To reduce the given ratio [tex]\(252 : 378 : 315\)[/tex] to its smallest terms, we need to follow a series of steps involving finding their greatest common divisor (GCD) and then simplifying each part of the ratio by this GCD.
1. Identify the numbers in the ratio: The numbers given are 252, 378, and 315.
2. Find the GCD of the numbers:
- The greatest common divisor (GCD) of 252, 378, and 315 is 63.
3. Divide each number by the GCD:
- For 252:
[tex]\( \frac{252}{63} = 4 \)[/tex]
- For 378:
[tex]\( \frac{378}{63} = 6 \)[/tex]
- For 315:
[tex]\( \frac{315}{63} = 5 \)[/tex]
4. Write the ratio in its reduced form:
The ratio 252 : 378 : 315 in its lowest terms is [tex]\( 4 : 6 : 5 \)[/tex].
Thus, the ratio 252:378:315 reduced to its smallest terms is [tex]\( 4 : 6 : 5 \)[/tex].
