. What is the common multiple in the proportion below ??
X/12= 24/36
2
3
4••
6
Solve the proportion
4/5= x/27
21.6
20••
33.75
18
To find the common multiple in the proportion X/12 = 24/36, you need to find the least common multiple (LCM) of the denominators 12 and 36.
Here's how you can do it:
1. Find the prime factorization of each denominator:
- Prime factorization of 12: 2^2 * 3
- Prime factorization of 36: 2^2 * 3^2
2. Identify the common prime factors with their highest exponents:
- Common prime factors: 2^2 and 3
3. Multiply the common prime factors:
- Common multiple: 2^2 * 3 = 4 * 3 = 12
Therefore, the common multiple in the proportion X/12 = 24/36 is 12. The correct answer is 4.
Now let's solve the proportion 4/5 = x/27.
To solve a proportion, you can use cross multiplication. It involves multiplying the numerator of the first fraction by the denominator of the second fraction, and then multiplying the denominator of the first fraction by the numerator of the second fraction.
Here's how to solve the proportion:
1. Cross multiply:
- (4 * 27) = (5 * x)
2. Simplify both sides:
- 108 = 5x
3. Solve for x:
- Divide both sides by 5:
108/5 = 5x/5
21.6 = x
Therefore, the value of x in the proportion 4/5 = x/27 is 21.6. The correct answer is 20.