how do you add and subtract fractions with different denomonaters?
You can not without making the denominators the same.
Do that by seeking the least common multiple of the denominators.
for example to add 3/17 + 1/2
look for a common multiple of 2 and 17.
by the way, the product will always work
2*17 = 34
so
multiply top and bottom of 3/17 by 2 to get
6/34
and
multiply top and bottom of 1/2 by 17 to get
17/34
Then instead of adding 3/17 +1/2
I add
6/34 + 17/34
which is
23/34
done
It is not possible with different denominators. So you would have to change them to make themt the same.
You need to find the lowest common denominator for both fractions. But the product of both denominators would work also.
3/6 + 5/3
The lowest denominator for the obove fractions would be 6. What you do to the bottom, you would do to the top. You multiply the 3 by 2 to get 6, so you would multiply the 5 by 2 to get 10. The new fractions would be...
3/6 + 10/6
Now, just add the numerators together, but leave the denominators as it is.
3/6 + 10/6 = 13/6
And don't forget to leave the fractions in lowest terms. In our case though it is already in lowest terms.
And don't forget
And for subtraction, you would do the exact same thing, but subtracting the numerators insteand of adding.
ANd don't forget to leave your answers in lowest terms.
To add or subtract fractions with different denominators, you need to find a common denominator first. Here's the step-by-step process:
1. Determine the least common multiple (LCM) of the denominators. The LCM is the smallest number that is divisible by both denominators.
2. Rewrite each fraction with the common denominator obtained from step one. To do this, multiply the numerator and denominator of each fraction by a number so that the denominators become the same.
3. Once the fractions have the same denominator, add or subtract the numerators directly while keeping the common denominator unchanged.
4. Simplify the resulting fraction, if possible, by reducing the numerator and denominator to their lowest terms.
5. If necessary, convert the fraction to a mixed number (a whole number combined with a fraction) or a decimal, whichever form is required.
For example, let's say we want to add 1/3 and 1/4:
Step 1: The LCM of 3 and 4 is 12.
Step 2: Rewrite the fractions to have a common denominator:
1/3 = (1/3) * (4/4) = 4/12
1/4 = (1/4) * (3/3) = 3/12
Step 3: Add the numerators:
4/12 + 3/12 = 7/12
Step 4: The fraction 7/12 is already in its simplest form.
Step 5: The answer is 7/12.
Note: The same process applies when subtracting fractions with different denominators, except you subtract the numerators instead of adding them in step 3.