What is 3/4 of 42?

How to calculate 3/4 of 42?

1. Multiply the whole number by the numerator of the fraction: 42 × 3 = 126
2. Divide this result by denominator of the fraction: 126/4 = 31.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 126/2 = 63
   • 4/2 = 2
4. Which gives: 63/2

Since 63/2 is an improper fraction, the result could also be expressed as a mixed number: 31 1/2

How does it work?

The principle behind finding a fraction of a number, such as 3/4 of 42, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{4}=\frac{x}{42}$ (where x represents 3/4 of 42)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $3\times 42=4x$
2. Which gives: $126=4x$
3. Divide both sides by 4 to isolate x: $\frac{126}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{126}{4}=x$ (or $\frac{63}{2}=x$)

Thus, 3/4 of 42 is equal to 63/2 (or 31.5 in its decimal form).