250x $\displaystyle 250x$

$\displaystyle 10x - 51$

$\displaystyle 10x - 25$

$\displaystyle 10x + 25$

Correct answer:

$\displaystyle 10x + 25$

Explanation:

$\displaystyle 17x + 38 - 7x - 13$

$\displaystyle =17x - 7x + 38 - 13$

$=\left (17 - 7 \right )x + 38 - 13$ $\displaystyle =\left (17 - 7 \right )x + 38 - 13$

$\displaystyle =10x + 25$

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Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Use the distributive property to expand:

$\displaystyle (-x-2)(2x+3)$

Possible Answers:

$-2x^{2}-x-6$ $\displaystyle -2x^{2}-x-6$

$-2x^{2}+7x-6$ $\displaystyle -2x^{2}+7x-6$

$-2x^{2}-7x-6$ $\displaystyle -2x^{2}-7x-6$

$2x^{2}-7x-6$ $\displaystyle 2x^{2}-7x-6$

Correct answer:

$-2x^{2}-7x-6$ $\displaystyle -2x^{2}-7x-6$

Explanation:

Remember: FOIL (first, outer, inner, last) to expand.

F: $(-x)(2x)= -2x^{2}$ $\displaystyle (-x)(2x)= -2x^{2}$

O: $\displaystyle (-x)(3) = -3x$

I: $\displaystyle (-2)(2x)=-4x$

L: $\displaystyle (-2)(3) =-6$

Now you have four terms: $-2x^{2}-3x-4x-6$ $\displaystyle -2x^{2}-3x-4x-6$

Simplify: $-2x^{2}-7x-6$ $\displaystyle -2x^{2}-7x-6$

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Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Evaluate.

$25 - 2(3 \times 2)$ $\displaystyle 25 - 2(3 \times 2)$

Possible Answers:

$\displaystyle 19$

None of the other answers.

$\displaystyle 22$

$\displaystyle 23$

$\displaystyle 13$

Correct answer:

$\displaystyle 13$

Explanation:

When there is any number next to a set of parentheses the operation is multiplication of that number and anything inside of the parentheses.

Therefore, $2(3 \times 2)$ $\displaystyle 2(3 \times 2)$ would be the same as $2(6)\: \: [Since \: 3 \times 2 = 6]$ $\displaystyle 2(6)\: \: [Since \: 3 \times 2 = 6]$ . The $\displaystyle 2$ would be multiplied by the $\displaystyle 6$ since 2(6) $\displaystyle 2(6)$ is the same as $2 \times 6$ $\displaystyle 2 \times 6$ .

The problem becomes $25 - 2 \times 6$ $\displaystyle 25 - 2 \times 6$ and based on the order of operations the multiplication operation would be solved first. $[2 \times 6 = 12]$ $\displaystyle [2 \times 6 = 12]$

It solves to $\displaystyle 25 - 12 = 13$ .

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Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Choose the expression that correctly uses the distributive property to solve:

$5\times (12-8)$ $\displaystyle 5\times (12-8)$

Possible Answers:

$(5\times 12)-8$ $\displaystyle (5\times 12)-8$

$(5\times 12)-(5\times 8)$ $\displaystyle (5\times 12)-(5\times 8)$

$(5+12)\times (5+8)$ $\displaystyle (5+12)\times (5+8)$

$(5\times 12)+(5\times 8)$ $\displaystyle (5\times 12)+(5\times 8)$

$5\times 12-8$ $\displaystyle 5\times 12-8$

Correct answer:

$(5\times 12)-(5\times 8)$ $\displaystyle (5\times 12)-(5\times 8)$

Explanation:

To properly use the distributive property, multiple the first number by every number in parentheses:

$(5\times 12)-(5\times 8)$ $\displaystyle (5\times 12)-(5\times 8)$

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Example Question #2 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Multiply:

$\displaystyle -x(4x+7)$

Possible Answers:

4x^2+7x $\displaystyle 4x^2+7x$

4x^2-7x $\displaystyle 4x^2-7x$

$\displaystyle -4x^2+7x$

$\displaystyle -4x^2-7x$

Correct answer:

$\displaystyle -4x^2-7x$

Explanation:

$\displaystyle -x(4x+7)=(-x)(4x)+(-x)(7)=(-4x^2)+(-7x)=-4x^2-7x$

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Example Question #10 : Numbers And Operations

Multiply:

$\displaystyle (3+x)(2-4x)$

Possible Answers:

$\displaystyle 6+10x-4x^2$

$\displaystyle 6-10x-4x^2$

$\displaystyle 6-14x+4x^2$

$\displaystyle 6+14x+4x^2$

Correct answer:

$\displaystyle 6-10x-4x^2$

Explanation:

Solve using the FOIL method:

First: $\displaystyle (3)(2)=6$

Outside: $\displaystyle (3)(-4x)=-12x$

Inside: $\displaystyle (x)(2)=2x$

Last: $\displaystyle (x)(-4x)=-4x^2$

Add together and combine like terms:

$\displaystyle 6-12x+2x-4x^2=6-10x-4x^2$

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All ISEE Lower Level Math Resources

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ISEE Lower Level Math : Distributive Property

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #1 : Numbers And Operations

Example Question #1 : Distributive Property

Example Question #3 : Numbers And Operations

Example Question #1 : Numbers And Operations

Example Question #1 : How To Find The Distributive Property

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #2 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #10 : Numbers And Operations

All ISEE Lower Level Math Resources

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