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Answer :
To solve the problem of multiplying and reducing the fractions [tex]\(\frac{10}{15}\)[/tex] and [tex]\(\frac{50}{75}\)[/tex], follow these steps:
1. Multiply the Fractions:
- Multiply the numerators together: [tex]\(10 \times 50 = 500\)[/tex].
- Multiply the denominators together: [tex]\(15 \times 75 = 1125\)[/tex].
- So, the product of the fractions is [tex]\(\frac{500}{1125}\)[/tex].
2. Reduce the Fraction:
- To reduce a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of 500 and 1125 is 125.
- Divide both the numerator and the denominator by the GCD:
- [tex]\(\frac{500 \div 125}{1125 \div 125} = \frac{4}{9}\)[/tex].
Thus, the product of the fractions [tex]\(\frac{10}{15}\)[/tex] and [tex]\(\frac{50}{75}\)[/tex] when multiplied and reduced is [tex]\(\frac{4}{9}\)[/tex].
1. Multiply the Fractions:
- Multiply the numerators together: [tex]\(10 \times 50 = 500\)[/tex].
- Multiply the denominators together: [tex]\(15 \times 75 = 1125\)[/tex].
- So, the product of the fractions is [tex]\(\frac{500}{1125}\)[/tex].
2. Reduce the Fraction:
- To reduce a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of 500 and 1125 is 125.
- Divide both the numerator and the denominator by the GCD:
- [tex]\(\frac{500 \div 125}{1125 \div 125} = \frac{4}{9}\)[/tex].
Thus, the product of the fractions [tex]\(\frac{10}{15}\)[/tex] and [tex]\(\frac{50}{75}\)[/tex] when multiplied and reduced is [tex]\(\frac{4}{9}\)[/tex].
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