Mr C. answered • 03/19/21
Together We Can Succeed! - Mr. C
We have the mixed numbers of 3-1/2 and 1-1/3 and want to add them.
There are several ways to work out this problem.
One way is to first add the fractional parts and then the whole numbers.
Since 1/2 and 1/3 do not have like denominators, we will need to find a common denominator for these fractions before they can be combined.
STEP 1: List several multiples of 2, which are found by multiplying the number 2 by the counting numbers: 1, 2, 3, etc.
2: 2, 4, 6, 8, 10, 12, ...
Do the same for the number 3.
3: 3, 6, 9, 12, ...
STEP 2: Now choose the lowest or least common number for each and that we see is the number 6.
The number 6 will become our new denominator. However, think about what multiple of the original number was multiplied to get 6 in each case in order to find the new equivalent fraction.
For 1/2 multiply top and bottom by 3. The new fraction is 3/6.
For 1/3 multiply top and bottom by 2. The new fraction is 2/6.
STEP 3: Next, we add two like fractions only the numerators are added, therefore:
3/6 + 2/6 = 5/6
STEP 4: Now add the whole numbers from the original mixed numbers.
3 + 1 = 4
STEP 5: The answer is found by combining the new whole number with the new fraction.
4-5/6 answer
Another method to do this problem is to convert the mixed numbers into improper fractions, combine them, and convert back to a mixed number.
To do so, multiply the denominator by the whole number, add the numerator value and place that new number over the existing denominator.
For 3-1/2: (2 x 3) + 1 = 7/2
For 1-1/3: (3 x 1) + 1 = 4/3
Repeat STEPS 1, 2, 3 above to add unlike fractions.
We get 7/2x3/3 = 21/6
and
4/3x2/2 = 8/6
Therefore: 21/6 + 8/6 = 29/6
Lastly, convert back to a mixed number by dividing the numerator by the denominator:
29 ÷ 6 = 4-5/6 answer
