I need help adding fractions with different denominators.
Here is the problem...
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
I can see that the demoninators increase. Since they are both addition and subtraction, how do I do this problem?
Thanks, Walter, New York.
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6
You need to find the common denominator -- the smallest number divisible by each of the denominators.
One way to do that is to find the multiples of the largest.
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Ahh -- the common denominator is 60.
1/2 = 60/2 = 30/60
1/3 = 60/3 = 20/60
That should give you a good start.
Okay, Now that the common demoninator is 60, I now multiply. But where do I start? for example, I just leave the 1 alone because its a whole number. So now I multiply the 1/2 to 1 * 30 = 30 and 2 * 30 = 60 Do I do the same for the 1/3 and so on?
1/2 = 30/60
1/3 = 20/60
What do you think 1/4 equals?
1/4 = 15/60
1/5 = 12/60
What do you think?
solve 5/30+3/40+1/8
what is 5/30 + 3/40 + 1/8
To add fractions with different denominators, you need to find a common denominator. In this case, the common denominator would be the least common multiple (LCM) of the denominators 2, 3, 4, 5, and 6.
Step 1: Find the LCM of the denominators.
- The prime factorization of each denominator is:
- 2: 2
- 3: 3
- 4: 2 * 2
- 5: 5
- 6: 2 * 3
- The LCM is calculated by multiplying the highest exponent of each prime factor:
- LCM = 2 * 2 * 3 * 5 = 60
Step 2: Convert each fraction to have the common denominator of 60.
- Multiply the numerator and denominator of each fraction by the appropriate factor to get the common denominator:
- 1/2 = (1 * 30)/(2 * 30) = 30/60
- 1/3 = (1 * 20)/(3 * 20) = 20/60
- 1/4 = (1 * 15)/(4 * 15) = 15/60
- 1/5 = (1 * 12)/(5 * 12) = 12/60
- 1/6 = (1 * 10)/(6 * 10) = 10/60
Step 3: Add or subtract the fractions as usual.
- Now that all fractions have the same denominator, you can add or subtract the numerators directly:
- 30/60 - 20/60 + 15/60 - 12/60 + 10/60
- Combine the numerators:
- = (30 - 20 + 15 - 12 + 10)/60
- = 23/60
So, the answer to the problem is 23/60.