What is 3/4 of 46?

How to calculate 3/4 of 46?

1. Multiply the whole number by the numerator of the fraction: 46 × 3 = 138
2. Divide this result by denominator of the fraction: 138/4 = 34.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 138/2 = 69
   • 4/2 = 2
4. Which gives: 69/2

Since 69/2 is an improper fraction, the result could also be expressed as a mixed number: 34 1/2

How does it work?

The principle behind finding a fraction of a number, such as 3/4 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{4}=\frac{x}{46}$ (where x represents 3/4 of 46)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $3\times 46=4x$
2. Which gives: $138=4x$
3. Divide both sides by 4 to isolate x: $\frac{138}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{138}{4}=x$ (or $\frac{69}{2}=x$)

Thus, 3/4 of 46 is equal to 69/2 (or 34.5 in its decimal form).