Compute the exact Highest Common Factor (HCF) for the fractions \frac{6}{25} and \frac{9}{… — State PSC Exam

Compute the exact Highest Common Factor (HCF) for the fractions $\frac{6}{25}$ and $\frac{9}{10}$ . Express your final result as a decimal.

Cevap: 0.06

Cevap

0.06

The Highest Common Factor (HCF) of a set of fractions is found by dividing the HCF of their numerators by the LCM of their denominators. In this case, HCF(6, 9) is 3, and LCM(25, 10) is 50. This gives the fraction 3/50, which perfectly evaluates to the decimal 0.06.

Adım Adım Çözüm

Identify the standard rule for calculating the HCF of fractional numbers.

HCF = (HCF of numerators) / (LCM of denominators)

This is the mathematical formula required to find the greatest common divisor of multiple fractions.

Find the Highest Common Factor (HCF) of the two numerators, 6 and 9.

HCF(6, 9) = 3

3 is the largest integer that divides both 6 and 9 without leaving a remainder.

Find the Least Common Multiple (LCM) of the two denominators, 25 and 10.

LCM(25, 10) = 50

50 is the smallest positive integer that is a multiple of both 25 and 10.

Substitute the results into the formula and convert the fraction to a decimal.

3 / 50 = 0.06

Dividing 3 by 50 yields the terminating decimal 0.06, which is the final required format.

Anahtar Kavram

HCF and LCM of fractions

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