Expand, Factorise, Rational Numbers, Percentages (Stage 4)

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• 1.

Expand the expression 8(S-7)

8s-56
Explanation
The given expression is 8(S-7). To expand this expression, we distribute the 8 to both terms inside the parentheses. This gives us 8S - 56. Therefore, the correct expanded form of the expression is 8S - 56.

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• 2.

Expand the expression a(3-b)

3a-ab
Explanation
The given expression "a(3-b)" can be expanded by applying the distributive property of multiplication over addition/subtraction. This means that we need to multiply each term inside the parentheses by the term outside the parentheses. So, when we multiply "a" with "3", we get "3a", and when we multiply "a" with "-b", we get "-ab". Therefore, the expanded expression is "3a - ab".

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• 3.

Expand n(7-y)

7n-ny
Explanation
The expression "n(7-y)" can be expanded by distributing the "n" to both terms inside the parentheses. This results in "7n-ny" as the expanded form.

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• 4.

Expand r(9+v)

9r+rv
Explanation
The given expression, r(9+v), can be expanded by distributing the r to both terms inside the parentheses. This results in 9r + rv.

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• 5.

Expand 6(2a+1)

12a+6
Explanation
The given expression is a multiplication problem where 6 is being multiplied by the expression (2a+1). To expand this expression, we distribute the 6 to both terms inside the parentheses. Multiplying 6 by 2a gives us 12a, and multiplying 6 by 1 gives us 6. Therefore, the expanded form of 6(2a+1) is 12a+6.

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• 6.

Expand 4(3p+2)

12p+8
Explanation
The given expression is 4(3p+2). To expand this, we distribute the 4 to both terms inside the parentheses. This gives us 4*3p + 4*2, which simplifies to 12p + 8.

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• 7.

Expand 8(3a-4b)

24a-32b
Explanation
The given expression is 8(3a-4b). To expand this expression, we distribute the 8 to both terms inside the parentheses. This gives us 24a-32b as the expanded form of the expression.

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• 8.

Expand 3(2-7y)

6-21y
Explanation
To expand the expression 3(2-7y), we distribute the 3 to both terms inside the parentheses. This gives us 3*2 - 3*7y, which simplifies to 6 - 21y.

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• 9.

Expand 8(3np-5h)

24np-40h
Explanation
The given expression is 8(3np-5h). To expand this expression, we distribute the 8 to both terms inside the parentheses. This gives us 24np-40h. So, the correct answer is 24np-40h.

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• 10.

Expand 2(3a+2c)

6a+4c
Explanation
The given expression is 2(3a+2c). To expand this expression, we distribute the 2 to both terms inside the parentheses. This gives us 2(3a) + 2(2c), which simplifies to 6a + 4c. Therefore, the correct answer is 6a + 4c.

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• 11.

Expand 6(4a-9y)

24a-54y
Explanation
The given expression is 6(4a-9y). To expand this, we distribute the 6 to both terms inside the parentheses. Multiplying 6 by 4a gives us 24a, and multiplying 6 by -9y gives us -54y. Therefore, the expanded form of 6(4a-9y) is 24a-54y.

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• 12.

Expand 7(3k-10v)

21k-70v
Explanation
The given expression is 7(3k-10v). To expand this expression, we distribute the 7 to both terms inside the parentheses. This gives us 7 * 3k - 7 * 10v, which simplifies to 21k - 70v. Therefore, the correct expanded form of 7(3k-10v) is 21k-70v.

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• 13.

Expand 3m(5r-6w)

15mr-6mw
Explanation
The given expression is 3m(5r-6w). To expand this expression, we distribute the 3m to both terms inside the parentheses.

First, we multiply 3m by 5r, which gives us 15mr.

Next, we multiply 3m by -6w, which gives us -18mw.

Therefore, the expanded form of 3m(5r-6w) is 15mr-18mw.

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• 14.

Expand  15a(3b+2c)

45ab+30ac
Explanation
The given expression is an expansion of 15a multiplied by the expression (3b+2c). To simplify the expression, we distribute the 15a to both terms inside the parentheses. This results in 45ab (15a multiplied by 3b) and 30ac (15a multiplied by 2c). Therefore, the correct answer is 45ab+30ac.

