Certainly! Let's work through each of the multiplications step by step.
1. Multiplying a whole number by a fraction:
[tex]\[
6 \times \frac{1}{8}
\][/tex]
- We start by converting the whole number to a fraction:
[tex]\[
6 = \frac{6}{1}
\][/tex]
- Now, we multiply the fractions:
[tex]\[
\frac{6}{1} \times \frac{1}{8} = \frac{6 \times 1}{1 \times 8} = \frac{6}{8}
\][/tex]
- Simplify [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[
\frac{6}{8} = \frac{3}{4} = 0.75
\][/tex]
2. Multiplying fractions and whole numbers:
[tex]\[
\frac{7}{8} \times 29
\][/tex]
- Convert the whole number to a fraction:
[tex]\[
29 = \frac{29}{1}
\][/tex]
- Multiply the fractions:
[tex]\[
\frac{7}{8} \times \frac{29}{1} = \frac{7 \times 29}{8 \times 1} = \frac{203}{8}
\][/tex]
- Convert [tex]\(\frac{203}{8}\)[/tex] to a decimal:
[tex]\[
\frac{203}{8} = 25.375
\][/tex]
3. Multiplying multiple fractions:
[tex]\[
\frac{4}{9} \times 27 \times \frac{1}{2}
\][/tex]
- Convert the whole number to a fraction:
[tex]\[
27 = \frac{27}{1}
\][/tex]
- Multiply the fractions:
[tex]\[
\frac{4}{9} \times \frac{27}{1} \times \frac{1}{2} = \frac{4 \times 27 \times 1}{9 \times 1 \times 2} = \frac{108}{18}
\][/tex]
- Simplify [tex]\(\frac{108}{18}\)[/tex]:
[tex]\[
\frac{108}{18} = 6
\][/tex]
4. Multiplying mixed numbers:
[tex]\[
8 \frac{2}{5} \times 18 \frac{1}{3}
\][/tex]
- Convert the mixed numbers to improper fractions:
[tex]\[
8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5}
\][/tex]
[tex]\[
18 \frac{1}{3} = \frac{18 \times 3 + 1}{3} = \frac{55}{3}
\][/tex]
- Multiply the improper fractions:
[tex]\[
\frac{42}{5} \times \frac{55}{3} = \frac{42 \times 55}{5 \times 3} = \frac{2310}{15}
\][/tex]
[tex]\[
\frac{2310}{15} = 154
\][/tex]
5. Multiplying a combination of whole number, fraction, and mixed number:
[tex]\[
6 \times \frac{2}{3} \times 2 \frac{1}{2}
\][/tex]
- Convert the mixed number to an improper fraction:
[tex]\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
\][/tex]
- Multiply the fractions:
[tex]\[
6 = \frac{6}{1}
\][/tex]
[tex]\[
\frac{6}{1} \times \frac{2}{3} \times \frac{5}{2} = \frac{6 \times 2 \times 5}{1 \times 3 \times 2} = \frac{60}{6}
\][/tex]
[tex]\[
\frac{60}{6} = 10
\][/tex]
Thus, the step-by-step solutions are:
1. [tex]\(6 \times \frac{1}{8} = 0.75\)[/tex]
2. [tex]\(\frac{7}{8} \times 29 = 25.375\)[/tex]
3. [tex]\(\frac{4}{9} \times 27 \times \frac{1}{2} = 6\)[/tex]
4. [tex]\(8 \frac{2}{5} \times 18 \frac{1}{3} = 154\)[/tex]
5. [tex]\(6 \times \frac{2}{3} \times 2 \frac{1}{2} = 10\)[/tex]
