Find the value of the given expression. 3 + 1/2 + 1/4 + 1/14 + 2/28

Concept: fractions can be added only after they are written over one common denominator. Reduce each fraction to lowest terms using a/b = (a ÷ k)/(b ÷ k), rewrite every term over the LCM of the denominators, and then add the numerators. A whole number written beside a fraction denotes their sum; the standard mixed-number form additionally requires that fraction to be proper, so a fractional part whose numerator is at least its denominator must be normalised by carrying the extra whole units into the whole-number part.

Applying this to the given expression 3 + 1/2 + 1/4 + 1/14 + 2/28:

1. Reduce the last term to lowest terms: 2/28 = (2 ÷ 2)/(28 ÷ 2) = 1/14, so the expression becomes 3 + 1/2 + 1/4 + 1/14 + 1/14.

2. Find the LCM of the denominators 2, 4 and 14. Their prime factorisations are 2 = 2, 4 = 22 and 14 = 2 × 7, so the LCM is 22 × 7 = 28.

3. Rewrite every fraction over 28: 1/2 = 14/28, 1/4 = 7/28, 1/14 = 2/28 and 1/14 = 2/28.

4. Add the numerators over the common denominator: (14 + 7 + 2 + 2)/28 = 25/28.

5. Since 25 is less than 28, the fractional total 25/28 is already a proper fraction, so it stays beside the whole number 3. The expression equals 3 25/28.

Cross-check with decimals: 1/2 = 0.5, 1/4 = 0.25, 1/14 ≈ 0.0714 and 2/28 ≈ 0.0714, and these add to about 0.8929. Since 25/28 ≈ 0.8929, the whole expression is about 3.893, which agrees with the fractional working.