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41. Simplifie puis calcule les produits.

a. [tex] \frac{45}{14} \times \frac{49}{60} [/tex]

b. [tex] \frac{5}{3} \times \frac{4}{5} [/tex]

c. [tex] \frac{45}{26} \times \frac{65}{72} [/tex]

d. [tex] 2 \times \frac{9}{6} [/tex]

e. [tex] \frac{7}{6} \times \frac{6}{7} [/tex]

f. [tex] \frac{12,4}{6} \times 8 [/tex]

g. [tex] \frac{2,5}{3} \times \frac{3}{0,5} [/tex]

h. [tex] 5,6 \times \frac{9}{0,7} [/tex]

i. [tex] 0,55 \times \frac{2}{11} [/tex]

j. [tex] \frac{25}{27} \times \frac{6}{15} [/tex]

Answer :

Sure, let's solve each part step by step:

### a. [tex]\(\frac{45}{14} \times \frac{49}{60}\)[/tex]

First, multiply the numerators and the denominators:
[tex]\[
\frac{45 \times 49}{14 \times 60} = \frac{2205}{840}
\][/tex]

To simplify [tex]\(\frac{2205}{840}\)[/tex], divide both the numerator and denominator by their greatest common divisor (GCD), which is 45:
[tex]\[
\frac{2205 \div 315}{840 \div 315} = \frac{7}{2}
\][/tex]

So the simplified result is [tex]\(\boxed{2.625}\)[/tex].

### f. [tex]\(\frac{12.4}{6} \times 8\)[/tex]

First, perform the division within the fraction:
[tex]\[
\frac{12.4}{6} = 2.06666667
\][/tex]

Then multiply by 8:
[tex]\[
2.06666667 \times 8 = \boxed{16.533333333333335}
\][/tex]

### b. [tex]\(\frac{5}{3} \times \frac{4}{5}\)[/tex]

First, multiply the numerators and the denominators:
[tex]\[
\frac{5 \times 4}{3 \times 5} = \frac{20}{15}
\][/tex]

To simplify [tex]\(\frac{20}{15}\)[/tex], divide both the numerator and denominator by their greatest common divisor (GCD), which is 5:
[tex]\[
\frac{20 \div 5}{15 \div 5} = \frac{4}{3}
\][/tex]

So the simplified result is [tex]\(\boxed{1.3333333333333333}\)[/tex].

### g. [tex]\(\frac{2.5}{3} \times \frac{3}{0.5}\)[/tex]

First, perform the division within the fractions:
[tex]\[
\frac{2.5}{3} \approx 0.83333333333
\][/tex]
[tex]\[
\frac{3}{0.5} = 6
\][/tex]

Then multiply:
[tex]\[
0.83333333333 \times 6 = \boxed{5.0}
\][/tex]

### c. [tex]\(\frac{45}{26} \times \frac{65}{72}\)[/tex]

First, multiply the numerators and the denominators:
[tex]\[
\frac{45 \times 65}{26 \times 72} = \frac{2925}{1872}
\][/tex]

To simplify [tex]\(\frac{2925}{1872}\)[/tex], divide both the numerator and denominator by their greatest common divisor (GCD), which is 117:
[tex]\[
\frac{2925 \div 117}{1872 \div 117} = \frac{25}{16}
\][/tex]

So the simplified result is [tex]\(\boxed{1.5625}\)[/tex].

### h. [tex]\(5.6 \times \frac{9}{0.7}\)[/tex]

First, perform the division within the fraction:
[tex]\[
\frac{9}{0.7} \approx 12.8571428571
\][/tex]

Then multiply:
[tex]\[
5.6 \times 12.8571428571 \approx \boxed{72.0}
\][/tex]

### d. [tex]\(2 \times \frac{9}{6}\)[/tex]

First, simplify [tex]\(\frac{9}{6}\)[/tex] by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{9 \div 3}{6 \div 3} = \frac{3}{2}
\][/tex]

Then multiply by 2:
[tex]\[
2 \times \frac{3}{2} = 2 \times 1.5 = \boxed{3.0}
\][/tex]

### i. [tex]\(0.55 \times \frac{2}{11}\)[/tex]

First, perform the division within the fraction:
[tex]\[
\frac{2}{11} \approx 0.1818181818
\][/tex]

Then multiply:
[tex]\[
0.55 \times 0.1818181818 = \boxed{0.1}
\][/tex]

### e. [tex]\(\frac{7}{6} \times \frac{6}{7}\)[/tex]

First, multiply the numerators and the denominators:
[tex]\[
\frac{7 \times 6}{6 \times 7} = \frac{42}{42}
\][/tex]

Simplifying [tex]\(\frac{42}{42}\)[/tex]:
[tex]\[
\frac{42}{42} = 1
\][/tex]

So the result is [tex]\(\boxed{1.0}\)[/tex].

### j. [tex]\(\frac{25}{27} \times \frac{6}{15}\)[/tex]

First, multiply the numerators and the denominators:
[tex]\[
\frac{25 \times 6}{27 \times 15} = \frac{150}{405}
\][/tex]

To simplify [tex]\(\frac{150}{405}\)[/tex], divide both the numerator and denominator by their greatest common divisor (GCD), which is 15:
[tex]\[
\frac{150 \div 15}{405 \div 15} = \frac{10}{27}
\][/tex]

So the simplified result is [tex]\(\boxed{0.37037037037037035}\)[/tex].

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