Examkin

Question

Difficulty: EasyHCF and LCM

What is the Highest Common Factor (HCF) of the fractions 23\frac{2}{3}, 49\frac{4}{9}, and 815\frac{8}{15}?

  1. A
    83\frac{8}{3}
  2. 245\frac{2}{45}Answer
  3. C
    23\frac{2}{3}
  4. D
    845\frac{8}{45}

Answer

The correct answer is 245\frac{2}{45}.
The HCF of a set of fractions is found by dividing the HCF of the numerators by the LCM of the denominators. The numerators are 2, 4, and 8, and their HCF is 2. The denominators are 3, 9, and 15, and their LCM is 45. Combining these yields the correct value of 245\frac{2}{45}.

Step-by-Step Solution

1
Identify the formula for finding the HCF of fractions.
HCF of fractions = (HCF of numerators) / (LCM of denominators).
This standard formula is required to correctly solve for the highest common factor of any set of fractions.
2
Extract the numerators and find their Highest Common Factor (HCF).
The numerators are 2, 4, and 8. Their HCF is 2.
2 is the largest integer that divides 2, 4, and 8 without leaving a remainder.
3
Extract the denominators and find their Least Common Multiple (LCM).
The denominators are 3, 9, and 15. Their LCM is 45.
45 is the smallest positive integer that is a multiple of 3, 9, and 15.
4
Apply the calculated values to the fraction HCF formula.
The final fraction is 245\frac{2}{45}.
Substituting the HCF of the numerators (2) and the LCM of the denominators (45) into the formula gives the final answer.

Key Concept

The HCF of two or more fractions is calculated by dividing the HCF of their numerators by the LCM of their denominators.
Rate this question

Topics

HCF and LCM

More questions from this topic