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Sagot :
Let's find the product of each given expression step-by-step:
### Expression 1
[tex]\[ \frac{8^3}{8} \times \frac{2}{3} = \frac{6}{14} \][/tex]
1. Calculate [tex]\(\frac{8^3}{8} \times \frac{2}{3}\)[/tex]:
[tex]\[ (8^3 / 8) \times \frac{2}{3} \][/tex]
Simplify [tex]\(8^3 / 8\)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Hence:
[tex]\[ 64 \times \frac{2}{3} \][/tex]
Simplify:
[tex]\[ \frac{128}{3} \][/tex]
2. Then multiply:
[tex]\[ \frac{128}{3} \times \frac{6}{14} \][/tex]
Simplify the fractions if possible:
[tex]\[ \frac{128 \times 6}{3 \times 14} = \frac{768}{42} = \frac{128}{7} \][/tex]
So, the final product is:
[tex]\[ 18.285714285714285 \][/tex]
### Expression 2
[tex]\[ \frac{1}{4} \times \frac{3}{9} = \frac{1}{12} \][/tex]
1. Simply multiply the fractions:
[tex]\[ \frac{1}{4} \times \frac{3}{9} \][/tex]
2. Simplify each fraction if possible and then multiply:
[tex]\[ \frac{1 \times 3}{4 \times 9} = \frac{3}{36} = \frac{1}{12} \][/tex]
So, the final product is:
[tex]\[ 0.08333333333333333 \][/tex]
### Expression 3
[tex]\[ 1 \frac{1}{2} \times 1 \frac{3}{5} \][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 1 + \frac{1}{2} = \frac{3}{2} \][/tex]
[tex]\[ 1 + \frac{3}{5} = \frac{8}{5} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{3}{2} \times \frac{8}{5} = \frac{24}{10} = 2.4 \][/tex]
So, the final product is:
[tex]\[ 2.4000000000000004 \][/tex]
### Expression 4
[tex]\[ 3 \times \frac{6}{10} \times \frac{5}{12} \][/tex]
1. Convert the decimal multiplication:
[tex]\[ 3 \times \frac{6}{10} \times \frac{5}{12} \][/tex]
2. Multiply the given fractions:
[tex]\[ \frac{6}{10} = \frac{3}{5} \][/tex]
[tex]\[ 3 \times \frac{3}{5} \times \frac{5}{12} = 3 \times \frac{3 \times 5}{5 \times 12} = 3 \times \frac{3}{12} = 3 \times \frac{1}{4} = \frac{3}{4} = 0.75 \][/tex]
So, the final product is:
[tex]\[ 0.75 \][/tex]
### Expression 5
[tex]\[ 2 \frac{1}{7} \times \frac{7}{10} \][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 2 + \frac{1}{7} = \frac{15}{7} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{15}{7} \times \frac{7}{10} \][/tex]
Simplify:
[tex]\[ = \frac{15 \times 7}{7 \times 10} = \frac{15}{10} = 1.5 \][/tex]
So, the final product is:
[tex]\[ 1.4999999999999998 \][/tex]
Thus, the results for all the expressions are as follows:
[tex]\[ (18.285714285714285, 0.08333333333333333, 2.4000000000000004, 0.75, 1.4999999999999998) \][/tex]
### Expression 1
[tex]\[ \frac{8^3}{8} \times \frac{2}{3} = \frac{6}{14} \][/tex]
1. Calculate [tex]\(\frac{8^3}{8} \times \frac{2}{3}\)[/tex]:
[tex]\[ (8^3 / 8) \times \frac{2}{3} \][/tex]
Simplify [tex]\(8^3 / 8\)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
Hence:
[tex]\[ 64 \times \frac{2}{3} \][/tex]
Simplify:
[tex]\[ \frac{128}{3} \][/tex]
2. Then multiply:
[tex]\[ \frac{128}{3} \times \frac{6}{14} \][/tex]
Simplify the fractions if possible:
[tex]\[ \frac{128 \times 6}{3 \times 14} = \frac{768}{42} = \frac{128}{7} \][/tex]
So, the final product is:
[tex]\[ 18.285714285714285 \][/tex]
### Expression 2
[tex]\[ \frac{1}{4} \times \frac{3}{9} = \frac{1}{12} \][/tex]
1. Simply multiply the fractions:
[tex]\[ \frac{1}{4} \times \frac{3}{9} \][/tex]
2. Simplify each fraction if possible and then multiply:
[tex]\[ \frac{1 \times 3}{4 \times 9} = \frac{3}{36} = \frac{1}{12} \][/tex]
So, the final product is:
[tex]\[ 0.08333333333333333 \][/tex]
### Expression 3
[tex]\[ 1 \frac{1}{2} \times 1 \frac{3}{5} \][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 1 + \frac{1}{2} = \frac{3}{2} \][/tex]
[tex]\[ 1 + \frac{3}{5} = \frac{8}{5} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{3}{2} \times \frac{8}{5} = \frac{24}{10} = 2.4 \][/tex]
So, the final product is:
[tex]\[ 2.4000000000000004 \][/tex]
### Expression 4
[tex]\[ 3 \times \frac{6}{10} \times \frac{5}{12} \][/tex]
1. Convert the decimal multiplication:
[tex]\[ 3 \times \frac{6}{10} \times \frac{5}{12} \][/tex]
2. Multiply the given fractions:
[tex]\[ \frac{6}{10} = \frac{3}{5} \][/tex]
[tex]\[ 3 \times \frac{3}{5} \times \frac{5}{12} = 3 \times \frac{3 \times 5}{5 \times 12} = 3 \times \frac{3}{12} = 3 \times \frac{1}{4} = \frac{3}{4} = 0.75 \][/tex]
So, the final product is:
[tex]\[ 0.75 \][/tex]
### Expression 5
[tex]\[ 2 \frac{1}{7} \times \frac{7}{10} \][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[ 2 + \frac{1}{7} = \frac{15}{7} \][/tex]
2. Multiply the fractions:
[tex]\[ \frac{15}{7} \times \frac{7}{10} \][/tex]
Simplify:
[tex]\[ = \frac{15 \times 7}{7 \times 10} = \frac{15}{10} = 1.5 \][/tex]
So, the final product is:
[tex]\[ 1.4999999999999998 \][/tex]
Thus, the results for all the expressions are as follows:
[tex]\[ (18.285714285714285, 0.08333333333333333, 2.4000000000000004, 0.75, 1.4999999999999998) \][/tex]
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