To simplify the expression, combine like terms:
-3/4r - 5/6r + 3 - 6 = (-3/4 - 5/6)r + (3 - 6)
To add the fractions -3/4 and -5/6, find a common denominator:
The common denominator of 4 and 6 is 12.
-3/4 = (-3/4)(3/3) = -9/12
-5/6 = (-5/6)(2/2) = -10/12
(-9/12 - 10/12)r + (3 - 6) = -19/12r - 3
Simplify −3/4r + 3 − 5/6r − 6 .(1 point)
11 answers
is it like this
-19
12
or this
-19/12
-19
12
or this
-19/12
Apologies for the confusion. The simplified expression would be -19/12r - 3.
Expand 7/4(8h+3) .(1 point)
To expand the expression, multiply the term outside the parentheses (7/4) by each of the terms inside the parentheses:
7/4(8h + 3) = (7/4)(8h) + (7/4)(3)
To multiply fractions, multiply the numerators together and the denominators together:
(7/4)(8h) = (7 * 8h) / (4 * 1) = 56h / 4 = 14h
(7/4)(3) = (7 * 3) / (4 * 1) = 21 / 4
Therefore, the expanded expression is 14h + 21/4.
7/4(8h + 3) = (7/4)(8h) + (7/4)(3)
To multiply fractions, multiply the numerators together and the denominators together:
(7/4)(8h) = (7 * 8h) / (4 * 1) = 56h / 4 = 14h
(7/4)(3) = (7 * 3) / (4 * 1) = 21 / 4
Therefore, the expanded expression is 14h + 21/4.
Expand −56(9b−12) .(1 point)
To expand the expression, multiply -56 by each of the terms inside the parentheses:
-56(9b - 12) = -56 * 9b + (-56) * (-12)
To simplify the expression, simplify each multiplication:
-56(9b - 12) = -504b + 672
Therefore, the expanded expression is -504b + 672.
-56(9b - 12) = -56 * 9b + (-56) * (-12)
To simplify the expression, simplify each multiplication:
-56(9b - 12) = -504b + 672
Therefore, the expanded expression is -504b + 672.
Expand −5/6(9b−12) .(1 point)
To expand the expression, multiply -5/6 by each of the terms inside the parentheses:
-5/6(9b - 12) = (-5/6)(9b) + (-5/6)(-12)
To simplify the expression, multiply the numerators together and the denominators together:
(-5/6)(9b) = (-5 * 9b) / (6 * 1) = -45b / 6 = -15/2b
(-5/6)(-12) = (-5 * -12) / (6 * 1) = 60 / 6 = 10
Therefore, the expanded expression is -15/2b + 10.
-5/6(9b - 12) = (-5/6)(9b) + (-5/6)(-12)
To simplify the expression, multiply the numerators together and the denominators together:
(-5/6)(9b) = (-5 * 9b) / (6 * 1) = -45b / 6 = -15/2b
(-5/6)(-12) = (-5 * -12) / (6 * 1) = 60 / 6 = 10
Therefore, the expanded expression is -15/2b + 10.
Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.
To add the expressions, first simplify each term separately, then combine like terms:
1/2(x + 4) = 1/2x + 1/2(4) = 1/2x + 2/2 = 1/2x + 1
1/4(4x - 2) = 1/4 * 4x - 1/4 * 2 = 4/4x - 2/4 = 1x - 1/2
Now, combine the simplified terms:
1/2x + 1 + 1x - 1/2 = (1/2 + 1)x + (1 - 1/2)
To add the fractions 1/2 and 1, find a common denominator:
The common denominator of 2 and 1 is 2.
1/2 = (1/2)(1/1) = 1/2
(1/2 + 1) = (1/2)(1/1) + (2/2)(1/1) = 1/2 + 2/2 = 3/2
Therefore, the expression simplifies to (3/2)x + (1 - 1/2) = (3/2)x + (1/2).
In mixed number form, this is expressed as:
1 1/2x + 1/2
1/2(x + 4) = 1/2x + 1/2(4) = 1/2x + 2/2 = 1/2x + 1
1/4(4x - 2) = 1/4 * 4x - 1/4 * 2 = 4/4x - 2/4 = 1x - 1/2
Now, combine the simplified terms:
1/2x + 1 + 1x - 1/2 = (1/2 + 1)x + (1 - 1/2)
To add the fractions 1/2 and 1, find a common denominator:
The common denominator of 2 and 1 is 2.
1/2 = (1/2)(1/1) = 1/2
(1/2 + 1) = (1/2)(1/1) + (2/2)(1/1) = 1/2 + 2/2 = 3/2
Therefore, the expression simplifies to (3/2)x + (1 - 1/2) = (3/2)x + (1/2).
In mixed number form, this is expressed as:
1 1/2x + 1/2