Answer :
To solve the expression [tex]\(6 \frac{3}{4}(-11.5)\)[/tex], let's break it down step by step.
First, it's helpful to convert the mixed number [tex]\(6 \frac{3}{4}\)[/tex] to an improper fraction.
1. Convert [tex]\(6 \frac{3}{4}\)[/tex] to an improper fraction:
- The whole number part is 6.
- The fractional part is [tex]\(\frac{3}{4}\)[/tex].
- To convert, multiply the whole number by the denominator of the fraction and add the numerator:
[tex]\(6 \times 4 + 3 = 24 + 3 = 27\)[/tex].
- Thus, [tex]\(6 \frac{3}{4}\)[/tex] equals [tex]\(\frac{27}{4}\)[/tex].
2. Now multiply the improper fraction by [tex]\(-11.5\)[/tex]:
[tex]\[
\frac{27}{4} \times -11.5
\][/tex]
3. Convert [tex]\(-11.5\)[/tex] to a fraction:
- [tex]\(-11.5\)[/tex] is equal to [tex]\(-\frac{23}{2}\)[/tex] (since 11.5 is the same as 11.5/1, which equals [tex]\( \frac{23}{2}\)[/tex]).
4. Multiply the two fractions:
[tex]\[
\frac{27}{4} \times -\frac{23}{2} = \frac{27 \times -23}{4 \times 2} = \frac{-621}{8}
\][/tex]
5. Convert [tex]\(\frac{-621}{8}\)[/tex] to a mixed number:
- Divide 621 by 8, which gives 77 with a remainder of 5. Thus, [tex]\(\frac{621}{8} = 77 \frac{5}{8}\)[/tex].
- Since our result is negative, we get [tex]\(-77 \frac{5}{8}\)[/tex].
Therefore, the value of the expression [tex]\(6 \frac{3}{4}(-11.5)\)[/tex] is:
[tex]\[
-77 \frac{5}{8}
\][/tex]
So the correct answer is:
(C) [tex]\( -77 \frac{5}{8} \)[/tex]
First, it's helpful to convert the mixed number [tex]\(6 \frac{3}{4}\)[/tex] to an improper fraction.
1. Convert [tex]\(6 \frac{3}{4}\)[/tex] to an improper fraction:
- The whole number part is 6.
- The fractional part is [tex]\(\frac{3}{4}\)[/tex].
- To convert, multiply the whole number by the denominator of the fraction and add the numerator:
[tex]\(6 \times 4 + 3 = 24 + 3 = 27\)[/tex].
- Thus, [tex]\(6 \frac{3}{4}\)[/tex] equals [tex]\(\frac{27}{4}\)[/tex].
2. Now multiply the improper fraction by [tex]\(-11.5\)[/tex]:
[tex]\[
\frac{27}{4} \times -11.5
\][/tex]
3. Convert [tex]\(-11.5\)[/tex] to a fraction:
- [tex]\(-11.5\)[/tex] is equal to [tex]\(-\frac{23}{2}\)[/tex] (since 11.5 is the same as 11.5/1, which equals [tex]\( \frac{23}{2}\)[/tex]).
4. Multiply the two fractions:
[tex]\[
\frac{27}{4} \times -\frac{23}{2} = \frac{27 \times -23}{4 \times 2} = \frac{-621}{8}
\][/tex]
5. Convert [tex]\(\frac{-621}{8}\)[/tex] to a mixed number:
- Divide 621 by 8, which gives 77 with a remainder of 5. Thus, [tex]\(\frac{621}{8} = 77 \frac{5}{8}\)[/tex].
- Since our result is negative, we get [tex]\(-77 \frac{5}{8}\)[/tex].
Therefore, the value of the expression [tex]\(6 \frac{3}{4}(-11.5)\)[/tex] is:
[tex]\[
-77 \frac{5}{8}
\][/tex]
So the correct answer is:
(C) [tex]\( -77 \frac{5}{8} \)[/tex]
