3. 2
7
and
3
7
are fractions with the same denominator.
These fractions are called similar fractions. To
add fractions, simply put fractions that are alike or
fractions with the same denominator.
However, fractions that do not have the same
denominators are called dissimilar fractions.
3
7
,
2
3
,
1
2
4. 1) Steps in adding similar
fractions
• Step 1: Add the numerators then copy the common
denominator.
2
7
+
3
7
=
2 + 3
7
=
5
7
• Step 2: Simplify the answer if possible.
5
7
(already in the
simplest form).
5. 2) Adding mixed numbers with similar
fractional parts:
Find the sum of
12
2
20
+ 21
5
20
+ 10
7
20
.
Step 1: Add the numerators and then copy the common denominator.
12 + 21 + 10
2 + 5 + 7
20
= 12 + 21 + 10 +
14
20
6. 2) Adding mixed numbers with similar
fractional parts:
Step 2: Add the whole numbers.
12 + 21 + 10
14
20
= 43
14
20
7. 2) Adding mixed numbers with similar
fractional parts:
Step 3: Simplify the answer if possible. In this matter, the fractional
part
14
20
can still be reduced to simplest form. To do that, divide its
numerator and denominator by their GCF (Greatest Common Factor),
which is 2.
43
14 ÷ 2
20 ÷ 2
= 43
7
10
8. 3) Adding dissimilar fractions:
What is the sum of:
2
3
+
1
5
+
1
4
= ?
Step 1: To add the fractions, transform the given fractions into similar
fractions through getting their LCD (Least Common Denominator). The LCD
of the given fractions is 60
2 𝑥 20
3 𝑥 20
=
40
60
1 𝑥 12
5 𝑥 12
=
12
60
1 𝑥 15
4 𝑥 15
=
15
60
9. 3) Adding dissimilar fractions:
Step 2: add the numerators then copy the common denominator.
40
60
+
12
60
+
15
60
=
67
60
= 1
7
60
10. 4) Adding mixed number with
dissimilar fractional parts:
Find the sum of
5
2
9
+ 3
2
3
.
Step 1: Make the dissimilar fractions into similar. Use the LCD of the
fractions to write equivalent fractions. In the given above, the LCD of the
fractions is 9
5
2 𝑥 1
9 𝑥 1
= 5
2
9
3
2 𝑥 3
3 𝑥 3
= 3
6
9
11. 4) Adding mixed number with
dissimilar fractional parts:
Step 2: Add the fractions, and add also the whole numbers
5
2
9
+ 3
6
3
= 5 + 3 +
2 + 6
9
= 8
8
9
Step 3: Simplify the answer if possible. In this case, the result above
is already simplified.
