What is 7/8 of 78?

How to calculate 7/8 of 78?

1. Multiply the whole number by the numerator of the fraction: 78 × 7 = 546
2. Divide this result by denominator of the fraction: 546/8 = 68.25
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 546/2 = 273
   • 8/2 = 4
4. Which gives: 273/4

Since 273/4 is an improper fraction, the result could also be expressed as a mixed number: 68 1/4

How does it work?

The principle behind finding a fraction of a number, such as 7/8 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{7}{8}=\frac{x}{78}$ (where x represents 7/8 of 78)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $7\times 78=8x$
2. Which gives: $546=8x$
3. Divide both sides by 8 to isolate x: $\frac{546}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{546}{8}=x$ (or $\frac{273}{4}=x$)

Thus, 7/8 of 78 is equal to 273/4 (or 68.25 in its decimal form).