What is 7/6 of 74?

How to calculate 7/6 of 74?

1. Multiply the whole number by the numerator of the fraction: 74 × 7 = 518
2. Divide this result by denominator of the fraction: 518/6 = 86.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 518/2 = 259
   • 6/2 = 3
4. Which gives: 259/3

Since 259/3 is an improper fraction, the result could also be expressed as a mixed number: 86 1/3

How does it work?

The principle behind finding a fraction of a number, such as 7/6 of 74, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{7}{6}=\frac{x}{74}$ (where x represents 7/6 of 74)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $7\times 74=6x$
2. Which gives: $518=6x$
3. Divide both sides by 6 to isolate x: $\frac{518}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{518}{6}=x$ (or $\frac{259}{3}=x$)

Thus, 7/6 of 74 is equal to 259/3 (or 86.333333333333 in its decimal form).