A-Temp
Introduction to Adding Fractions
What Are Fractions?
A fraction represents a part of a whole. It consists of two numbers:
- Numerator: The top number, which represents how many parts we have.
- Denominator: The bottom number, which represents the total number of equal parts the whole is divided into.
Adding Fractions with the Same Denominator
When fractions have the same denominator (the bottom number), you can simply add the numerators (the top numbers) together. The denominator remains the same.
Example:
1
4
+
1
2
=
1 + 2
4
=
3
4
Adding Fractions with Different Denominators
When fractions have different denominators, you need to find a common denominator before adding them. The common denominator is typically the least common multiple (LCM) of the two denominators.
Steps:
1. Find the LCM of the denominators.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Add the numerators of the converted fractions.
4. Simplify the resulting fraction, if necessary.
Example:
1
3
+
1
4
1. Find the LCM of 3 and 4, which is 12.
2. Convert fractions.
1
3
=
1 x 4
3 x 4
=
4
12
1
4
=
1 x 3
4 x 3
=
3
12
3. Add the numerators:
4
12
+
3
12
=
4 + 3
12
=
7
12
Exercises:
Part A: Adding Fractions with the Same Denominator
1.
2
5
+
1
5
=
2.
3
8
+
2
8
=
3.
5
9
+
2
9
=
Part B: Adding Fractions with the Different Denominators
1.
1
6
+
1
4
=
2.
2
3
+
1
5
=
3.
3
7
+
2
5
=
Solutions:
Part A: Adding Fractions with the Different Denominators
1.
2
5
+
1
5
=
3
5
2.
3
8
+
2
8
=
5
8
3.
5
9
+
2
9
=
7
9
Part B: Adding Fractions with Different Denominators
1.
1
6
+
1
4
• LCM of 6 and 4 is 12.
• Convert
1
6
=
2
12
and
1
4
=
3
12
• Add
2
12
+
3
12
=
5
12
2.
2
3
+
1
5
• LCM of 3 and 5 is 15.
• Convert
2
3
=
10
15
and
1
5
=
3
15
• Add
10
15
+
3
15
=
13
15
3.
3
7
+
2
5
• LCM of 7 and 5 is 35.
• Convert
3
7
=
15
35
and
2
5
=
14
35
• Add
15
35
+
14
35
=
29
35