How to simplify a ratio with fractions

  1. Convert to improper fractions

  2. Find the least common denominators

  3. Multiply the least common denominators

  4. Express as a simplified ratio

Step 1: Convert to improper fractions

Check for any mixed fractions and change them to improper fractions first. If there are no mixed fractions, proceed to Step 2 right away. Given a ratio with fractions such as 1 5/12 ∶7/30 , we can first change the mixed fraction to an improper fraction.

Step 2: Find the least common denominators

Find the least common multiple of the denominators. Now that we have 17/12 ∶7/30 , we determine the LCD shared by the two fractions.

Step 3: Multiply the least common denominators

Multiply the LCD on the values of the given ratio. This means that for our example, we multiply 60 to both 17/12 and 7/30 .

Step 4: Express as a simplified ratio

Express the product as the new ratio. Simplify the ratio whenever possible. Hence, we have:

Examples of how to simplify ratios with fractions

Q1) Simplify the ratio 12/17 ∶15/68.

We first determine the least common denominator (LCD) shared by 17 and 68. 17=17×1 68=17×4 LCD=17×4=68

Multiply the LCD to the values in the ratio so that we end up with whole numbers on both sides.

Once we have the products as a whole number, we can now cancel common factors out to further simplify the new ratio. 48÷3:15÷3 =16:5

Hence, we have:

Q2) Simplify the ratio 3 2/9 ∶5/18 ∶11/24 to its lowest term.

We first change 3 2/9 to an improper fraction.

Rewriting the ratio with the improper fraction, we have:

Let’s now look for the least common denominator shared by the fractions. 9=3×3 18=3×3×2 24=3×2×2×2 LCD=3×3×2×2×2=72

Multiply 72 on all three fractions. Simplify when needed.