Which expression is equivalent to quantity negative three and one third times d plus three fourths end quantity minus quantity three and five sixths times d plus seven eighths end quantity?
To simplify this expression, we need to distribute and combine like terms.
The expression can be written as:
(-3 1/3)d + 3/4 - (3 5/6)d - 7/8
First, let's distribute the negative sign throughout the second quantity:
(-3 1/3)d + 3/4 - 3(5/6)d - 3(7/8)
Now, we can simplify each of the terms:
(-3)d - (1/3)d + 3/4 - (15/6)d - (21/8)
Simplifying the fractions:
-3d - (1/3)d + 3/4 - (5/2)d - (21/8)
Next, let's combine like terms:
-3d - (1/3)d - (5/2)d + 3/4 - 21/8
To combine the fractions, we need a common denominator:
-3d - (8/24)d - (60/24)d + 6/8 - 21/8
In the terms -3d and - (8/24)d, we notice that the fractions have a common denominator of 24. We can combine these terms:
-71/24 d + 6/8 - 21/8
Now, let's combine the fractions in the same way:
-71/24 d + (6 - 21)/8
Simplifying the numerator:
-71/24 d - 15/8
Therefore, the expression is equivalent to:
-71/24d - 15/8
To simplify the expression, let's break it down step-by-step:
Step 1: Distribute the negative three and one third to both terms inside the first parenthesis:
-3 1/3 * d = -10/3 * d
Step 2: Distribute the three and five sixths to both terms inside the second parenthesis:
3 5/6 * d = 23/6 * d
Step 3: Combine like terms within each parenthesis:
-10/3 * d + 3/4 - 23/6 * d + 7/8
Step 4: Simplifying further, we need to find a common denominator for the different fractions involved. The least common denominator (LCD) for 3, 4, 6, and 8 is 24.
Step 5: Convert the fractions to have a common denominator of 24:
(-10/3) * (8/8) * d + (3/4) * (6/6) - (23/6) * (4/4) * d + (7/8) * (3/3)
This simplifies to:
-80/24 * d + 18/24 - 92/24 * d + 21/24
Step 6: Combine like terms:
(-80d - 92d)/24 + (18 + 21)/24
Step 7: Simplify the expression further:
(-172d + 39)/24
Therefore, the expression is equivalent to (-172d + 39)/24.
To find the equivalent expression, let's break down the given expression step by step and simplify it:
1. Start with the expression:
Quantity (-3 1/3) * d + 3/4 - Quantity (3 5/6) * d + 7/8
2. Simplify the first part:
(-3 1/3) * d = (-10/3) * d = -10d/3
3. Simplify the second part:
(3 5/6) * d = (23/6) * d = 23d/6
4. Combine the simplified parts:
-10d/3 + 3/4 - 23d/6 + 7/8
Now, we need to find a common denominator to combine the fractions.
5. The common denominator for 3, 4, 6, and 8 is 24.
6. Multiply each fraction by the necessary factors to get the common denominator:
-10d/3 * (8/8) = -80d/24
3/4 * (6/6) = 18/24
-23d/6 * (4/4) = -92d/24
7/8 * (3/3) = 21/24
7. Combine the fractions:
-80d/24 + 18/24 - 92d/24 + 21/24
8. Simplify the combined expression:
(-80d - 92d + 18 + 21) / 24
(-172d + 39) / 24
Therefore, the equivalent expression is (-172d + 39) / 24.