What is 3/8 of 78?

How to calculate 3/8 of 78?

1. Multiply the whole number by the numerator of the fraction: 78 × 3 = 234
2. Divide this result by denominator of the fraction: 234/8 = 29.25
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 234/2 = 117
   • 8/2 = 4
4. Which gives: 117/4

Since 117/4 is an improper fraction, the result could also be expressed as a mixed number: 29 1/4

How does it work?

The principle behind finding a fraction of a number, such as 3/8 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{8}=\frac{x}{78}$ (where x represents 3/8 of 78)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $3\times 78=8x$
2. Which gives: $234=8x$
3. Divide both sides by 8 to isolate x: $\frac{234}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{234}{8}=x$ (or $\frac{117}{4}=x$)

Thus, 3/8 of 78 is equal to 117/4 (or 29.25 in its decimal form).