Basic 5 · Mathematics · Fractions
Adding and Subtracting Mixed Numbers
In this topic you will add and subtract fractions greater than one, including mixed numbers and improper fractions.
By the end of these notes you should be able to:
- Convert between mixed numbers and improper fractions
- Add mixed numbers
- Subtract mixed numbers, including with renaming
What you already know
- Adding and subtracting fractions
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Fractions
- Indicator
- B5.1.3.1.3 – Use the concept of equivalent fractions for addition and subtraction of fractions greater than one
Introduction
A carpenter has a plank 3¼ metres long. He cuts off 1⅔ metres. How much is left? We must subtract mixed numbers.
1. Converting
| Mixed number | Improper fraction |
|---|---|
| 2½ | 5/2 |
| 1¾ | 7/4 |
| 3⅖ | 17/5 |
Mixed to improper: multiply the whole number by the denominator and add the numerator.
Improper to mixed: divide the numerator by the denominator; the remainder is the new numerator.
2. Adding Mixed Numbers
Example 1
2½ + 1⅓ = ?
- Add the wholes: 2 + 1 = 3
- Add the fractions: ½ + ⅓ = 3/6 + 2/6 = 5/6
Answer: 3⅚
Example 2
1¾ + 2⅝ = ?
- Wholes: 1 + 2 = 3
- Fractions: ¾ + ⅝ = 6/8 + 5/8 = 11/8 = 1⅜
- 3 + 1⅜
Answer: 4⅜
3. Subtracting Mixed Numbers
Example 3
3¼ − 1⅔ = ? (the carpenter's plank)
- Change to improper fractions: 13/4 − 5/3
- LCD = 12: 39/12 − 20/12
- 39/12 − 20/12 = 19/12
Answer: 1 7/12 metres are left.
Tip: Changing to improper fractions avoids renaming problems in subtraction.
4. Subtracting by Renaming
Another way to subtract mixed numbers is to rename one whole as a fraction. In 3¼ − 1⅔, first write both fractions as twelfths: 3 3/12 − 1 8/12. We cannot take 8/12 from 3/12, so we take one whole from the 3 and change it to 12/12. Now 3 3/12 becomes 2 15/12. Then 2 15/12 − 1 8/12 = 1 7/12, the same answer as before. Use whichever method you find clearer, and check that your answer is smaller than the number you started with.
New words
- mixed number
- A whole number and a fraction together.
- improper fraction
- A fraction greater than or equal to one.
- convert
- To change from one form to another.
- rename
- To change a whole into fractional parts.
- LCD
- Lowest common denominator.
- remainder
- What is left after dividing.
Summary
- Convert mixed numbers to improper fractions when needed.
- Add wholes and fractions separately, then combine.
- For subtraction, improper fractions make the working easier.
- Always use a common denominator.
Class activity: Measure and Calculate
- Use string lengths marked in halves and quarters of a metre.
- Add and subtract two lengths.
- Check your calculation by measuring.
You need: Fraction strips cut from old cartons, Bottle tops, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. 2¾ as an improper fraction is…
- A. 11/4
- B. 9/4
- C. 8/4
- D. 6/4
Show answer
Answer: 11/42 × 4 + 3 = 11.2. 1½ + 2½ = ?
- A. 4
- B. 3
- C. 3½
- D. 4½
Show answer
Answer: 41 + 2 = 3 and ½ + ½ = 1.3. 4⅓ − 2⅙ = ?
- A. 2⅙
- B. 2⅓
- C. 2½
- D. 1⅙
Show answer
Answer: 2⅙4 − 2 = 2; 2/6 − 1/6 = 1/6.4. 7/2 = 3½
- A. True
- B. False
Show answer
Answer: True7 ÷ 2 = 3 remainder 1.5. 2⅓ + 1⅓ = 3⅔
- A. True
- B. False
Show answer
Answer: True3 wholes and 2/3.6. 9/4 as a mixed number = ______
Show answer
Answer: 2¼9 ÷ 4 = 2 remainder 1.7. Work out 3⅖ + 1½.
Show answer
Answer: 4 9/104/10 + 5/10 = 9/10.8. Esi had 5 kg of rice. She used 1¾ kg on Monday and 2⅓ kg on Tuesday. How much is left?
Show answer
Answer: 11/12 kg1¾ + 2⅓ = 4 1/12; 5 − 4 1/12 = 11/12.
Homework
- Solve 2⅝ + 3¾ and 6½ − 2⅘. Show your working.