What is 7/4 of 46?

How to calculate 7/4 of 46?

1. Multiply the whole number by the numerator of the fraction: 46 × 7 = 322
2. Divide this result by denominator of the fraction: 322/4 = 80.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 322/2 = 161
   • 4/2 = 2
4. Which gives: 161/2

Since 161/2 is an improper fraction, the result could also be expressed as a mixed number: 80 1/2

How does it work?

The principle behind finding a fraction of a number, such as 7/4 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{7}{4}=\frac{x}{46}$ (where x represents 7/4 of 46)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $7\times 46=4x$
2. Which gives: $322=4x$
3. Divide both sides by 4 to isolate x: $\frac{322}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{322}{4}=x$ (or $\frac{161}{2}=x$)

Thus, 7/4 of 46 is equal to 161/2 (or 80.5 in its decimal form).