What is the best way to add fractions and reduced them to the lowest terms example 3/8+1/3+5/6
First, find the lowest common denominator. What does 8, 3, and 6 go into evenly? Let's take the largest number -- 8. Multiples of 8 are 8, 16, 24, 32 . . .
Which of those numbers can be divided evenly by 8, 3, and 6?
Did you get 24?
Next -- divide 24 by the denominators in each fraction.
24/8 = 3
Multiply your answer by the numerator.
3 * 3 = 9
3/8 = 9/24
1/3 = 8/24
5/6 = 20/24
9/24 + 8/24 + 20/24
Add the numerators
9/24 + 8/24 + 20/24 = 37/24
Divide 37 by 24 to get the lowest term.
37/24 = 1 13/24
i got the same thing
To add fractions and reduce them to the lowest terms, follow these steps:
Step 1: Find a common denominator
To add fractions, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions involved. In this case, the denominators are 8, 3, and 6.
To find the LCM of 8, 3, and 6:
- Prime factorize each denominator: 8 = 2^3, 3 = 3^1, 6 = 2^1 × 3^1
- Take the highest power of each prime factor: 2^3 × 3^1 = 24
So, 24 is the least common multiple (LCM) of 8, 3, and 6, which will be our common denominator.
Step 2: Convert the fractions to have the common denominator
To convert each fraction to have the common denominator, you need to multiply both the numerator and denominator of each fraction by a number that will result in the common denominator.
For 3/8:
- Multiply the numerator and denominator by 3 to get: (3 × 3) / (8 × 3) = 9/24
For 1/3:
- Multiply the numerator and denominator by 8 to get: (1 × 8) / (3 × 8) = 8/24
For 5/6:
- Multiply the numerator and denominator by 4 to get: (5 × 4) / (6 × 4) = 20/24
After this step, all the fractions have the same denominator of 24.
Step 3: Add the fractions
Now that the fractions have the same denominator, you can simply add the numerators together while keeping the denominator the same.
(9/24) + (8/24) + (20/24) = (9 + 8 + 20) / 24 = 37/24
Step 4: Reduce the fraction (if necessary)
To reduce the fraction to its lowest terms, find the greatest common divisor (GCD) of the numerator and denominator. If the GCD is greater than 1, divide both the numerator and denominator by the GCD.
For 37/24, the GCD is 1, meaning the fraction is already in its lowest terms.
Therefore, the sum of 3/8 + 1/3 + 5/6, when reduced to the lowest terms, is 37/24.