To express the ratio 54 : 63 in simplest form, follow these steps:
### Step 1: Write the ratio
We start with the ratio 54 : 63.
### Step 2: Find the HCF (Highest Common Factor)
To simplify the ratio, we need to find the HCF of the two numbers, 54 and 63.
- The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
- The factors of 63 are: 1, 3, 7, 9, 21, 63
The common factors are 1, 3, and 9. The highest of these is 9. Therefore, the HCF of 54 and 63 is 9.
### Step 3: Divide both numbers by the HCF
Now, we divide both numbers in the ratio by their HCF (9):
- 54 ÷ 9 = 6
- 63 ÷ 9 = 7
### Step 4: Write the simplified ratio
After dividing, we get the simplified ratio:
6 : 7
### Final Answer
The simplest form of the ratio 54 : 63 is 6 : 7.
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