Arithmetic

5/8 - 1/3

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Find the least common denominator

To subtract fractions, they need the same denominator. The smallest number both 8 and 3 divide into evenly is 24.
2

Convert first fraction to 24ths

Multiply the top and bottom of 5/8 by 3. This gives an equivalent fraction with denominator 24.
3

Convert second fraction to 24ths

Multiply the top and bottom of 1/3 by 8. Now both fractions share the same denominator.
4

Subtract the numerators

Once the denominators match, just subtract the numerators. Keep the denominator the same.
5

Check if the fraction simplifies

7 is a prime number and does not divide evenly into 24, so the fraction is already in its simplest form.

Understanding this problem

Learning Insight

Fractions can only be added or subtracted when they represent pieces of the same size. Finding a common denominator is how we resize the pieces so they match — then combining them is straightforward.

Quick Tip

To find the LCD of two numbers quickly, multiply them together and then divide by their GCF. Here: 8 × 3 = 24, and GCF(8,3) = 1, so LCD = 24.

Common Mistake

A common mistake is subtracting both the numerators AND the denominators — for example, writing 5-1 over 8-3 = 4/5. The denominator never changes during addition or subtraction; only the numerators are combined.