Simplify 6/7c - 5/9d - 1/2c + 1/3d.
A. 5/1c + 2/9d
B. 5/14c - 2/9d
C. 5/9c - 1/3d
D. 5/9c + 4/12 = 5/9c + 1/3d
To simplify the expression, you need to combine like terms. The like terms in the expression are the terms that have the same variable and exponent.
The expression 6/7c - 1/2c simplifies to (6/7 - 1/2)c. To find a common denominator for 7 and 2, you multiply them together: 7 * 2 = 14. So, the expression becomes (12/14 - 7/14)c, which simplifies to 5/14c.
Similarly, the expression -5/9d + 1/3d simplifies to (-5/9 + 3/3)d. To find a common denominator for 9 and 3, you multiply them together: 9 * 3 = 27. So, the expression becomes (-5/9 + 9/27)d, which simplifies to (1/9)d.
Therefore, the simplified expression is 5/14c + 1/9d.
The correct answer is B. 5/14c - 2/9d
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Expand 6 (x + 1)
To expand the expression 6(x + 1), you need to distribute the 6 to both terms inside the parentheses.
6(x + 1) = 6 * x + 6 * 1
Simplifying, we have:
6x + 6
Therefore, the expanded form of 6(x + 1) is 6x + 6.
Expand 4(3z - 7)
To expand the expression 4(3z - 7), you need to distribute the 4 to both terms inside the parentheses.
4(3z - 7) = 4 * 3z - 4 * 7
Simplifying, we have:
12z - 28
Therefore, the expanded form of 4(3z - 7) is 12z - 28.
Expand -5(2q + 8)
To expand the expression -5(2q + 8), you need to distribute the -5 to both terms inside the parentheses.
-5(2q + 8) = -5 * 2q - 5 * 8
Simplifying, we have:
-10q - 40
Therefore, the expanded form of -5(2q + 8) is -10q - 40.
Expand 7/10 (5d + 6)
To expand the expression 7/10 (5d + 6), you need to distribute the 7/10 to both terms inside the parentheses.
7/10 (5d + 6) = (7/10) * 5d + (7/10) * 6
Simplifying, we have:
35/10 * d + 42/10
To further simplify, we can divide both the numerator and denominator of each fraction by their greatest common divisor, which is 5:
(35/10) * d + (42/10) = (7/2) * d + (42/10) = (7/2)d + (21/5)
Therefore, the expanded form of 7/10 (5d + 6) is (7/2)d + (21/5).
Expand -5/8(3p + 8)
To expand the expression -5/8(3p + 8), you need to distribute the -5/8 to both terms inside the parentheses.
-5/8(3p + 8) = (-5/8) * 3p + (-5/8) * 8
Simplifying, we have:
-15/8 * p - 40/8
To further simplify, we can divide both the numerator and denominator of each fraction by their greatest common divisor, which is 8:
(-15/8) * p - (40/8) = (-15/8) * p - 5
Therefore, the expanded form of -5/8(3p + 8) is (-15/8)*p - 5.
Expand 5(y + 2)
To expand the expression 5(y + 2), you need to distribute the 5 to both terms inside the parentheses.
5(y + 2) = 5 * y + 5 * 2
Simplifying, we have:
5y + 10
Therefore, the expanded form of 5(y + 2) is 5y + 10.
Expand -5 (-3 - 11g)
To expand the expression -5(-3 - 11g), you need to distribute the -5 to both terms inside the parentheses.
-5(-3 - 11g) = -5 * -3 - 5 * (-11g)
Simplifying, we have:
15 + 55g
Therefore, the expanded form of -5(-3 - 11g) is 15 + 55g.
Expand 1/3 (1 -6)
To expand the expression 1/3 (1 - 6), you need to distribute the 1/3 to both terms inside the parentheses.
1/3 (1 - 6) = 1/3 * 1 + 1/3 * (-6)
Simplifying, we have:
1/3 - 2/3
Therefore, the expanded form of 1/3 (1 - 6) is 1/3 - 2/3.
Expand 1/3 (q -6) using distributive property.
