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ISEE Lower Level Math : How to find the distributive property

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Example Question #21 : How To Find The Distributive Property

Simplify the expression using the distributive property:

5(x+y+9-6)

Possible Answers:

x+y+8

x+y+3

5x+5y+20

5(x+y)

5x+5y+15

Correct answer:

5x+5y+15

Explanation:

5(x+y+9-6)

The first step is to reduce the value in the parenthesis by subtracting the numbers 9 and 6. This results in:

5(x+y+3)

Next, the distributive property is applied by multiplying 5 by each number within the parenthesis.

$(5\times x)+(5\times y)+(5\times3)$

5x+5y+15

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Example Question #22 : How To Find The Distributive Property

Which of the following is equivalent to 3(y+4) ?

Possible Answers:

y+y+8+4

3y+11

None of these

y+2y+8+3

y+2y+8+4

Correct answer:

y+2y+8+4

Explanation:

Let's start by expanding the give expression using the distributive property:

3(y+4)

$(3\times y)+(3\times4)$

3y+12

Looking at our answer choices, we need to find the option that is equivalent. To do so, group together like-terms.

y+2y+8+4

(y+2y)+(8+4)

3y+12

The correct answer is y+2y+8+4 because it also simplifies to 3y+12 .

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Example Question #23 : How To Find The Distributive Property

Simplify the expression:

$24(x+\frac{1}{2})-9$

Possible Answers:

24x+3

12x-9

24x-9

27x

Correct answer:

24x+3

Explanation:

In order to simplify this expression, the distributive property should be applied. Multiply each term within parenthesis by the term outside the parenthesis.

$24(x+\frac{1}{2})-9$

$(24\times x)+(24\times \frac{1}{2})-9$

24x+12-9

Next, 9 is subtracted from 12, resulting in:

24x+3

Since these are not like-terms, we cannot simplify any further.

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Example Question #24 : How To Find The Distributive Property

Simplify the expression:

$5(\frac{1}{5}+2b)+2b$

Possible Answers:

2+12b

The expression cannot be simplified

1+4b

1+12b

2+3b

Correct answer:

1+12b

Explanation:

To simplify this expression, we need to apply the distributive property. Multiply each term within parenthesis by the term outside the parenthesis.

$5(\frac{1}{5}+2b)+2b$

$(5\times\frac{1}{5})+(5\times2b)+2b$

1+10b+2b

Next, we combine like-terms:

1+12b

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Example Question #25 : How To Find The Distributive Property

Which of the following is equivalent to the expression:

5x(4y-5)+2x

Possible Answers:

20x+23xy

20xy+23x

20xy-23x

20x-23xy

20xy-18x

Correct answer:

20xy-23x

Explanation:

The first step in reducing the expression is to apply the distributive property:

5x(4y-5)+2x

$(5x\times4y)-(5x\times5)+2x$

This results in:

20xy-25x+2x

This can further be reduced by combining like terms:

20xy-23x

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Example Question #26 : How To Find The Distributive Property

Simplify the expression.

4x(x+4)+2x

Possible Answers:

$4x^{2}+4$

4x+6

4x^2+18x

4+6x

4x^2+4x

Correct answer:

4x^2+18x

Explanation:

The first step to solve this problem is to apply the distributive property.

4x(x+4)+2x

$(4x\times x)+(4x\times4)+2x$

$4x^{2}+16x+2x$

Next, combine 16x and by adding them together.

4x^2+18x

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Example Question #21 : How To Find The Distributive Property

What is the simplified version of this expression?

$\frac{1}{5}(x+10)-5$

Possible Answers:

$\frac{1}{5}x+3$

$\frac{1}{5}x+2$

None of these

$\frac{1}{5}x-3$

$\frac{1}{5}x-2$

Correct answer:

$\frac{1}{5}x-3$

Explanation:

In order to solve this problem, the distributive property must first be applied. Multiply each term in parenthesis by the term outside the parenthesis.

$\frac{1}{5}(x+10)-5$

$\left(\frac{1}{5}\times x\right)+\left(\frac{1}{5}\times10\right)-5$

$\frac{1}{5}x+2-5$

Combine like-terms to further reduce the expression.

$\frac{1}{5}x-3$

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Example Question #28 : How To Find The Distributive Property

Sharon purchased pieces of candy and wants to make Halloween treat bags for the children in her neighborhood. How many different ways can Sharon make treat bags with an even number of pieces of candy in each bag?

Possible Answers:

Correct answer:

Explanation:

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sharon’s candy.

$1\times 12=12$

$2\times6=12$

$3\times 4=12$

Do not forget to list their reciprocals.

$4\times 3=12$

$6\times2=12$

$12\times1=12$

Sharon can make different treat bag combinations with an even amount of candy in each bag.

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Example Question #29 : How To Find The Distributive Property

Possible Answers:

Correct answer:

Explanation:

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sharon’s candy.

$1\times 20=20$

$2\times10=20$

$4\times 5=20$

Do not forget to list their reciprocals.

$5\times 4=20$

$10\times2=20$

$20\times1=20$

Sharon can make different treat bag combinations with an even amount of candy in each bag.

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Example Question #30 : How To Find The Distributive Property

Possible Answers:

Correct answer:

Explanation:

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sharon’s candy.

$1\times 16=16$

$2\times8=16$

$4\times 4=16$

Do not forget to list their reciprocals.

$8\times2=16$

$16\times1=16$

Sharon can make different treat bag combinations with an even amount of candy in each bag.

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ISEE Lower Level Math : How to find the distributive property

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #21 : How To Find The Distributive Property

Example Question #22 : How To Find The Distributive Property

Example Question #23 : How To Find The Distributive Property

Example Question #24 : How To Find The Distributive Property

Example Question #25 : How To Find The Distributive Property

Example Question #26 : How To Find The Distributive Property

Example Question #21 : How To Find The Distributive Property

Example Question #28 : How To Find The Distributive Property

Example Question #29 : How To Find The Distributive Property

Example Question #30 : How To Find The Distributive Property

All ISEE Lower Level Math Resources

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