Question

Simplify: $\frac{1\frac{1}{4} + 18.75 - 12\frac{2}{6} - 7\frac{6}{9}}{0.6 \times 8.7 - 6.98 \times 10.9}$

• A. 1.6
• B. 0
• C. 1
• D. 0.75

Answer 1

Answer:

B. 0

The simplified value of the expression is 0.

1. Simplify the Numerator:
Let's solve the numerator by converting the fractions into decimals or combining like terms:

• $1\frac{1}{4} = 1.25$

• Combine the first two terms: $1.25 + 18.75 = \mathbf{20}$

Now look at the remaining terms in the numerator:

• $12\frac{2}{6}$ reduces to $12\frac{1}{3}$

• $7\frac{6}{9}$ reduces to $7\frac{2}{3}$

Combine these two negative terms:

• $-\left(12\frac{1}{3} + 7\frac{2}{3}\right) = -\left(12 + 7 + \frac{1}{3} + \frac{2}{3}\right) = -(19 + 1) = \mathbf{-20}$

Putting the numerator together:

• $\text{Numerator} = 20 - 20 = \mathbf{0}$

2. Evaluate the Denominator:
Since the numerator is exactly 0, the entire expression evaluates to 0 as long as the denominator is not zero. Let's verify:

• $0.6 \times 8.7 = 5.22$

• $6.98 \times 10.9 = 76.082$

• $\text{Denominator} = 5.22 - 76.082 = -70.862$ (which is not zero)

3. Final Answer:
$\frac{0}{-70.862} = \mathbf{0}$