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• 15.

Expand 4(a+b+c)

4a+4b+4c
Explanation
The expression 4(a+b+c) can be expanded by distributing the 4 to each term inside the parentheses. This results in 4a + 4b + 4c, which is the given correct answer.

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• 16.

Expand 2(p+q-3)

2p+2q-6
Explanation
The given expression is 2(p+q-3). To expand this expression, we distribute the 2 to each term inside the parentheses. So, we get 2p+2q-6. This is the expanded form of the given expression.

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• 17.

Expand 12a(2-2p+n)

24a-24p+12n
Explanation
The given expression is (12a)(2-2p+n). By using the distributive property, we can expand this expression by multiplying 12a with each term inside the parentheses. This gives us 24a - 24ap + 12an. Therefore, the correct expansion of the given expression is 24a - 24p + 12n.

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• 18.

Expand -5(9-y+b) Remember: opposite signs make a positive, same signs make a negative

-45+5y-5b
Explanation
The given expression is -5(9-y+b). To expand this expression, we distribute the -5 to each term inside the parentheses. So, -5 multiplied by 9 is -45, -5 multiplied by -y is +5y, and -5 multiplied by +b is -5b. Therefore, the expanded form of the expression is -45+5y-5b.

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• 19.

Expand -3(k-2+p)

-3k+6-3p
Explanation
The given expression is -3(k-2+p). To expand this expression, we distribute the -3 to each term inside the parentheses. This gives us -3k + 6 - 3p. Therefore, the correct answer is -3k + 6 - 3p.

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• 20.

Expand (2a-3n)-m

-2am+3nm
Explanation
The given expression is (2a-3n)-m. To expand this expression, we distribute the negative sign to both terms inside the parentheses. This gives us -2a + 3n - m. Therefore, the correct expanded form of the expression is -2am + 3nm.

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• 21.

Select the follow fractions equivalent to 15/45 There is more than one correct answer. HINT: What ever you do to the top (numerator) , you also do to the bottom (denominator)

• A.

5/15

• B.

3/15

• C.

30/90

• D.

3/9

• E.

150/450

B. 3/15
C. 30/90
D. 3/9
E. 150/450
Explanation
The given fractions are equivalent to 15/45 because they can be simplified to the same value. When we simplify 3/15, we divide both the numerator and denominator by 3, resulting in 1/5. Similarly, when we simplify 30/90, we divide both the numerator and denominator by 30, resulting in 1/3. When we simplify 3/9, we divide both the numerator and denominator by 3, resulting in 1/3. Lastly, when we simplify 150/450, we divide both the numerator and denominator by 150, resulting in 1/3.

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• 22.

True or False? To convert 2/8 into a decimal I could say 2 divided 8 = 0.25

• A.

True

• B.

False

A. True
Explanation
The given statement is true. To convert a fraction into a decimal, you divide the numerator (2) by the denominator (8). In this case, 2 divided by 8 equals 0.25.

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• 23.

Give your answer in one word A negative times a positive equals a ___________

negative
Explanation
When a negative number is multiplied by a positive number, the result is always negative. This is because when we multiply two numbers with different signs, the product will always have the opposite sign of the larger number. In this case, the negative sign is larger than the positive sign, so the product is negative.

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• 24.

A pronumeral is a letter in place of a number?

• A.

True

• B.

False

A. True
Explanation
A pronumeral is a letter that is used to represent an unknown number or a variable in mathematical equations. It is commonly used in algebraic expressions and equations where the value of the pronumeral is not specified. Therefore, it can be said that a pronumeral is indeed a letter used in place of a number.

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• 25.

The fraction 3/5 =

• A.

0.6 and/or 60%

• B.

0.6 and or 6%

• C.

0.35 and/or 35%

A. 0.6 and/or 60%
Explanation
The fraction 3/5 can be expressed as a decimal by dividing the numerator (3) by the denominator (5), which gives us 0.6. This means that 3/5 is equal to 0.6. Additionally, it can also be expressed as a percentage by multiplying the decimal form (0.6) by 100, which gives us 60%. Therefore, 3/5 is equal to both 0.6 and 60%.

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• Mar 11, 2024
Quiz Edited by
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• Jun 06, 2011
Quiz Created by
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