How To Add And Subtract, Adding And Subtracting Mixed Numbers With Like Common Denominators

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In this video we discuss how to add and subtract mixed numbers with like, common denominators. We go through the process using example problems and cover some more difficult types of situations.

Transcript/notes
When adding and subtracting mixed numbers, which have a whole number and a fraction, and the fractions have the same denominator, such as 3 and 2 over 5, plus 1 and 1 over 5, all we do is add the whole numbers together, 3 plus 1, which equals 4 and then as you would normally do with like fractions, add the numerators together, 2 plus 1, which gives us 3. And keep the denominator of 5, so we have 4 and 3 over 5 as the final answer.

Now, if the problem were 3 and 2 over 5 plus 1 and 4 over 5. Our answer would be 4 and 6 over 5, which is an improper fraction. We would then convert the improper fraction to a proper fraction, and I have written that process out here. 6 over 5 becomes 5 over 5 plus 1 over 5, 5 over 5 is equal to 1, which we then add to the other whole number of 4 and the final answer is 5 and 1 over 5.

If we were subtracting, 3 and 2 over 5 minus 1 and 1 over 5. Pretty much the same here, subtract the whole numbers, 3 minus 1 equals 2, then subtract the numerators, 2 minus 1 is 1, and keep the denominator of 5, so we have 2 and 1 over 5 as the final answer.

If we were subtracting, 3 and 2 over 5 minus 1 and 4 over 5, then it does require a little more work. In this problem the numerator in the second fraction is greater than the numerator in the first fraction as 4 is greater than 2. So, we need to borrow from the 3, and one concept to understand about mixed numbers is that they can be viewed as addition, so 3 and 2 over 5 is 3 plus 2 over 5. So, borrowing from the 3 gives us 2 plus 1 plus 2 over 5, which we can write as 2 plus 5 over 5 plus 2 over 5, which is 2 and 7 over 5. And now we can do the subtraction, 2 and 7 over 5 minus 1 and 4 over 5.

Subtract the whole numbers, 2 minus 1 is 1, subtract the numerators of the fractions, 7 minus 4 is 3 and keep the same denominator of 5, so, the final answer is 1 and 3 over 5.

Timestamps
0:00 Adding mixed numbers, numerators total less than denominator
0:27 Adding mixed numbers, numerators total more than denominator
0:53 Subtracting mixed numbers, 1st numerator greater than 2nd numerator
1:09 Subtracting mixed numbers, 1st numerator less than 2nd numerator
2:01 More example problems