Arithmetic

30/12 + 4/8

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Simplify each fraction first

Reduce each fraction to lowest terms by dividing the top and bottom by their greatest common factor. 30/12 simplifies by dividing both by 6. 4/8 simplifies by dividing both by 4.
2

Check for a common denominator

Both fractions already have the same denominator of 2. When denominators match, we can add the numerators directly.
3

Add the numerators together

Keep the denominator the same and just add the tops: 5 + 1 = 6. This gives us 6/2.
4

Simplify the result

Divide 6 by 2 to get the whole number 3. The answer simplifies to a clean whole number.

Understanding this problem

Learning Insight

Adding fractions requires a common denominator because fractions represent parts of a whole — you can only combine parts that are the same size. Simplifying first makes the numbers smaller and easier to work with before you add.

Quick Tip

Always simplify fractions before adding if you can — smaller numbers mean less chance of arithmetic errors and you may find the denominators already match!

Common Mistake

A common mistake is adding both the numerators AND the denominators — for example, writing 30+4 over 12+8 to get 34/20. You never add the denominators; only the numerators change when the denominators are the same.