Download Adding and Subtracting Fractions

Adding and Subtracting Fractions
Vocabulary
-
Fraction: a part of a whole consisting of a numerator and denominator
Example:
-
2
=
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
Improper Fraction: a fraction that has a larger numerator than denominator
Example:
-
1
5
3
=
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
Mixed Number: a whole number with a fraction
3
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
4
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
2 = 𝑤ℎ𝑜𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟
Example:
How to add or subtract fractions with like denominators
Step 1: If the fractions have like denominators, add or subtract the numerators and keep the same denominator.
Do not add the denominators.
Step 2: Once the fractions are added or subtracted, simplify the result if you can. The result may also be
changed to a mixed number, if the question requires it.
Note: The same steps apply to improper fractions that have like denominators.
3
2
7
7
Example 1: +
Example 2:
Example 3:
Example 4:
5
12
7
11
13
15
+
−
−
7
9
5
5
Example 5: +
=
5
12
3
11
7
15
=
5
7
=
=
=
10
12
4
11
6
15
16
5
𝑜𝑟
6
17
−
6
9
17
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
𝑜𝑟 3
1
5
Remember when simplifying, divide the numerator
and denominator by the same number (factor).
5
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
=−
2
5
3
17
Be careful of negative fractions.
Changing improper fractions to mixed numbers:
- Divide the numerator by the denominator
- The number of times that the denominator divides into the numerator becomes the whole number
- If the denominator does not divide evenly, the number that is left over becomes the new numerator
- To find the left over number, multiply the denominator by the whole number that was found and subtract that
result from the original numerator. The difference becomes the new numerator
- The denominator will stay the same, unless the fractional part can be simplified
5
7
2
2
Example 6: −
2
= − 𝑜𝑟 − 1
2
How to add or subtract mixed numbers with like denominators
Adding:
Step 1: When adding mixed numbers, add the whole numbers then add the numerators.
Step 2: If the numerator is larger than the denominator, divide the numerator by the denominator and add the
number of times the denominator divides into the numerator to the current whole number. The number that is
left over becomes the new numerator. Note: You can follow the directions on how to change an improper
fraction to a mixed number.
If the numerator is smaller than the denominator, leave the mixed number the way it is unless the
fraction can be simplified.
3
1
4
8
8
8
5
7
12
9
9
9
Example 1:
2 +1 =3
Example 2:
5 + 6 = 11
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
3
1
2
Follow step 2.
12
3
9
Simplify
12
1
3
Subtracting:
Step 1: When subtracting mixed numbers, subtract the whole numbers then subtract the numerators if the first
numerator is larger than the second numerator.
If the first numerator is smaller than the second numerator, before you subtract, you must borrow from
the whole number. Note: To borrow from the whole number, subtract one from the whole number and add the
value of the denominator to the numerator.
Step 2: Simplify the fraction if necessary.
Example 1:
3
1
2
8
8
8
2 −1 =1
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 1
1
4
5
7
9
9
5 −3
Example 2:
𝐹𝑜𝑙𝑙𝑜𝑤 𝑆𝑡𝑒𝑝 1 𝑡𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 4
14
9
7
7
9
9
−3 =1
Changing a Mixed Number to an Improper Fraction
-
To change a mixed number to an improper fraction, multiply the denominator by the whole number and
add the numerator.
This result becomes the numerator and the denominator stays the same.
3
18
5
5
3 =5×3+3=
Example 3:
How to add or subtract fractions with unlike denominators
Step 1: If the denominators are not the same, we must make them the same by finding a common denominator.
This can be done by multiplying the denominators together or finding a number that both denominators can
divide into evenly. Once you have found the new denominator, you must change the numerator to keep the
fractions balanced. To change the numerator, multiply it by the same number you multiplied the denominator by
to get the common denominator.
Step 2: Once the fractions have the same denominator, follow the steps from the previous sections.
3
4
4
5
2
5
3
6
Example 1: +
Example 2: −
=
=
3×5
4×5
2×2
3×2
+
4×4
5×4
=
15
20
+
16
20
=
5
4
5
1
6
6
6
6
− = − =−
31
20
=1
11
20
Note: The second fraction does not change because we can
multiply 3 by 2 to get 6 to create a common denominator.
5
2
5×5
8
5
8×5
Example 3:
3 +2 =3
Example 4:
5 −2
5
7
6
12
=5
+2
5×2
6×2
2×8
5×8
−2
7
12
=3
=5
25
40
10
12
+2
−2
16
40
7
12
=5
=3
41
40
3
12
=6
1
40
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
3
1
4