To compare the number of girls to the number of boys using a ratio, we need to find the lowest common multiple (LCM) of the two numbers, 12 and 14. The LCM is the smallest number that both 12 and 14 can divide into evenly.
To find the LCM, we can list the multiples of each number until we find a common multiple.
For 12, the first few multiples are: 12, 24, 36, 48, 60, 72, ...
For 14, the first few multiples are: 14, 28, 42, 56, 70, 84, ...
From the lists, we can see that 84 is the smallest number that both 12 and 14 can divide into evenly. So, the LCM of 12 and 14 is 84.
To express the comparison between the number of girls and boys in the lowest terms, we need to divide both numbers by their greatest common divisor (GCD). The GCD is the largest number that can divide both 12 and 14 evenly.
To find the GCD of 12 and 14, we can list their common factors:
- For 12, the factors are: 1, 2, 3, 4, 6, 12
- For 14, the factors are: 1, 2, 7, 14
The greatest common divisor of 12 and 14 is 2.
To express the ratio of girls to boys in the lowest terms, we divide both numbers by 2:
- The number of girls becomes 12 ÷ 2 = 6
- The number of boys becomes 14 ÷ 2 = 7
Therefore, the ratio of girls to boys, expressed in lowest terms, is 6:7.