How to Find the Middle of Two Fractions?

The middle of two fractions can be found by averaging them.

Here's a breakdown of how to do it:

Steps to Find the Middle of Two Fractions

1. Add the two fractions together. To do this, you'll need to find a common denominator if the fractions don't already have one.

2. Divide the sum by 2. This is the same as multiplying the sum by 1/2.

Example

Let's say you want to find the fraction halfway between 1/5 and 2/5 (as demonstrated in the reference video).

1. Add the fractions: 1/5 + 2/5 = 3/5

2. Divide by 2 (or multiply by 1/2): (3/5) / 2 = (3/5) * (1/2) = 3/10

Therefore, 3/10 is the fraction halfway between 1/5 and 2/5.

General Formula

The middle of two fractions, a/b and c/d, can be calculated using the following formula:

Middle Fraction = (1/2) ( a/b + c/d* )

First, find a common denominator for a/b and c/d. Let's assume the fractions can be rewritten as x/y and z/y.

Then, the formula becomes:

Middle Fraction = (1/2) ( x/y + z/y ) = (1/2) ((x+z)/y) = (x+z) / (2y)