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Sagot :
Sure! Let's go through each problem step-by-step.
### (5) [tex]\(\frac{20}{9} \times \frac{2}{6} \times \frac{12}{58}\)[/tex]
1. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{20 \times 2 \times 12}{9 \times 6 \times 58} \][/tex]
2. Simplify the result:
[tex]\[ \frac{480}{3132} \][/tex]
3. Reduce the fraction:
[tex]\[ 0.1532567049808429 \][/tex]
The result is approximately [tex]\(0.153256705\)[/tex].
### (6) [tex]\(\frac{19}{9} \div \frac{13}{6} \times \frac{2}{76}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{19}{9} \times \frac{6}{13} \times \frac{2}{76} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{19 \times 6 \times 2}{9 \times 13 \times 76} \][/tex]
3. Simplify the result:
[tex]\[ \frac{228}{8892} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.025641025641025644 \][/tex]
The result is approximately [tex]\(0.025641026\)[/tex].
### (7) [tex]\(\frac{7}{6} \div \frac{15}{8} \times \frac{36}{35}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{7}{6} \times \frac{8}{15} \times \frac{36}{35} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{7 \times 8 \times 36}{6 \times 15 \times 35} \][/tex]
3. Simplify the result:
[tex]\[ \frac{2016}{3150} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.6399999999999999 \][/tex]
The result is approximately [tex]\(0.64\)[/tex].
### (8) [tex]\(\frac{13}{8} \times \frac{4}{3} \div \frac{26}{16}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{13}{8} \times \frac{4}{3} \times \frac{16}{26} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{13 \times 4 \times 16}{8 \times 3 \times 26} \][/tex]
3. Simplify the result:
[tex]\[ \frac{832}{624} \][/tex]
4. Reduce the fraction:
[tex]\[ 1.3333333333333333 \][/tex]
The result is exactly [tex]\(1.333333\)[/tex].
### (9) [tex]\(\frac{3}{8} \times \frac{18}{42} \div \frac{12}{16}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{3}{8} \times \frac{18}{42} \times \frac{16}{12} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{3 \times 18 \times 16}{8 \times 42 \times 12} \][/tex]
3. Simplify the result:
[tex]\[ \frac{864}{4032} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.21428571428571427 \][/tex]
The result is approximately [tex]\(0.214286\)[/tex].
### (10) [tex]\(\frac{29}{10} \div \frac{7}{2} \times \frac{5}{58}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{29}{10} \times \frac{2}{7} \times \frac{5}{58} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{29 \times 2 \times 5}{10 \times 7 \times 58} \][/tex]
3. Simplify the result:
[tex]\[ \frac{290}{4060} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.07142857142857142 \][/tex]
The result is approximately [tex]\(0.071429\)[/tex].
There you go! Each fraction problem is broken down and solved step-by-step.
### (5) [tex]\(\frac{20}{9} \times \frac{2}{6} \times \frac{12}{58}\)[/tex]
1. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{20 \times 2 \times 12}{9 \times 6 \times 58} \][/tex]
2. Simplify the result:
[tex]\[ \frac{480}{3132} \][/tex]
3. Reduce the fraction:
[tex]\[ 0.1532567049808429 \][/tex]
The result is approximately [tex]\(0.153256705\)[/tex].
### (6) [tex]\(\frac{19}{9} \div \frac{13}{6} \times \frac{2}{76}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{19}{9} \times \frac{6}{13} \times \frac{2}{76} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{19 \times 6 \times 2}{9 \times 13 \times 76} \][/tex]
3. Simplify the result:
[tex]\[ \frac{228}{8892} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.025641025641025644 \][/tex]
The result is approximately [tex]\(0.025641026\)[/tex].
### (7) [tex]\(\frac{7}{6} \div \frac{15}{8} \times \frac{36}{35}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{7}{6} \times \frac{8}{15} \times \frac{36}{35} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{7 \times 8 \times 36}{6 \times 15 \times 35} \][/tex]
3. Simplify the result:
[tex]\[ \frac{2016}{3150} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.6399999999999999 \][/tex]
The result is approximately [tex]\(0.64\)[/tex].
### (8) [tex]\(\frac{13}{8} \times \frac{4}{3} \div \frac{26}{16}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{13}{8} \times \frac{4}{3} \times \frac{16}{26} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{13 \times 4 \times 16}{8 \times 3 \times 26} \][/tex]
3. Simplify the result:
[tex]\[ \frac{832}{624} \][/tex]
4. Reduce the fraction:
[tex]\[ 1.3333333333333333 \][/tex]
The result is exactly [tex]\(1.333333\)[/tex].
### (9) [tex]\(\frac{3}{8} \times \frac{18}{42} \div \frac{12}{16}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{3}{8} \times \frac{18}{42} \times \frac{16}{12} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{3 \times 18 \times 16}{8 \times 42 \times 12} \][/tex]
3. Simplify the result:
[tex]\[ \frac{864}{4032} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.21428571428571427 \][/tex]
The result is approximately [tex]\(0.214286\)[/tex].
### (10) [tex]\(\frac{29}{10} \div \frac{7}{2} \times \frac{5}{58}\)[/tex]
1. Division of fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{29}{10} \times \frac{2}{7} \times \frac{5}{58} \][/tex]
2. Multiply the numerators and multiply the denominators:
[tex]\[ \frac{29 \times 2 \times 5}{10 \times 7 \times 58} \][/tex]
3. Simplify the result:
[tex]\[ \frac{290}{4060} \][/tex]
4. Reduce the fraction:
[tex]\[ 0.07142857142857142 \][/tex]
The result is approximately [tex]\(0.071429\)[/tex].
There you go! Each fraction problem is broken down and solved step-by-step.
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