Arithmetic

4/7 - 1/14

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Find a common denominator for both fractions

Before we can subtract fractions, they must have the same denominator. The least common denominator of 7 and 14 is 14 because 14 is the smallest number both 7 and 14 divide into evenly.
2

Convert 4/7 to an equivalent fraction

We multiply the top and bottom of 4/7 by 2 to get a denominator of 14. This keeps the fraction equal in value — we are just writing it a different way.
3

Subtract the fractions with like denominators

Now that both fractions share the same denominator, we simply subtract the numerators and keep the denominator the same.
4

Simplify the result to lowest terms

Both 7 and 14 share a common factor of 7, so we divide the top and bottom by 7. The fraction is now fully reduced.

Understanding this problem

Learning Insight

Fractions can only be added or subtracted when they share a common denominator because the denominator tells you the 'size' of each piece. You need equal-sized pieces to combine them fairly. Finding the LCD is just finding a common unit for both fractions.

Quick Tip

When one denominator is already a multiple of the other (like 7 and 14), the bigger one IS the LCD — no extra work needed! Just scale up the smaller-denominator fraction.

Common Mistake

A common mistake is subtracting the denominators too — writing 8/14 - 1/14 = 7/0. Keep the denominator the same; only subtract the numerators.