Transcript Subtracting Mixed Numbers

Subtracting Mixed Numbers
Topic 10-5
The Process:
• Use the least common multiple to write
equivalent fractions if the denominators
are not the same.
• Subtract numerators. If you cannot
subtract numerators, then rename the first
mixed number.
• Subtract whole numbers.
• Simplify.
Borrowing not required:
7
5
3
4
5
8
7
5
2
6
8
5
8
1
8
This answer is in simplest form.
A Picture of Renaming:
3
1
1
3
5
6
•This is a picture of three and one third.
•We want to take away one whole and five
sixths.
•To do this, we need to rename to sixths.
•Now we have two sixths, but we need to
take away five sixths. We don’t have
enough sixths.
•Rename one whole to six sixths.
•Now we can cross out five of the
sixths.
•We have subtracted the fractions.
Now subtract the wholes.
•Take away one whole.
•We are left with one whole and
three sixths.
Rename Mathematically:
3
1
1
3
5
6
The LCM of 3 and 6 is 6.
We have equivalent
fractions, but we don’t
have enough sixths to
subtract.
Borrow from the whole
number. Rename the
whole as six sixths.
x2
x1
2
3
1
28
6
5
6
3
6
1
=1
1
2
1=
6
6
We already had two sixths,
and now we have
borrowed one whole, which
is six more sixths.
Two and six are eight. We
now have eight sixths.
Subtract the fractions, then
the whole numbers.
Simplify.
Another Example:
9
4
1
2
5
7
x7
x2
The LCM of 2 and 7 is 14.
We do not have enough
fourteenths, so we must
borrow from the 9.
This answer is in simplest form.
87
9
4
21
14
10
14
4
11
14
1=
14
14
Subtracting from a whole
number:
• If you are subtracting a mixed number
from a whole number, then rename the
whole number.
• Borrow one whole and use the
denominator from the fraction.
• Note: What you’ve just learned is about
the hardest process you’ll learn with
fractions so if you’re getting it…good job!!!
Example:
7
88
3
8
5
8
4
3
8
1=
8
8
We choose eight eighths
because the denominator of the
fraction is 8.
Homework Time!