Arithmetic

What is the value of 30/12 + 4/8

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Simplify each fraction first

We reduce each fraction to lowest terms by dividing the top and bottom by their greatest common factor. 30 and 12 share a GCF of 6, and 4 and 8 share a GCF of 4.
2

Check for a common denominator

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

Add the numerators together

Since the denominators are the same, we just add the tops: 5 + 1 = 6. The denominator stays 2.
4

Simplify the result

6 divided by 2 equals 3. The fraction simplifies to a 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 adding.

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 = 34/20. You never add the denominators; only the numerators combine once the denominators are the same.