add the fractions 2/3, 3/8, and 5/12 and reduce your answer to the lowest terms
You need to find the lowest common denominator. Then, change these fractions to their equivalents.
Do you know how to do that?
To add fractions, follow these steps:
Step 1: Find a common denominator for all the fractions.
The common denominator for 3, 8, and 12 is 24.
Step 2: Convert each fraction to have a denominator of 24.
2/3 = (2/3) * (8/8) = 16/24
3/8 = (3/8) * (3/3) = 9/24
5/12 = (5/12) * (2/2) = 10/24
Step 3: Add the numerators of the fractions and keep the denominator the same.
16/24 + 9/24 + 10/24 = 35/24
Step 4: Reduce the fraction to lowest terms.
To reduce the fraction to lowest terms, find the greatest common divisor (GCD) of the numerator (35) and the denominator (24). In this case, the GCD is 1.
Divide both the numerator and denominator by the GCD:
35/24 ÷ 1/1 = (35 ÷ 1) / (24 ÷ 1) = 35/24
So, the final answer, in lowest terms, is 35/24.
To add fractions and reduce the answer to the lowest terms, you need to find a common denominator for all the fractions. The common denominator is the least common multiple (LCM) of the denominators.
Let's find the LCM of the denominators 3, 8, and 12:
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, ...
The multiples of 8 are: 8, 16, 24, 32, ...
The multiples of 12 are: 12, 24, 36, ...
From these lists, we can see that the least common multiple (LCM) of 3, 8, and 12 is 24.
Now, we need to convert each fraction to have the same denominator of 24:
For 2/3:
Multiply the numerator and denominator by 8:
(2/3) * (8/8) = 16/24
For 3/8:
Multiply the numerator and denominator by 3:
(3/8) * (3/3) = 9/24
For 5/12:
Multiply the numerator and denominator by 2:
(5/12) * (2/2) = 10/24
Now we can add the fractions:
16/24 + 9/24 + 10/24 = 35/24
To reduce the fraction to the lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is 1 in this case.
Divide both the numerator and denominator by the GCD:
35/24 ÷ 1/1 = 35/24
So the final answer, when reduced to the lowest terms, is 35/24.