Multiplying Fractions
What type of fraction do you have?
Only Fractions
Mixed Numbers
How do you want to answer the problem?
Change all mixed numbers into improper fractions.
I want to simplify
First.
I want to simplify at
the last step
Look at the cross angles –
can you divided a number
out of both of them?
Multiply the numerator times the numerator to
equal the numerator. (Multiply straight across)
2
18
×
=
3
20
Denominator X Whole Number + Numerator
Original denominator
Multiply the denominator times the denominator
to equal the denominator. (Multiply straight
across)
5
If you have a whole number with no fraction put it over 1.
2
3
6
×
=
5
7
35
Did you end up
with a
Fraction?
2
17
=
3
3
20 =
20
1
Did you end up
with an
Improper
Fraction?
Divide the numerator by the denominator to get a
mixed number.
Simplify/reduce if necessary. When you have finished you are done!
Dividing Fractions
What type of problem do you have?
Only Fractions
3
3
Mixed Numbers 5 8
8
Change to a multiplication problem
Change all mixed numbers into improper fractions.
COPY, DOT, FLIP
5
2
÷
6
3
Denominator X Whole Number + Numerator
Original denominator
5
3
→
×
6
2
5
How do you want to solve the problem?
2
17
=
3
3
If you have a whole number with no fraction put it over 1.
I want to Simplify First
I want to simplify at the end.
20 =
Look at the cross angles – can
you divided a number out of
both of them?
2
18
×
=
3
20
Multiply the numerator times the numerator
to equal the numerator. (Multiply straight
across)
20
1
Multiply the denominator times the
denominator to equal the denominator.
(Multiply straight across)
2
3
6
×
=
5
7
35
Did you end up with a
Fraction?
Did you end up with an Improper Fraction?
Divide the numerator by the denominator to get a
mixed number
Simplify/reduce if necessary. When you have finished you are done!
Subtracting Fractions
Is the problem subtracting only fractions?
No:
Please look on flow chart about Subtracting Mixed Numbers.
Yes
Do the fractions have a common denominator? (Same bottom #)
NO
YES
Find the common denominator
Subtract the numerators
Denominator stays the same.
1. Multiply the denominators (bottom #)
together.
Did you end up
with a Fraction?
Did you end up with an
𝟑
𝟖
8
3
Improper Fraction?
Divide the numerator by
the denominator to get a
mixed number.
2. Does one denominator (bottom #) go
into the other evenly?
3. Find the LCD = LCM
Make an Equivalent Fraction:
2
=
5
25
1. How many times can you multiply the old
denominator to the new denominator?
(5x5=25)
Simplify(Reduce) if needed if not you are Done!!
2. What you multiplied in the denominator, you
multiply in the numerator. (2 x 5 = 10)
Subtracting Fractions with Mixed Numbers
Do the fractions have a common denominator? (same bottom number)
Yes
No
What method do I want to solve the problem?
Find the common
denominator:
Using Whole Numbers
Using Improper Numbers
Can you subtract the first fraction by the
second fraction?
1. Multiply the
denominators
(bottom #) together.
Change all mixed numbers into improper
fractions.
2. Does one
denominator (bottom
#) go into the other
evenly?
Denominator X Whole Number + Numerator
Original denominator
YES
NO
5
Subtract the numerators
Denominator stays the same.
Borrow from the whole
number.
Subtract the whole
numbers together
Subtract 1 from the whole
number and add the
denominator to the
numerator.
Add the number that
you found with the
fraction with the number
of the whole numbers.
6
2
5
→5
3
3
If you have a whole number with no fraction
put it over 1.
20 =
Make an Equivalent
Fraction:
20
1
2
=
5
25
Subtract the numerators
Denominator stays the same.
Did you end
up with a
𝟑
fraction? 𝟖
Simplify if needed: if not YOU ARE DONE
3. Find the LCD = LCM
2
17
=
3
3
Did you end up
with an improper
𝟖
fraction? 𝟑
Divide the numerator
by the denominator
1. How many times
can you multiply the
old denominator
(bottom #) to the
new denominator?
(5 x 5 = 25)
2. What you multiplied
in the denominator,
you multiply in the
numerator.
(2 x 5 = 10)
Adding Fractions
What type of problem do you have?
Only Fractions?
Mixed Numbers?
Do the fractions have a common denominator?
(same bottom number)
Do the fractions have a common denominator?
(same bottom number)
YES
Add the numerators
Denominator stays the same.
NO
YES
Find the common
denominator
Only look at the fractions
Did you end
up with an
Improper
Fraction?
2. Does one
denominator (bottom #)
go into the other evenly?
3. Find the LCD = Find
the LCM
Make an Equivalent
Fraction:
Divide the
numerator
by the
denominator
Simplify (Reduce) if
needed if not you are
Done!!
Find the common
denominator:
1.
1. Multiply the
denominators (bottom #)
together.
Did you end
up with a
Fraction?
NO
2
=
5
25
1. How many times can
you multiply the old
denominator to the new
denominator? (5x5 = 25)
2. What you multiplied in
the denominator, you
multiply in the numerator.
(Be fair to both #’s)
Add the numerators
Denominator stays the same.
2.
Did you end up
with a fraction?
(top # smaller
than bottom #)
Did you end up with an
improper fraction?
Top number bigger
than bottom
Divide the
numerator (top #)
by the denominator
(bottom #)
Now add the whole numbers together
Add the answer to the whole numbers with the
answer to the fractions.
Simplify if needed: if not YOU ARE DONE
3.
Multiply the
denominators (bottom
#) together.
Does one
denominator go into
the other evenly?
Find the LCD = LCM
Make an Equivalent
Fraction:
2
=
5
25
1. How many times can
you multiply the old
denominator to the new
denominator? (5x5 =25)
2. What you multiplied in
the denominator, you
multiply in the
numerator. (Be fair to
both #’s)