What is 5/4 of 34?

How to calculate 5/4 of 34?

1. Multiply the whole number by the numerator of the fraction: 34 × 5 = 170
2. Divide this result by denominator of the fraction: 170/4 = 42.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 170/2 = 85
   • 4/2 = 2
4. Which gives: 85/2

Since 85/2 is an improper fraction, the result could also be expressed as a mixed number: 42 1/2

How does it work?

The principle behind finding a fraction of a number, such as 5/4 of 34, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{4}=\frac{x}{34}$ (where x represents 5/4 of 34)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 34=4x$
2. Which gives: $170=4x$
3. Divide both sides by 4 to isolate x: $\frac{170}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{170}{4}=x$ (or $\frac{85}{2}=x$)

Thus, 5/4 of 34 is equal to 85/2 (or 42.5 in its decimal form).