Express the ratio in simplest form.
120cm to 45cm
Both are divisible by 15.
What do you get?
14 to 49
To express a ratio in its simplest form, we need to find the greatest common divisor (GCD) of the two numbers in the ratio and divide both numbers by the GCD.
In this case, the ratio is 120cm to 45cm. The GCD of 120 and 45 is 15.
To find the GCD, we can use the Euclidean algorithm, which involves finding the remainder when dividing the larger number by the smaller number and then repeating the process with the smaller number and the remainder until the remainder is 0. The last non-zero remainder is the GCD.
Let's go through the steps:
1. Divide 120 by 45: 120 ÷ 45 = 2 remainder 30
2. Divide 45 by 30: 45 ÷ 30 = 1 remainder 15
3. Divide 30 by 15: 30 ÷ 15 = 2 remainder 0
The last non-zero remainder is 15, so the GCD of 120 and 45 is 15.
Now, to express the ratio in its simplest form, divide both numbers by the GCD:
120 ÷ 15 = 8
45 ÷ 15 = 3
Therefore, the simplest form of the ratio 120cm to 45cm is 8:3.