What is a part?
A fraction shows us part of one whole.
It has two parts:
• Part → Number at the top (how many parts you have)
• Number in each (how many similar parts are divided)
Example:
25 \ Frac {2} {5} 52 means that the whole is divided into 5 equal parts, and we have 2 parts.
Why learn parts of parts and subtractions?
Adding and subtracting parts helps us in many daily life situations, such as:
• Sharing pizza 🍕 (how much is left if 2/8 is eaten and then another 3/8 is eaten?)
• Cooking (if you add 1/2 cup sugar and 1/4 cup sugar, how much sugar is used?)
• Time ⏰ (if you study 3/4 of one hour and play 1/4 of one hour, how much time?)
So, it is useful in real life, not only in mathematics class!
Golden law
You can only add or decrease the fractions when each is the same.
The ruler tells us the size of parts. If the parts are different, we cannot directly add or decrease them.
Example:
• 27+37 \ Frac {2} {7}+\ Frac {3} {7} 72+73 ✅ (Same Divisional → Easy!)
• 25+23 \ FRAC {2} {5}+\ Frac {2} {3} 52+32 ❌ (separate ruler → needs to be fixed first)
Pilot
This is the easiest case.
Rule:
• Keep everyone equal.
• Add fractions.
👉 Example 1:
38+28 = 58 \ frac {3} {8}+\ frac {2} {8} = \ Frac {5} {5} {8} 83+82 = 85
We added parts (3 + 2 = 5) and kept the ruler 8.
👉 Example 2:
You ate 16 \ Frac {1} {6} 61 a cake, and your friend ate 26 \ Frac {2} {6} 62.
Total eaten = 1+26 = 36 = 12 \ frac {1+2} = \ \ \ \ Frac {3} {6} = \ Frac {1 {1} {2} 61+2 = 63 = 21.
So together you ate half a cake.
Decrease
It is like this, but instead of adding fractions, we reduce them.
Rule:
• Keep everyone equal.
• Decrease fractions.
👉 Example 1:
59–29 = 39 = 13 \ frac {5} {9} – \ Frac {2} {9} = \ Frac {3} {9} = \ Frac
👉 Example 2:
You had 47 \ Frac {4} {7} 74 of the chocolate bar. You gave your friend 27 \ Frac {2} {7} 72.
= 47–27 = 27 \ Frac {4} {7} – \ Frac {2} {7} = \ Frac {2} {7} {7} left with 74–72 = 72.
Splitting
It’s a bit difficult but fun!
phase:
1. Find a common dilative (usually at least normal (LCM)) of a normal division.
2. Change both parts into the same each.
3. Add the fractions.
👉 Example 1:
12+14 \ Frac {1} {2}+\ Frac {1 {4} 21+41
• Every: 2 and 4.
• LCM of 2 and 4 = 4.
• Convert 12 = 24 \ frac {1} {2} = \ Frac {2} {4} 21 = 42.
• Now, 24+14 = 34 \ frac {2} {4}+\ Frac {1} {4} = \ Frac {3} {4} 42+41 = 43.
👉 Example 2:
23+16 \ frac {2} {3}+\ frac {1} {6} 32+61
• Every: 3 and 6.
• LCM = 6.
• Convert 23 = 46 \ Frac {2 {3} = \ Frac {4} {6} 32 = 64.
• Now, 46+16 = 56 \ frac {4} {6}+\ frac {1} {6} = \ frac {5} {6} 64+61 = 65.
Decrease
The same procedure in the form of joints, but subtract instead of add.
👉 Example 1:
34 AC12 \ Frac {3} {4} – \ Frac {1} {2} 43–21
• Every: 4 and 2.
• LCM = 4.
• Convert 12 = 24 \ frac {1} {2} = \ Frac {2} {4} 21 = 42.
• Now, 34–24 = 14 \ Frac {3} {4} – \ Frac {2} {4} = \ Frac {1} {4} 43–42 = 41.
👉 Example 2:
58
• Every: 6 and 3.
• LCM = 6.
• Convert 13 = 26 \ Frac {1} {3} = \ Frac {2} {6} 31 = 62.
• Now, 56–26 = 36 = 12 \ Frac {5} {6} – \ Frac {2} {6} = \ Frac {3} {6} = \ Frac {1 {1 {2 {2} 65–62 = 63 = 21.
Mixed number and unfair fraction
Sometimes fractions come in the form of mixed number (full + fraction).
Example: 2132 \ Frac {1} {3} 231 (meaning 2 + 13 \ Frac {1} {3} 31).
Before adding or subtracts:
• Convert mixed numbers into improper fractions.
👉 Example:
213 = 732 \ Frac {1} {3} = \ Frac {7} {3} 231 = 37
How? (2 × 3 + 1 = 7, every = 3).
Also example:
112+2131 \ Frac {1} {2} +2 \ Frac {1 {1} {3} 121+231
• Convert: 32+73 \ Frac {3} {2}+\ Frac {7} {3} 23+37
• Every 2 and 3 → LCM = 6
• Convert: 96+146 = 236 \ frac {9} {6}+\ frac {14} {6} = \ Frac {23} {6} 69+614 = 623
• As a mixed number = 3563 \ Frac {5} {6} 365.
Examples with subtraction:
225 – 1122 \ frac {2} {5} – 1 \ Frac {1} {2} 252–121
• Convert: 125–32 \ Frac {12} {5} – \ Frac {3} {2} 512–23
• Every 5 and 2 → LCM = 10
• Convert: 2410 = 1510 = 910 \ Frac {24} {10} – \ Frac {15} {10} = \ Frac {9} {10} 1024–1015 = 109.
Simplify the fraction
Always check if the answer can be simplified.
👉 Example:
48 = 12 \ Frac {4} {8} = \ Frac {1 {2} 84 = 21 (divide below and below 4).
👉 Example:
69 = 23 \ Frac {6} {9} = \ Frac {2} {3} 96 = 32 (divide below 3 above and below 3).
Word problems
Let’s practice excerpts from real life!
Example 1 (in addition):
Riya drank 13 \ Frac {1} {3} 31 liter juice and 23 \ Frac {2} {3} 32 liters in the evening.
How much he drank overall?
13+23 = 33 = 1 \ frac {1} {3}+\ Frac {2} {3} = \ Frac {3} {3} = 3} = 131+32 = 33 = 1 liter.
Example 2 (subtraction):
A rope is 78 \ Frac {7} {8} is 87 meters long. If you cut 38 \ Frac {3} {8} 83 meters, how much is there?
78 = 38 = 48 = 12 \ Frac {7} {8} – \ Frac {3} {8} = \ Frac {4} {8} = \ Frac {1 {1 {1 {2} 87–83 = 84 = 21 m.
