Arithmetic

Reduce to lowest terms: 20/80

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Find the Greatest Common Factor

\text{Factors of } 20: 1, 2, 4, 5, 10, 20\text{Factors of } 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
To reduce a fraction, we need to find the biggest number that divides evenly into both the top and bottom. The greatest common factor (GCF) of 20 and 80 is 20.
2

Divide Both Parts by the GCF

We divide both the numerator and denominator by 20. Dividing both parts by the same number keeps the fraction equal in value.
3

Simplify to Lowest Terms

20 divided by 20 is 1, and 80 divided by 20 is 4. Since 1 and 4 share no common factors other than 1, the fraction is fully reduced.

Understanding this problem

Learning Insight

Reducing a fraction doesn't change its value — it just rewrites it in a simpler form. Dividing the top and bottom by the same number is the same as dividing by 1, so the fraction stays equivalent. This works because of the Identity Property of Division.

Quick Tip

If one number divides evenly into the other (like 20 into 80), that smaller number is automatically the GCF — just divide both by it in one step!

Common Mistake

Students often only divide by a small common factor (like 2 or 4) instead of the GCF, ending up with 5/20 or 2/8, and forget to keep reducing until no common factors remain.