By the end of this lesson, you will be able to:
Add fractions with like denominators (Objectives 53-54)
Add fractions with unlike denominators (Objectives 55-56)
Subtract fractions with like and unlike denominators (Objective 57)
Find fractions of collections (Objectives 58-59)
Find the whole when given a part (Objectives 58-59)
Fraction operations appear in Section I, II, and III of the SEA Math paper. These are essential for all fraction work! (SEA Framework Page 21-22)
Start by watching this video to learn how to add fractions with the same denominator. Take notes as you watch! 📝
Adding Fractions with Like Denominators – Mathematics Video Lesson
VIDEO
Did you understand the video? Review the notes below before continuing! ✅
When fractions have the same denominator , adding is easy! Just add the numerators and keep the denominator the same.
Add the numerators (top numbers)Keep the denominator (bottom number) the SAMESimplify if possible
📊 Example 1: Adding Like Denominators
2/7 + 3/7 = ?
Solution:
Add numerators: 2 + 3 = 5Keep denominator: 7 stays the sameAnswer: 5/7Check: 5/7 cannot be simplified further ✓
Answer: 5/7
📊 Example 2: Adding Like Denominators (Simplifying Needed)
3/8 + 5/8 = ?
Solution:
Add numerators: 3 + 5 = 8Keep denominator: 8 stays the sameAnswer: 8/8 = 1 (whole)
Answer: 1 (or 8/8)
Now watch this video to learn how to add fractions with different denominators. Pay attention to finding the LCD! 🎯
Adding Fractions with Unlike Denominators – Mathematics Video Lesson
VIDEO
When fractions have different denominators , you must find a common denominator first!
Find the LCD (Lowest Common Denominator)Convert both fractions to equivalent fractions with the LCDAdd the numerators and keep the LCDSimplify if possible
📊 Example 3: Adding Unlike Denominators
1/4 + 1/3 = ?
Solution:
Find LCD: Multiples of 4: 4, 8, 12… Multiples of 3: 3, 6, 12… LCD = 12Convert: 1/4 = 3/12, 1/3 = 4/12Add: 3/12 + 4/12 = 7/12Check: 7/12 cannot be simplified ✓
Answer: 7/12
📊 Example 4: Adding Unlike Denominators (Simplifying Needed)
1/6 + 1/2 = ?
Solution:
Find LCD: LCD of 6 and 2 = 6Convert: 1/6 = 1/6, 1/2 = 3/6Add: 1/6 + 3/6 = 4/6Simplify: 4/6 = 2/3 (divide both by 2)
Answer: 2/3
Never add the denominators! Only add the numerators. The denominator stays the same after you find the LCD.
Subtracting fractions follows the SAME rules as adding! Just subtract the numerators instead of adding.
📋 Subtracting Like Denominators:
5/8 − 2/8 = ?
Solution:
Subtract numerators: 5 − 2 = 3Keep denominator: 8 stays the sameAnswer: 3/8
Answer: 3/8
📋 Subtracting Unlike Denominators:
3/4 − 1/3 = ?
Solution:
Find LCD: LCD of 4 and 3 = 12Convert: 3/4 = 9/12, 1/3 = 4/12Subtract: 9/12 − 4/12 = 5/12Check: 5/12 cannot be simplified ✓
Answer: 5/12
Fractions aren’t just about shapes – they’re also about groups of objects (collections)!
🔑 Finding a Fraction of a Collection:
Divide the total by the denominator (bottom number)Multiply the answer by the numerator (top number)Answer: This is the fraction of the collection
📊 Example 5: Fraction of a Collection
Find 2/3 of 15 apples
Solution:
Divide by denominator: 15 ÷ 3 = 5Multiply by numerator: 5 × 2 = 10Answer: 10 apples
Answer: 10 apples
🔑 Finding the Whole from a Part:
Divide the part by the numerator (top number)Multiply the answer by the denominator (bottom number)Answer: This is the whole
📊 Example 6: Finding the Whole from a Part
2/5 of a number is 10. What is the number?
Solution:
Divide by numerator: 10 ÷ 2 = 5Multiply by denominator: 5 × 5 = 25Check: 2/5 of 25 = 10 ✓
Answer: 25
Fraction of Collection: Divide by bottom, Multiply by top (DBMT)Finding Whole: Divide by top, Multiply by bottom (DTMB)
Great job finishing Lesson 1.10! You’re mastering fraction operations for the SEA exam! 🎉