A.-1/3 q +6
B. -1/3 q + 2
C. 1/3q - 6
D.1/3q -2
To expand the expression 1/3 (q - 6) using the distributive property, you need to distribute the 1/3 to both terms inside the parentheses.
1/3 (q - 6) = (1/3) * q + (1/3) * (-6)
Simplifying, we have:
1/3 * q - 6/3
Therefore, the expanded form of 1/3 (q - 6) is 1/3 q - 2.
The correct answer is D. 1/3q - 2.
Expand 2/5 (-5c + 10)
A.2c - 10
B.-2c. + 4
C.2c - 4
D.-2c+10
To expand the expression 2/5 (-5c + 10), you need to distribute the 2/5 to both terms inside the parentheses.
2/5 (-5c + 10) = (2/5) * -5c + (2/5) * 10
Simplifying, we have:
-10/5c + 20/5
To further simplify, we can simplify the fractions:
-2c + 4
Therefore, the expanded form of 2/5 (-5c + 10) is -2c + 4.
The correct answer is B. -2c + 4.
Expand -7/6 (3g + 2)
A. 7/2 g + 2
B. 7/2g - 7/3
C. -7/2g - 7/3
D. -7/2g +2
To expand the expression -7/6 (3g + 2), you need to distribute the -7/6 to both terms inside the parentheses.
-7/6 (3g + 2) = (-7/6) * 3g + (-7/6) * 2
Simplifying, we have:
-21/6g - 14/6
To further simplify, we can simplify the fractions:
-7/2g - 7/3
Therefore, the expanded form of -7/6 (3g + 2) is -7/2g - 7/3.
The correct answer is C. -7/2g - 7/3.
Find the GFC of 15q + 6.
To find the Greatest Common Factor (GCF) of 15q and 6, we need to find the largest number or term that can divide both 15q and 6 evenly.
To start, let's look at the factors of each term individually:
Factors of 15q: 1, 3, 5, 15, q, q
Factors of 6: 1, 2, 3, 6
From the lists of factors, we can determine that 3 is the largest factor that both terms have in common.
Therefore, the GCF of 15q and 6 is 3.
Find the GCF of 8d - 20.
To find the Greatest Common Factor (GCF) of 8d and -20, or any expression, we need to find the largest factor or term that can divide both 8d and -20 evenly.
To start, let's factor each term individually:
Factors of 8d: 1, 2, 4, 8, d
Factors of -20: 1, 2, 4, 5, 10, 20
From the lists of factors, we can determine that the largest factor that divides both 8d and -20 evenly is 4.
Therefore, the GCF of 8d and -20 is 4.
Find the GCF of 45g + 30h
To find the Greatest Common Factor (GCF) of 45g and 30h, we need to find the largest number or term that can divide both 45g and 30h evenly.
To start, let's analyze the factors of each term individually:
Factors of 45g: 1, 3, 5, 9, 15, 45, g, g
Factors of 30h: 1, 2, 3, 5, 6, 10, 15, 30, h, h
From the lists of factors, we can determine that the largest factor that both terms have in common is 15.
Therefore, the GCF of 45g and 30h is 15.
Factor 9Z + 18 using the GCF.
To factor 9Z + 18 using the Greatest Common Factor (GCF), we first need to identify the GCF of 9Z and 18.
The factors of 9Z are 1, 3, 9, and Z.
The factors of 18 are 1, 2, 3, 6, 9, 18.
From the lists of factors, we can see that the GCF of 9Z and 18 is 9.
Next, we divide each term by the GCF, 9, to factor out the common factor:
9Z + 18 = (9Z/9) + (18/9)
Simplifying, we have:
9Z + 18 = Z + 2 * 9
So, the factored form of 9Z + 18 using the GCF is:
9Z + 18 = 9(Z + 2)
Factor 16d - 12 using the GCF.
To factor 16d - 12 using the Greatest Common Factor (GCF), we first need to identify the GCF of 16d and 12.
The factors of 16d are 1, 2, 4, 8, 16, and d.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
From the lists of factors, we can see that the GCF of 16d and 12 is 4.
