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?
one half times d minus one eighth"
one half times d minus one and five eighths"
forty three over 6 times d minus one eighth"
negative forty three over six times d minus one eighth"
The expression equivalent to the given expression is "negative forty three over six times d minus one eighth".
To find the expression that is equivalent to the given quantity, we can simplify the expression step by step.
First, let's simplify the expression:
-3 1/3 * d + 3/4 - (3 5/6 * d + 7/8)
Next, we'll convert the mixed numbers to improper fractions:
(-10/3 * d + 3/4) - (23/6 * d + 7/8)
To simplify further, we'll distribute the negative sign in front of the second quantity:
-10/3 * d + 3/4 - 23/6 * d - 7/8
Now, we'll combine the like terms:
(-10/3 * d - 23/6 * d) + (3/4 - 7/8)
To add the fractions, we need a common denominator. The least common denominator of 3 and 6 is 6, and of 4 and 8 is 8.
Let's write the fractions with the common denominators:
(-20/6 * d - 23/6 * d) + (6/8 * 3/4 - 7/8)
Now, we'll combine the like terms in each set of parentheses:
(-43/6 * d) + (45/32 - 7/8)
To find a common denominator for 32 and 8, we multiply 32 by 4 and 8 by 4 to get 128.
Now, we can write the fractions with the common denominator:
(-43/6 * d) + (45/32 * 4/4 - 7/8)
Simplifying the numerators of the second fraction:
(-43/6 * d) + (180/32 - 7/8)
Now, let's simplify the second fraction further:
(-43/6 * d) + (180/32 - 28/32)
Combine the numerators of the second fraction:
(-43/6 * d) + (152/32)
Next, let's simplify the fractions and convert the improper fraction into a mixed number:
(-43/6 * d) + (19/4)
Finally, we can write the expression in a simplified form:
-43/6 * d + 19/4
So the equivalent expression is "negative forty-three over six times d minus nineteen over four." Therefore, the correct option is "negative forty three over six times d minus one eighth."
To find the equivalent expression, we need to simplify the given expression step by step.
The given expression is:
(-3 1/3)d + (3/4) - (3 5/6)d - (7/8)
First, let's simplify the expression inside each quantity. Start with:
(-3 1/3)d - (3 5/6)d
To subtract fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. So, we rewrite the fractions with a denominator of 6:
(-10/3)d - (23/6)d
Next, we need to combine like terms by adding or subtracting coefficients of the same variable. In this case, both terms have the variable d. Combine the coefficients:
(-10/3 - 23/6)d
To add or subtract fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. So, we rewrite the fractions with a denominator of 6:
(-20/6 - 23/6)d
Now, combine the coefficients:
(-43/6)d
The expression now becomes:
(-43/6)d + (3/4) - (7/8)
To subtract fractions, we need a common denominator. The least common multiple of 4 and 8 is 8. So, we rewrite the fractions with a denominator of 8:
(-43/6)d + (6/8) - (7/8)
Now, combine the fractions:
(-43/6)d + (6/8 - 7/8)
To add or subtract fractions, we can only do so when they have a common denominator. These fractions already have a common denominator of 8, so we can combine them directly:
(-43/6)d - (1/8)
Now, the expression is:
(-43/6)d - (1/8)
To write this expression as a mixed number, we divide the numerator (-43) by the denominator (6):
-43 ÷ 6 = -7 remainder 5
So, the mixed number is:
-7 5/6
Therefore, the equivalent expression is:
(-7 5/6)d - (1/8)
Out of the answer choices provided, the equivalent expression is closest to:
negative forty three over six times d minus one eighth