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Sagot :
Let's solve the given multiplication of fractions step-by-step:
### Problem 1: [tex]\( 1 \frac{2}{5} \times 3 \frac{2}{4} \)[/tex]
First, we need to convert the mixed numbers to improper fractions.
1. [tex]\( 1 \frac{2}{5} \)[/tex]:
- Convert [tex]\( 1 \)[/tex] to a fraction with the same denominator: [tex]\( 1 = \frac{5}{5} \)[/tex]
- [tex]\( 1 \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \)[/tex]
2. [tex]\( 3 \frac{2}{4} \)[/tex]:
- Convert [tex]\( 2 \)[/tex] to a fraction with the same denominator: [tex]\(3 = \frac{12}{4}\)[/tex]
- [tex]\( 3 \frac{2}{4} = \frac{12}{4} + \frac{2}{4} = \frac{14}{4} \)[/tex]
- Simplify: [tex]\( \frac{14}{4} = \frac{7}{2} \)[/tex]
Now, multiply the fractions:
[tex]\[ \frac{7}{5} \times \frac{7}{2} = \frac{7 \times 7}{5 \times 2} = \frac{49}{10} \][/tex]
### Problem 2: [tex]\( \frac{9}{10} \times \frac{5}{4} \)[/tex]
Multiply the fractions directly:
[tex]\[ \frac{9}{10} \times \frac{5}{4} = \frac{9 \times 5}{10 \times 4} = \frac{45}{40} \][/tex]
Simplify the result:
[tex]\[ \frac{45}{40} = \frac{9}{8} \][/tex]
### Problem 3: [tex]\( 2.5 \times \frac{4}{7} \)[/tex]
First, convert [tex]\( 2.5 \)[/tex] to a fraction.
[tex]\[ 2.5 = \frac{25}{10} = \frac{5}{2} \][/tex]
Now, multiply the fractions:
[tex]\[ \frac{5}{2} \times \frac{4}{7} = \frac{5 \times 4}{2 \times 7} = \frac{20}{14} \][/tex]
Simplify the result:
[tex]\[ \frac{20}{14} = \frac{10}{7} \][/tex]
### Problem 4: [tex]\( 9 \frac{1}{3} \times \frac{12}{20} \)[/tex]
Convert the mixed number to an improper fraction.
1. [tex]\( 9.5 \frac{1}{3} \)[/tex]:
- Convert [tex]\( 9.5 = \frac{19}{2} \)[/tex]
- [tex]\( 9.5 \frac{1}{3} = \frac{19}{2} \frac{3}{1} + \frac{1}{3} = \left(9.5 \times \frac{3}{3} + \frac{1}{3}\right)\)[/tex]
- [tex]\( = (19 \times \frac{3}{1} + 1)\)[/tex]=\frac{19 \cdot 3 + 1}{ 3} = \frac{58}{3} \)
Now, multiply the fractions:
[tex]\[ \frac{58}{3} \times \frac{12}{20} = \frac{58 \times 12}{3 \times 20} = \frac{696}{60} \][/tex]
Simplify the result:
[tex]\[ \frac{696}{60} = \frac{29}{5} \][/tex]
### Summary of Results:
1. [tex]\( 1 \frac{2}{5} \times 3 \frac{2}{4} = \frac{49}{10} \)[/tex]
2. [tex]\( \frac{9}{10} \times \frac{5}{4} = \frac{45}{40} = \frac{9}{8} \)[/tex]
3. [tex]\( 2.5 \times \frac{4}{7} = \frac{20}{14} = \frac{10}{7} \)[/tex]
4. [tex]\( 9.5 \frac{1}{3} \times \frac{12}{20} = \frac{696}{60} = \frac{29}{5} \)[/tex]
### Problem 1: [tex]\( 1 \frac{2}{5} \times 3 \frac{2}{4} \)[/tex]
First, we need to convert the mixed numbers to improper fractions.
1. [tex]\( 1 \frac{2}{5} \)[/tex]:
- Convert [tex]\( 1 \)[/tex] to a fraction with the same denominator: [tex]\( 1 = \frac{5}{5} \)[/tex]
- [tex]\( 1 \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \)[/tex]
2. [tex]\( 3 \frac{2}{4} \)[/tex]:
- Convert [tex]\( 2 \)[/tex] to a fraction with the same denominator: [tex]\(3 = \frac{12}{4}\)[/tex]
- [tex]\( 3 \frac{2}{4} = \frac{12}{4} + \frac{2}{4} = \frac{14}{4} \)[/tex]
- Simplify: [tex]\( \frac{14}{4} = \frac{7}{2} \)[/tex]
Now, multiply the fractions:
[tex]\[ \frac{7}{5} \times \frac{7}{2} = \frac{7 \times 7}{5 \times 2} = \frac{49}{10} \][/tex]
### Problem 2: [tex]\( \frac{9}{10} \times \frac{5}{4} \)[/tex]
Multiply the fractions directly:
[tex]\[ \frac{9}{10} \times \frac{5}{4} = \frac{9 \times 5}{10 \times 4} = \frac{45}{40} \][/tex]
Simplify the result:
[tex]\[ \frac{45}{40} = \frac{9}{8} \][/tex]
### Problem 3: [tex]\( 2.5 \times \frac{4}{7} \)[/tex]
First, convert [tex]\( 2.5 \)[/tex] to a fraction.
[tex]\[ 2.5 = \frac{25}{10} = \frac{5}{2} \][/tex]
Now, multiply the fractions:
[tex]\[ \frac{5}{2} \times \frac{4}{7} = \frac{5 \times 4}{2 \times 7} = \frac{20}{14} \][/tex]
Simplify the result:
[tex]\[ \frac{20}{14} = \frac{10}{7} \][/tex]
### Problem 4: [tex]\( 9 \frac{1}{3} \times \frac{12}{20} \)[/tex]
Convert the mixed number to an improper fraction.
1. [tex]\( 9.5 \frac{1}{3} \)[/tex]:
- Convert [tex]\( 9.5 = \frac{19}{2} \)[/tex]
- [tex]\( 9.5 \frac{1}{3} = \frac{19}{2} \frac{3}{1} + \frac{1}{3} = \left(9.5 \times \frac{3}{3} + \frac{1}{3}\right)\)[/tex]
- [tex]\( = (19 \times \frac{3}{1} + 1)\)[/tex]=\frac{19 \cdot 3 + 1}{ 3} = \frac{58}{3} \)
Now, multiply the fractions:
[tex]\[ \frac{58}{3} \times \frac{12}{20} = \frac{58 \times 12}{3 \times 20} = \frac{696}{60} \][/tex]
Simplify the result:
[tex]\[ \frac{696}{60} = \frac{29}{5} \][/tex]
### Summary of Results:
1. [tex]\( 1 \frac{2}{5} \times 3 \frac{2}{4} = \frac{49}{10} \)[/tex]
2. [tex]\( \frac{9}{10} \times \frac{5}{4} = \frac{45}{40} = \frac{9}{8} \)[/tex]
3. [tex]\( 2.5 \times \frac{4}{7} = \frac{20}{14} = \frac{10}{7} \)[/tex]
4. [tex]\( 9.5 \frac{1}{3} \times \frac{12}{20} = \frac{696}{60} = \frac{29}{5} \)[/tex]
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