Here is a quick reference table for arithmetic operations with fractions, complete with formulas, rules or descriptions, examples, and a pizza chart to help you understand arithmetic operations with fractions.
| Operation | Description | Formula | Example | Pizza Visual |
|---|---|---|---|---|
| Addition (Same Denominator) | Add the numerators together. Keep the denominator the same. |
ac
+
bc
=
a + bc
|
15
+
25
=
35
|
 +  = 
|
| Addition (Different Denominators) | Find a common denominator by multiplying the denominators, then cross-multiply numerators and add. |
ab
+
cd
=
a × d + b × cb × d
|
12
+
13
=
56
|
 +  = 
|
| Subtraction (Same Denominator) | Subtract the second numerator from the first. Keep the denominator the same. |
ac
−
bc
=
a − bc
|
47
−
17
=
37
|
 −  = 
|
| Subtraction (Different Denominators) | Find a common denominator, cross-multiply numerators, and subtract the second from the first. |
ab
−
cd
=
a × d − b × cb × d
|
34
−
13
=
512
|
 − = 
|
| Multiplication | Multiply the numerators together to get the new numerator. Multiply the denominators together. |
ab
×
cd
=
a × cb × d
|
23
×
45
=
815
|
 ×  = 
|
| Division | "Keep, Change, Flip." Keep the first fraction, change ÷ to ×, and flip the second fraction. |
ab
÷
cd
=
ab
×
dc
=
a × db × c
|
12
÷
34
=
46
|
÷ = 
|
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