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ISEE Middle Level Math : How to find the distributive property

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Example Questions

Example Question #101 : How To Find The Distributive Property

Solve using the distributive property:

18(9+7)=

Possible Answers:

278

298

288

268

Correct answer:

288

Explanation:

To solve, multiply each number inside the parentheses by 18:

18*9=162

18*7=126

Then solve: 162+126=288

Answer: 288

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Example Question #102 : How To Find The Distributive Property

Solve using the distributive property:

60(12+6)=

Possible Answers:

1060

1080

1100

1180

Correct answer:

1080

Explanation:

To solve, multiply each number inside the parentheses by 60:

60*12=720

60*6=360

Then, solve: 720+360=1080

Answer: 1080

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Example Question #103 : How To Find The Distributive Property

Which of the following is equivalent to this expression?

$\frac{1}{3} \left ( 2 x+ 5\right ) + \frac{1}{6} (x- 7)$

Possible Answers:

$\frac{1}{2}x +\frac{17}{6}$

$\frac{5}{6} x + \frac{17}{6}$

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

$\frac{5}{6} x + \frac{1}{2}$

Correct answer:

$\frac{5}{6} x + \frac{1}{2}$

Explanation:

$\frac{1}{3} \left ( 2 x+ 5\right ) + \frac{1}{6} (x- 7)$

$= \frac{1}{3} \cdot 2 x+ \frac{1}{3} \cdot 5 + \frac{1}{6} \cdot x- \frac{1}{6} \cdot 7$

$= \frac{2}{3} x+ \frac{5}{3} + \frac{1}{6} x- \frac{7}{6}$

$= \frac{2}{3} x + \frac{1}{6} x + \frac{5}{3}- \frac{7}{6}$

$= \frac{4}{6} x + \frac{1}{6} x + \frac{10}{6}- \frac{7}{6}$

$= \frac{5}{6} x + \frac{3}{6}$

$= \frac{5}{6} x + \frac{1}{2}$

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Example Question #104 : How To Find The Distributive Property

Which of the following is equivalent to this expression?

4(7t - 8) + 3 (7 - 4t)

Possible Answers:

40 t - 53

16t - 11

16 t - 53

40 t - 11

Correct answer:

16t - 11

Explanation:

Using the distributive property:

4(7t - 8) + 3 (7 - 4t)

$= 4 \cdot 7t - 4 \cdot 8 + 3 \cdot 7 - 3 \cdot 4t$

= 28 t - 32+ 21 - 12t

= 28 t - 12t - 32+ 21

= 16 t - 11

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Example Question #105 : How To Find The Distributive Property

Which of the following is equivalent to this expression?

0.4 (0.2 t - 2.6 ) + 0.2 (0.7t - 1.3 )

Possible Answers:

2.2 t - 7.8

2.2 t - 1.3

0.22 t - 0.78

0.22 t - 1.3

Correct answer:

0.22 t - 1.3

Explanation:

To find an equivalent expression first distribute the terms outside of the parentheses to each term within the parentheses.

0.4 (0.2 t - 2.6 ) + 0.2 (0.7t - 1.3 )

$= 0.4 \cdot 0.2 t - 0.4 \cdot 2.6 + 0.2 \cdot 0.7t - 0.2 \cdot 1.3$

= 0.08 t - 1.04 + 0.14 t - 0.26

After distributing the terms and performing the multiplication, combine the like terms.

= 0.08 t+ 0.14 t - 1.04 - 0.26

= 0.22 t - 1.30

= 0.22 t - 1.3

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Example Question #106 : How To Find The Distributive Property

Simplify the following:

3(a +2b + 3c)

Possible Answers:

3a+2b+3c

3a+6b+9c

3a+5b+6c

3+a+2b+3c

18abc

Correct answer:

3a+6b+9c

Explanation:

To distribute, we will take the coefficient in front, and multiply each term by it.

So, we get

3(a +2b + 3c)

${\color{Blue} 3}({\color{Blue} a} +2b + 3c) = {\color{Blue} 3a}$

${\color{Green} 3}(a {\color{Green} +2b} + 3c) = {\color{Green} + 6b}$

${\color{Red} 3}(a +2b {\color{Red} + 3c}) = {\color{Red} + 9c}$

${\color{Blue} 3a}{\color{Green} + 6b}{\color{Red} +9c}$

3a+6b+9c

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Example Question #107 : How To Find The Distributive Property

Simplify the following terms: 2x(x^2+2x-1)

Possible Answers:

2x^3+4x^2-2x

2x^3+2x^2-2x

2x^3+4x^2-2

2x^3+2x^2-2

3x^2-4x+2

Correct answer:

2x^3+4x^2-2x

Explanation:

Use the distributive property to simplify the expression.

Multiply the monomial with the terms of the trinomial.

2x(x^2+2x-1) = (2x)(x^2)+ (2x)(2x)+(2x)(-1)

Expand the terms.

The answer is: 2x^3+4x^2-2x

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to find the distributive property

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #101 : How To Find The Distributive Property

Example Question #102 : How To Find The Distributive Property

Example Question #103 : How To Find The Distributive Property

Example Question #104 : How To Find The Distributive Property

Example Question #105 : How To Find The Distributive Property

Example Question #106 : How To Find The Distributive Property

Example Question #107 : How To Find The Distributive Property

All ISEE Middle Level Math Resources

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