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Answer :
Sure! Let's solve the problem step-by-step.
We want to multiply the fractions [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
Step 1: Multiply the Fractions
To multiply two fractions, we multiply the numerators together and the denominators together:
- Numerator: [tex]\(24 \times 5 = 120\)[/tex]
- Denominator: [tex]\(30 \times 6 = 180\)[/tex]
So, the resulting fraction is [tex]\(\frac{120}{180}\)[/tex].
Step 2: Simplify the Fraction
To simplify [tex]\(\frac{120}{180}\)[/tex], we need to find the greatest common divisor (GCD) of 120 and 180.
- The GCD of 120 and 180 is 60.
We now divide both the numerator and the denominator by the GCD:
- Simplified Numerator: [tex]\(120 \div 60 = 2\)[/tex]
- Simplified Denominator: [tex]\(180 \div 60 = 3\)[/tex]
Thus, the simplified fraction is [tex]\(\frac{2}{3}\)[/tex].
Therefore, [tex]\(\frac{24}{30} \times \frac{5}{6}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
We want to multiply the fractions [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
Step 1: Multiply the Fractions
To multiply two fractions, we multiply the numerators together and the denominators together:
- Numerator: [tex]\(24 \times 5 = 120\)[/tex]
- Denominator: [tex]\(30 \times 6 = 180\)[/tex]
So, the resulting fraction is [tex]\(\frac{120}{180}\)[/tex].
Step 2: Simplify the Fraction
To simplify [tex]\(\frac{120}{180}\)[/tex], we need to find the greatest common divisor (GCD) of 120 and 180.
- The GCD of 120 and 180 is 60.
We now divide both the numerator and the denominator by the GCD:
- Simplified Numerator: [tex]\(120 \div 60 = 2\)[/tex]
- Simplified Denominator: [tex]\(180 \div 60 = 3\)[/tex]
Thus, the simplified fraction is [tex]\(\frac{2}{3}\)[/tex].
Therefore, [tex]\(\frac{24}{30} \times \frac{5}{6}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
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