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ISEE Lower Level Quantitative : Distributive Property

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Example Questions

Example Question #1 : How To Find The Distributive Property

Which expression demonstrates the Distributive Property?

Possible Answers:

$\dpi{100} 2+4=4+2$

$\dpi{100} 2\times 1=2$

$\dpi{100} 2(4+3)=(2\times 4)+(2\times 3)$

$\dpi{100} 2+3+4=3+2+4$

Correct answer:

$\dpi{100} 2(4+3)=(2\times 4)+(2\times 3)$

Explanation:

The distributive property involves multiplying each term inside of the parentheses by the term outside of the parentheses. The distributive property is:

$\dpi{100} a(b+c)=(a\times b)+(b\times c)$

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Example Question #2 : How To Find The Distributive Property

Use the distributive property to expand:

(x-3)(-2x+5)

Possible Answers:

$2x^{2}+11x-15$

$-2x^{2}+11x-15$

$-2x^{2}-11x-15$

$2x^{2}+11x+15$

Correct answer:

$-2x^{2}+11x-15$

Explanation:

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

F: $-2x^{2}$

Now you have four terms: $-2x^{2}+5x+6x-15$

Simplify: $-2x^{2}+11x-15$

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Example Question #3 : How To Find The Distributive Property

Use the distributive property to evaluate this expression:

3(6+4)

Possible Answers:

Correct answer:

Explanation:

When you multiply it out using the distributive property, you get 18+12 . Add those together to get .

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Example Question #4 : Distributive Property

Calculate the value of .

$(3*2)^{2} - (2-x) = 40$

Possible Answers:

Correct answer:

Explanation:

(3*2)^2 - (2 - x) = 40

(6)^2 - 2 +x = 40

36 - 2 + x = 40

34 + x = 40

x = 6

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Example Question #4 : How To Find The Distributive Property

Simplify.

6(3-7x) + 8(4-2x) =

Possible Answers:

54 + 14x

18 - 42x

56 - 60x

58x - 63

50 - 58x

Correct answer:

50 - 58x

Explanation:

By the distributive property, you must multiply both numbers within the parentheses by the number outside the parentheses. In this case, the expression becomes

18 -42x + 32 -16x = 50 - 58x

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Example Question #1 : How To Find The Distributive Property

Which answer choice represents the distributive property?

$\bigstar (\bigoplus +\blacktriangledown )$

Possible Answers:

$\bigstar \bigoplus +\bigstar \blacktriangledown$

$\star \bigstar +\bigstar \blacktriangledown$

$\bigstar \bigodot+\bigstar \bigoplus$

$\bigstar \bigstar$

$\bigoplus +\blacktriangledown$

Correct answer:

$\bigstar \bigoplus +\bigstar \blacktriangledown$

Explanation:

The distributive property involves multiplying the outside term by the first term in the parentheses and then adding/subtracting it to the product of the outside term and the second term of the parentheses. Since there's a plus sign, we're adding. Therefore, the result is $\bigstar \bigoplus +\bigstar \blacktriangledown$ .

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Example Question #5 : How To Find The Distributive Property

Solve for :

3(x+8)=42

Possible Answers:

x=18

x=3

x=-4

x=6

x=4

Correct answer:

x=6

Explanation:

The distributive property is needed to solve this problem. The distributive property is a(b+c)=(ab) + (cb) .

3(x+8)=42
3x + 24= 42

Now to solve for x we need to subtract 24 from both sides.

3x + 24= 42

- 24 -24

From here we need to divide by 3.
3x=18
x=6

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Example Question #1 : How To Find The Distributive Property

Use the distributive property to expand the expression:

(x+8)(x+7)

Possible Answers:

x^2 + 8x + 54

x^2 + 7x + 15

x^2 + 15x + 54

x^2 + 15x + 56

Correct answer:

x^2 + 15x + 56

Explanation:

The distributive property is needed to solve this problem. The distributive property is a(b+c)= (ab) + (ac) . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.

(x+8)(x+7)
$x\cdot x=x^2$
$x\cdot 7=7x$
$8\cdot x=8x$
$8\cdot 7=56$

The final step to expand this expression is to combine like terms. Thus, the correct answer is

x^2 + 15x + 56

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Example Question #2 : Distributive Property

Use the distributive property to expand the expression:

(x-9)(x+3)

Possible Answers:

x^2 - 6x - 27

x^2 - 6x + 27

x^2 - 6x - 6

x^2 + 6x - 27

x^2 + 3x + 27

Correct answer:

x^2 - 6x - 27

Explanation:

The distributive property is needed to solve this problem. The distributive property is a(b+c)= (ab) + (ac) . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.

(x-9)(x+3)
$x\cdot x=x^2$

$x\cdot 3=3x$

$-9\cdot x=-9x$

$-9\cdot x=-9x$

The last step to solving this problem is to combine like terms. Thus, the correct answer is:
x^2 - 6x - 27

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Example Question #2 : How To Find The Distributive Property

Use the distributive property to simply the expression

9(4-5)=?

Possible Answers:

Correct answer:

Explanation:

The distributive property is needed to evaluate this expression. The distributive property is a(b+c)= (ab) + (ac)

9(4-5)=?

We will apply the distributive property to both terms inside the parentheses.
$9\cdot 4=36$
$9\cdot 5=45$

Now we plug these values back into the expression to get:
36-45=-9

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ISEE Lower Level Quantitative : Distributive Property

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1 : How To Find The Distributive Property

Example Question #2 : How To Find The Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #4 : Distributive Property

Example Question #4 : How To Find The Distributive Property

Example Question #1 : How To Find The Distributive Property

Example Question #5 : How To Find The Distributive Property

Example Question #1 : How To Find The Distributive Property

Example Question #2 : Distributive Property

Example Question #2 : How To Find The Distributive Property

All ISEE Lower Level Quantitative Resources

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