Sure, let's break down each multiplication of mixed numbers and fractions step-by-step to find the solutions.
### Problem 1:
[tex]\[ \frac{4}{5} \times \frac{2}{3} \times 4 \frac{1}{4} \][/tex]
First, convert the mixed number [tex]\(4 \frac{1}{4}\)[/tex] to an improper fraction:
[tex]\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}
\][/tex]
Next, multiply the fractions:
[tex]\[
\frac{4}{5} \times \frac{2}{3} \times \frac{17}{4}
\][/tex]
First, multiply [tex]\(\frac{4}{5}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{4}{5} \times \frac{2}{3} = \frac{4 \times 2}{5 \times 3} = \frac{8}{15}
\][/tex]
Then, multiply the result by [tex]\(\frac{17}{4}\)[/tex]:
[tex]\[
\frac{8}{15} \times \frac{17}{4} = \frac{8 \times 17}{15 \times 4} = \frac{136}{60}
\][/tex]
Simplify [tex]\(\frac{136}{60}\)[/tex]:
[tex]\[
\frac{136}{60} = \frac{34}{15} \approx 2.2666666666666666
\][/tex]
### Problem 2:
[tex]\[ 6 \frac{4}{10} \times 2 \][/tex]
First, convert [tex]\(6 \frac{4}{10}\)[/tex] to an improper fraction:
[tex]\[
6 \frac{4}{10} = \frac{6 \times 10 + 4}{10} = \frac{64}{10}
\][/tex]
Next, multiply by 2:
[tex]\[
\frac{64}{10} \times 2 = 2 \times \frac{64}{10} = \frac{2 \times 64}{10} = \frac{128}{10} = 12.8
\][/tex]
### Problem 3:
[tex]\[ 6 \frac{1}{4} \times 3 \frac{2}{5} \][/tex]
First, convert both mixed numbers to improper fractions:
[tex]\[
6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{25}{4}
\][/tex]
[tex]\[
3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}
\][/tex]
Next, multiply the fractions:
[tex]\[
\frac{25}{4} \times \frac{17}{5} = \frac{25 \times 17}{4 \times 5} = \frac{425}{20}
\][/tex]
Simplify [tex]\(\frac{425}{20}\)[/tex]:
[tex]\[
\frac{425}{20} = 21.25
\][/tex]
### Problem 4:
[tex]\[ 4 \frac{6}{7} \times 5 \][/tex]
First, convert [tex]\(4 \frac{6}{7}\)[/tex] to an improper fraction:
[tex]\[
4 \frac{6}{7} = \frac{4 \times 7 + 6}{7} = \frac{34}{7}
\][/tex]
Next, multiply by 5:
[tex]\[
\frac{34}{7} \times 5 = 5 \times \frac{34}{7} = \frac{5 \times 34}{7} = \frac{170}{7} = 24.285714285714285
\][/tex]
### Problem 5:
[tex]\[ 7 \frac{1}{6} \times 3 \frac{2}{3} \][/tex]
First, convert both mixed numbers to improper fractions:
[tex]\[
7 \frac{1}{6} = \frac{7 \times 6 + 1}{6} = \frac{43}{6}
\][/tex]
[tex]\[
3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}
\][/tex]
Next, multiply the fractions:
[tex]\[
\frac{43}{6} \times \frac{11}{3} = \frac{43 \times 11}{6 \times 3} = \frac{473}{18}
\][/tex]
Simplify [tex]\(\frac{473}{18}\)[/tex]:
[tex]\[
\frac{473}{18} \approx 26.27777777777778
\][/tex]
So, the answers are:
1. [tex]\( \frac{4}{5} \times \frac{2}{3} \times 4 \frac{1}{4} = 2.27 \)[/tex]
2. [tex]\( 6 \frac{4}{10} \times 2 = 12.8 \)[/tex]
3. [tex]\( 6 \frac{1}{4} \times 3 \frac{2}{5} = 21.25 \)[/tex]
4. [tex]\( 4 \frac{6}{7} \times 5 = 24.29 \)[/tex]
5. [tex]\( 7 \frac{1}{6} \times 3 \frac{2}{3} = 26.28 \)[/tex] (approximations)
