What is 1/4 of 78?

How to calculate 1/4 of 78?

1. Multiply the whole number by the numerator of the fraction: 78 × 1 = 78
2. Divide this result by denominator of the fraction: 78/4 = 19.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 78/2 = 39
   • 4/2 = 2
4. Which gives: 39/2

Since 39/2 is an improper fraction, the result could also be expressed as a mixed number: 19 1/2

How does it work?

The principle behind finding a fraction of a number, such as 1/4 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{1}{4}=\frac{x}{78}$ (where x represents 1/4 of 78)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $1\times 78=4x$
2. Which gives: $78=4x$
3. Divide both sides by 4 to isolate x: $\frac{78}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{78}{4}=x$ (or $\frac{39}{2}=x$)

Thus, 1/4 of 78 is equal to 39/2 (or 19.5 in its decimal form).