What is 6/8 of 69?

How to calculate 6/8 of 69?

1. Multiply the whole number by the numerator of the fraction: 69 × 6 = 414
2. Divide this result by denominator of the fraction: 414/8 = 51.75
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 414/2 = 207
   • 8/2 = 4
4. Which gives: 207/4

Since 207/4 is an improper fraction, the result could also be expressed as a mixed number: 51 3/4

How does it work?

The principle behind finding a fraction of a number, such as 6/8 of 69, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{8}=\frac{x}{69}$ (where x represents 6/8 of 69)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 69=8x$
2. Which gives: $414=8x$
3. Divide both sides by 8 to isolate x: $\frac{414}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{414}{8}=x$ (or $\frac{207}{4}=x$)

Thus, 6/8 of 69 is equal to 207/4 (or 51.75 in its decimal form).