Welcome to a video that will show
two methods for adding mixed numbers.
We will add the mixed numbers using improper fractions,
and then using mixed numbers.
We will also model the sum using the fraction bars below.
We are given 2 3/4 plus 1 1/2,
notice here's the model for 2 3/4,
and here's your model for 1 1/2.
Using the method of improper fractions,
the first step is to write 2 3/4, and 1 1/2,
as improper fractions.
2 3/4 as an improper fraction,
will have the denominator of four,
the numerator is four times two plus three,
four times two is eight, eight plus three is 11,
2 3/4 equals 11/4.
Looking at the model, if we break these units into fourths,
we can see that 2 3/4 does equal 11/4.
For 1 1/2, the denominator remains two,
the numerator is two times one plus one which is three,
1 1/2 equals 3/2.
Looking at the model for 1 1/2,
we can easily see, 1 1/2 equals 3/2.
In order to add fractions,
we must always have a common denominator,
so that the pieces that we're adding are the same size.
The least common denominator,
is the least common multiple of two and four, which is four,
if we're unable to determine the least common multiple,
we can always multiply the two denominators,
notice four times two is equal to eight,
but because the LCD or least common denominator is four,
we need to write both fractions
with the denominator of four.
11/4 already has a denominator of four,
to write 3/2 as an equivalent fraction
with the denominator of four,
we multiply the numerator and denominator by two.
Three times two is six, two times two is four,
3/2 is equal to 6/4.
Going back to the model, here's our model for 3/2,
if we break this up into fourths,
we can see, 3/2 equals 6/4.
Notice now all of the pieces are the same size.
And now that we have a common denominator,
we can add the fractions.
The denominator remains four,
the numerator is 11 plus six which equals 17.
Looking at our model, notice how we have
11 plus six or 17 copies of 1/4, which is 17/4,
but notice how this result is an improper fraction,
let's also write this as a mixed number.
To do this, we divide 17 by four.
There are four fours in 17, four times four is 16,
we subtract, the difference is one, our quotient is 4 1/4.
So the sum is 17/4, which is also equal to 4 1/4.
And now to find the sum again, using mixed numbers.
Using mixed numbers the first step
is to write 3/4 and 1/2 with a common denominator.
We already know the least common denominator is four,
and therefore we multiply the numerator
and denominator of 1/2 by two.
We leave 2 3/4 in its current form,
and 1 1/2 is equal 1 2/4.
Looking at our model for 1 1/2,
if we break this bar up into fourths,
we can see 1 1/2 equals 1 2/4.
And now we add, we first add the fractions,
and then we add the whole numbers.
3/4 plus 2/4 is 5/4, and two plus one is three.
Looking at our model, here's the three, and here's the 5/4.
The 5/4 is an improper fraction,
we need to convert this to a mixed number,
and then add it to three.
To do this we divide five by four,
so one four in five, one times four is four,
we subtract, the difference is one, the quotient is 1 1/4.
Which means 3 5/4
is equal to three plus 1 1/4,
which is the same as, plus one plus 1/4,
which equals 4 1/4.
So the final sum as a mixed number is 4 1/4.
I hope you found this helpful.