Combined Ratio for 5:4 and 6:5

Given a:b = 5 : 4 and b:c = 6 : 5, Calculate a:c

Step 1: We need to match the b portions of each ratio:

Using our LCM Calculator, we find that the least common multiple of 4 and 6 is 12

Step 2: For our a:b ratio of 5 : 4, we need to multiply each portion of the ratio by 12 ÷ 4 = 3

3 x 5 : 3 x 4 = 15 : 12 ← Our new a : b ratio

Step 3: For our b:c ratio of 6 : 5, we need to multiply each portion of the ratio by 12 ÷ 6 = 2

2 x 6 : 2 x 5 = 12 : 10 ← Our new b : c ratio

The b portions of each ratio match, and we have a : c = 15 : 10
Using our GCF Calculator, we can simplify both parts of our ratio by 5
We can express our ratio as a fraction

15/5
10/5

3
2

Since the b portions of each ratio match, we just take a : c = 3 : 2

What is the Answer?

Since the b portions of each ratio match, we just take a : c = 3 : 2

How does the Combined Ratio Calculator work?

Given a ratio a:b and a ratio b:c, this determines the combined ratio a:c
This calculator has 2 inputs.

What 1 formula is used for the Combined Ratio Calculator?

a:b and b:c → a * c = b * b

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Combined Ratio Calculator?

combined ratio: genrated by taking the product of the antecedents of all the ratios as antecedents and the product of the consequents of all the ratios as consequents
fraction: how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
least common multiple: Given 2 numbers a and b, the least common multiple LCM is the smallest positive integer that is divisible by both. It is commonly denoted as LCM(a, b)
ratio: indicates how many times one number contains another

Example calculations for the Combined Ratio Calculator

9:5 and 7:2

Combined Ratio Calculator Video

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