Answer :
To solve the expression [tex]\( 6 \frac{3}{4} \times (-11.5) \)[/tex], follow these steps:
1. Convert the mixed number to an improper fraction or a decimal:
- The mixed number [tex]\( 6 \frac{3}{4} \)[/tex] can be converted. First, recognize that [tex]\( 6 \frac{3}{4} = 6 + \frac{3}{4} \)[/tex].
- Converting [tex]\( 6 \frac{3}{4} \)[/tex] to a decimal:
[tex]\[
6 \frac{3}{4} = 6 + 0.75 = 6.75
\][/tex]
2. Multiply the decimal by [tex]\(-11.5\)[/tex]:
- Then, multiply [tex]\( 6.75 \)[/tex] by [tex]\(-11.5\)[/tex]:
[tex]\[
6.75 \times (-11.5) = -77.625
\][/tex]
3. Convert the result back to a mixed number if necessary:
- -77.625 can be expressed as [tex]\(-77 \frac{5}{8}\)[/tex] because:
[tex]\[
0.625 = \frac{5}{8}
\][/tex]
So, the value of the expression [tex]\( 6 \frac{3}{4} \times (-11.5) \)[/tex] is:
[tex]\[
-77 \frac{5}{8}
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{-77 \frac{5}{8}}
\][/tex]
1. Convert the mixed number to an improper fraction or a decimal:
- The mixed number [tex]\( 6 \frac{3}{4} \)[/tex] can be converted. First, recognize that [tex]\( 6 \frac{3}{4} = 6 + \frac{3}{4} \)[/tex].
- Converting [tex]\( 6 \frac{3}{4} \)[/tex] to a decimal:
[tex]\[
6 \frac{3}{4} = 6 + 0.75 = 6.75
\][/tex]
2. Multiply the decimal by [tex]\(-11.5\)[/tex]:
- Then, multiply [tex]\( 6.75 \)[/tex] by [tex]\(-11.5\)[/tex]:
[tex]\[
6.75 \times (-11.5) = -77.625
\][/tex]
3. Convert the result back to a mixed number if necessary:
- -77.625 can be expressed as [tex]\(-77 \frac{5}{8}\)[/tex] because:
[tex]\[
0.625 = \frac{5}{8}
\][/tex]
So, the value of the expression [tex]\( 6 \frac{3}{4} \times (-11.5) \)[/tex] is:
[tex]\[
-77 \frac{5}{8}
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{-77 \frac{5}{8}}
\][/tex]
