Question

Add 38+112 by using the LCM as the common denominator. What is the LCM of 8 and 12? Enter your answer in the box.

Answer 1

Answer:The answer is 113/6 when you add 38 and 112 using the LCM (Least Common Multiple) as the common denominator.

Explanation:

To add 38 and 112 using the LCM (Least Common Multiple) as the common denominator, you need to find the LCM of 8 and 12 first.

The prime factorization of 8 is 2^3, and the prime factorization of 12 is 2^2 * 3. To find the LCM, take the highest power of each prime factor:

LCM(8, 12) = 2^3 * 3 = 8 * 3 = 24

So, the LCM of 8 and 12 is 24.

Now, you can express both 38 and 112 with a common denominator of 24:

38 = (38/2) * (2/2) = 19/2

112 = (112/4) * (6/6) = 28/3

Now, you can add them with the common denominator of 24:

(19/2) + (28/3)

To add fractions with different denominators, you need to find a common denominator. In this case, the common denominator is 2 * 3 = 6:

(19/2) * (3/3) + (28/3) * (2/2)

Now, both fractions have a common denominator of 6:

(57/6) + (56/6)

Now, add the fractions:

(57/6) + (56/6) = (57 + 56) / 6 = 113/6

So, the sum of 38 and 112 when expressed with the LCM as the common denominator is 113/6.
(hope this helps :D)

Answer 2

The LCM (Least Common Multiple) of 8 and 12 is 24.

To add 38 and 112 using the LCM as the common denominator, we need to convert the fractions to have the same denominator of 24.

To do this, we need to find the equivalent fractions of 38 and 112 with a denominator of 24.

For 38:

38 multiplied by 3 equals 114.

So, 38/1 is equivalent to 114/3 when the denominator is 24.

For 112:

112 multiplied by 2 equals 224.

So, 112/1 is equivalent to 224/2 when the denominator is 24.

Now, we can add the fractions:

114/3 + 224/2

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 3 multiplied by 2, which is 6.

So, we need to convert the fractions to have a denominator of 6.

For 114/3:

3 multiplied by 2 equals 6.

114 multiplied by 2 equals 228.

So, 114/3 is equivalent to 228/6 when the denominator is 6.

For 224/2:

2 multiplied by 3 equals 6.

224 multiplied by 3 equals 672.

So, 224/2 is equivalent to 672/6 when the denominator is 6.

Now, we can add the fractions with the common denominator of 6:

228/6 + 672/6 = 900/6

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common factor, which is 6:

900 divided by 6 equals 150.

6 divided by 6 equals 1.

So, 900/6 simplifies to 150/1, which is equal to 150.

Therefore, when adding 38 and 112 using the LCM as the common denominator, the sum is 150.