Basic 4 · Mathematics · Fractions
Improper Fractions and Mixed Numbers
In this topic you will recognise fractions greater than one and change between improper fractions and mixed numbers.
By the end of these notes you should be able to:
- Recognise improper fractions
- Change improper fractions to mixed numbers
- Change mixed numbers to improper fractions
What you already know
- Equivalent 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
- B4.1.3.1.3 – Recognise fractions that are greater than one (improper fractions) draw and label such fractions with their symbols
Introduction
Mother cut 2 loaves into quarters. The children ate 5 quarters. That is 5/4 of a loaf, more than one whole loaf!
1. Kinds of Fractions
| Type | Meaning | Example |
|---|---|---|
| proper fraction | numerator smaller than denominator | ¾ |
| improper fraction | numerator equal to or bigger than denominator | 5/4 |
| mixed number | a whole number and a proper fraction | 1¼ |
2. Improper to Mixed
Example
Change 11/4 to a mixed number.
- Divide: 11 ÷ 4 = 2 remainder 3.
- 2 wholes and 3 quarters.
Answer: 11/4 = 2¾
3. Mixed to Improper
Example
Change 3⅖ to an improper fraction.
- Multiply the whole number by the denominator: 3 × 5 = 15.
- Add the numerator: 15 + 2 = 17.
- Keep the denominator: 5.
Answer: 3⅖ = 17/5
Tip: An improper fraction equal to a whole number has no remainder: 8/4 = 2.
New words
- proper fraction
- A fraction less than one.
- improper fraction
- A fraction equal to or greater than one.
- mixed number
- A whole number and a fraction together.
- whole
- One complete thing.
- remainder
- What is left after dividing.
- convert
- To change from one form to another.
Summary
- An improper fraction has a numerator equal to or bigger than its denominator.
- Divide to change an improper fraction into a mixed number.
- Multiply and add to change a mixed number into an improper fraction.
- 11/4 = 2¾ and 3⅖ = 17/5.
Class activity: Fraction Pieces
- Use fraction strips cut into thirds.
- Make 7/3 with the pieces.
- Group them into wholes and write the mixed number.
You need: Fraction strips cut from old cartons, Bottle tops, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. Which is an improper fraction?
- A. 7/5
- B. 2/5
- C. 1/5
- D. 4/5
Show answer
Answer: 7/57 is bigger than 5.2. 9/2 as a mixed number is…
- A. 4½
- B. 2½
- C. 9½
- D. 4¼
Show answer
Answer: 4½9 ÷ 2 = 4 remainder 1.3. 2⅓ as an improper fraction is…
- A. 7/3
- B. 5/3
- C. 6/3
- D. 2/3
Show answer
Answer: 7/32 × 3 + 1 = 7.4. 1¾ is a mixed number.
- A. True
- B. False
Show answer
Answer: TrueA whole and a fraction.5. 12/4 = 3
- A. True
- B. False
Show answer
Answer: True12 ÷ 4 = 3 exactly.6. 6/6 = ______ whole
Show answer
Answer: 1Six sixths make one whole.7. Change 13/5 to a mixed number.
Show answer
Answer: 2⅗13 ÷ 5 = 2 remainder 3.8. Kofi ate 1½ oranges and Ama ate 5/2 oranges. Who ate more? Show working.
Show answer
Answer: Ama: 5/2 = 2½, which is more than 1½.Convert to the same form.
Homework
- Draw pictures to show 5/3 and 9/4 as mixed numbers.