Next, we divide each term by the GCF, 4, to factor out the common factor:
16d - 12 = (16d/4) - (12/4)
Simplifying, we have:
16d - 12 = 4d - 3
So, the factored form of 16d - 12 using the GCF is:
16d - 12 = 4(d - 3)
Find the GCF of 18j + 27.
a. 9
b. 18
c. 54
d. 3
To find the Greatest Common Factor (GCF) of 18j and 27, we need to find the largest number or term that can divide both 18j and 27 evenly.
To start, let's analyze the factors of each term individually:
Factors of 18j: 1, 2, 3, 6, 9, 18, j
Factors of 27: 1, 3, 9, 27
From the lists of factors, we can determine that the largest factor that both terms have in common is 9.
Therefore, the GCF of 18j and 27 is 9.
The correct answer is a. 9.
Find the GCF of 42m - 28n
A. 2
B. 7
C. 14
D. 84
To find the Greatest Common Factor (GCF) of 42m and 28n, we need to find the largest number or term that can divide both 42m and 28n evenly.
To start, let's analyze the factors of each term individually:
Factors of 42m: 1, 2, 3, 6, 7, 14, 21, 42, m
Factors of 28n: 1, 2, 4, 7, 14, 28, n
From the lists of factors, we can determine that the largest factor that both terms have in common is 14.
Therefore, the GCF of 42m and 28n is 14.
The correct answer is C. 14.
Use properties of operations to factor 8w + 16 using GCF.
A. 2(4w+)
B. 4(2w+4)
C. 8(w+2)
D. 6)2w+10)
To factor 8w + 16 using the Greatest Common Factor (GCF), we first need to identify the GCF of 8w and 16.
The factors of 8w are 1, 2, 4, 8, and w.
The factors of 16 are 1, 2, 4, 8, 16.
From the lists of factors, we can see that the GCF of 8w and 16 is 8.
Next, we divide each term by the GCF, 8, to factor out the common factor:
8w + 16 = (8w/8) + (16/8)
Simplifying, we have:
8w + 16 = w + 2
Therefore, the factored form of 8w + 16 using the GCF is:
8w + 16 = w + 2
The correct answer is C. 8(w+2).
Factor -27h + 6 using the GCF.
A. 3(9h +2)
B. 3(-9H -2)
C. 3(9h +2)
D. 3(-9h-2)
To factor -27h + 6 using the Greatest Common Factor (GCF), we first need to identify the GCF of -27h and 6.
The factors of -27h are 1, -1, 3, -3, 9, -9, 27, -27, and h.
The factors of 6 are 1, -1, 2, -2, 3, -3, 6, -6.
From the lists of factors, we can see that the GCF of -27h and 6 is 3.
Next, we divide each term by the GCF, 3, to factor out the common factor:
-27h + 6 = (-27h/3) + (6/3)
Simplifying, we have:
-9h + 2
Therefore, the factored form of -27h + 6 using the GCF is:
-27h + 6 = -9h + 2
The correct answer is B. 3(-9h - 2).
Expand and distri ute. -5(-3-11g)
A. 55g - 15
B. 55g + 15
C. 55g - 15
D. -55 +15
To expand and distribute -5(-3-11g), we need to multiply -5 by each term inside the parentheses.
-5(-3-11g) = -5 * -3 - 5 * (-11g)
Simplifying, we get:
15 + 55g
Therefore, the expanded form of -5(-3-11g) is 15 + 55g.
The correct answer is C. 15 + 55g.
Simplify by combining like terms. 2/8x + 3/10y - 5/8x+ 4/10y
A. -3/8x+7/10y
B. 7/10x + 7/8y
C. 14/18xy
D. 4/18xy
To simplify the expression, we need to combine like terms.
Combining the x terms, we have:
2/8x - 5/8x = (2/8 - 5/8)x = -3/8x
Combining the y terms, we have:
3/10y + 4/10y = (3/10 + 4/10)y = 7/10y
Evaluate when a = 9, b = 6.
A-b over 3
A. 6
B. 9
C. 1
D. 3