Improper Fractions Worksheet | Grade 4-6 Math Resources - Free Printable

It looks like you've uploaded a worksheet titled "Improper Fractions" that includes two main sections:

1. Visual representation of improper fractions using shapes (circles, rectangles)
2. Converting improper fractions to mixed numbers and vice versa

Let’s go through each section and solve the problems step-by-step.

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✔ Section 1: Visual Representation (Left Page)

#### Task:
Write the improper fraction and mixed number represented by each shape.

We’ll analyze each part:

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#### a) Circles: 4 full circles + 3/4 of a circle

- Each circle represents 1 whole.
- There are 4 full circles → 4 wholes
- One circle is divided into 4 parts; 3 are shaded → $ \frac{3}{4} $
- So total = $ 4 + \frac{3}{4} = \frac{19}{4} $

✔ Improper Fraction: $ \frac{19}{4} $
✔ Mixed Number: $ 4\frac{3}{4} $

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#### b) Circles: 5 full circles + 1/4 of a circle

- 5 full circles = 5
- One circle has 1/4 shaded → $ \frac{1}{4} $
- Total = $ 5 + \frac{1}{4} = \frac{21}{4} $

✔ Improper Fraction: $ \frac{21}{4} $
✔ Mixed Number: $ 5\frac{1}{4} $

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#### c) Circles: 6 full circles + 1/2 of a circle

- 6 full circles = 6
- One circle half-shaded → $ \frac{1}{2} $
- Total = $ 6 + \frac{1}{2} = \frac{13}{2} $

✔ Improper Fraction: $ \frac{13}{2} $
✔ Mixed Number: $ 6\frac{1}{2} $

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#### d) Rectangles: 3 full rectangles + 1/10 of a rectangle

- Each rectangle is divided into 10 parts.
- 3 full rectangles = 3
- 1 out of 10 parts shaded in the last rectangle → $ \frac{1}{10} $
- Total = $ 3 + \frac{1}{10} = \frac{31}{10} $

✔ Improper Fraction: $ \frac{31}{10} $
✔ Mixed Number: $ 3\frac{1}{10} $

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#### e) Circles: 3 full circles + 3/8 of a circle

- 3 full circles = 3
- One circle divided into 8 parts; 3 shaded → $ \frac{3}{8} $
- Total = $ 3 + \frac{3}{8} = \frac{27}{8} $

✔ Improper Fraction: $ \frac{27}{8} $
✔ Mixed Number: $ 3\frac{3}{8} $

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#### f) Rectangles: 4 full rectangles + 3/5 of a rectangle

- 4 full rectangles = 4
- One rectangle divided into 5 parts; 3 shaded → $ \frac{3}{5} $
- Total = $ 4 + \frac{3}{5} = \frac{23}{5} $

✔ Improper Fraction: $ \frac{23}{5} $
✔ Mixed Number: $ 4\frac{3}{5} $

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✔ Section 2: Converting Improper Fractions (Right Page)

#### Problem 1: Ring or write down any mixed number equivalent to the improper fraction

This is a grid with improper fractions. You need to convert them to mixed numbers.

Let’s go through some examples:

| Improper Fraction | Mixed Number |
|-------------------|--------------|
| $ \frac{13}{3} $ | $ 4\frac{1}{3} $ (since $ 13 ÷ 3 = 4 R1 $) |
| $ \frac{2}{2} $ | $ 1 $ (or $ 1\frac{0}{2} $) |
| $ \frac{4}{3} $ | $ 1\frac{1}{3} $ |
| $ \frac{9}{1} $ | $ 9 $ |
| $ \frac{4}{2} $ | $ 2 $ |
| $ \frac{2}{1} $ | $ 2 $ |
| $ \frac{14}{3} $ | $ 4\frac{2}{3} $ |
| $ \frac{3}{4} $ | $ \frac{3}{4} $ (already proper) |
| $ \frac{4}{1} $ | $ 4 $ |
| $ \frac{3}{1} $ | $ 3 $ |
| $ \frac{1}{2} $ | $ \frac{1}{2} $ |
| $ \frac{1}{1} $ | $ 1 $ |
| $ \frac{16}{10} $ | $ 1\frac{6}{10} = 1\frac{3}{5} $ |
| $ \frac{1}{4} $ | $ \frac{1}{4} $ |
| $ \frac{4}{5} $ | $ \frac{4}{5} $ |
| $ \frac{3}{5} $ | $ \frac{3}{5} $ |
| $ \frac{1}{10} $ | $ \frac{1}{10} $ |
| $ \frac{8}{10} $ | $ \frac{4}{5} $ |
| $ \frac{20}{2} $ | $ 10 $ |
| $ \frac{3}{2} $ | $ 1\frac{1}{2} $ |
| $ \frac{2}{5} $ | $ \frac{2}{5} $ |
| $ \frac{3}{10} $ | $ \frac{3}{10} $ |
| $ \frac{1}{10} $ | $ \frac{1}{10} $ |
| $ \frac{19}{4} $ | $ 4\frac{3}{4} $ |
| $ \frac{4}{5} $ | $ \frac{4}{5} $ |
| $ \frac{2}{3} $ | $ \frac{2}{3} $ |
| $ \frac{4}{3} $ | $ 1\frac{1}{3} $ |
| $ \frac{3}{1} $ | $ 3 $ |
| $ \frac{1}{1} $ | $ 1 $ |

> Note: For this task, students should ring the correct mixed number from the list (if given), or write it.

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#### Problem 2: Write the following improper fractions as mixed numbers

Now let's convert these:

##### a) $ \frac{22}{3} $

- $ 22 ÷ 3 = 7 $ remainder $ 1 $
- $ \frac{22}{3} = 7\frac{1}{3} $

✔ Answer: $ 7\frac{1}{3} $

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##### b) $ \frac{18}{2} $

- $ 18 ÷ 2 = 9 $
- $ \frac{18}{2} = 9 $

✔ Answer: $ 9 $

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##### c) $ \frac{21}{4} $

- $ 21 ÷ 4 = 5 $ remainder $ 1 $
- $ \frac{21}{4} = 5\frac{1}{4} $

✔ Answer: $ 5\frac{1}{4} $

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##### d) $ \frac{24}{10} $

- Simplify first: $ \frac{24}{10} = \frac{12}{5} $
- $ 12 ÷ 5 = 2 $ remainder $ 2 $
- $ \frac{12}{5} = 2\frac{2}{5} $

✔ Answer: $ 2\frac{2}{5} $

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##### e) $ \frac{22}{10} $

- $ \frac{22}{10} = \frac{11}{5} $
- $ 11 ÷ 5 = 2 $ remainder $ 1 $
- $ \frac{11}{5} = 2\frac{1}{5} $

✔ Answer: $ 2\frac{1}{5} $

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##### f) $ \frac{14}{3} $

- $ 14 ÷ 3 = 4 $ remainder $ 2 $
- $ \frac{14}{3} = 4\frac{2}{3} $

✔ Answer: $ 4\frac{2}{3} $

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##### g) $ \frac{18}{3} $

- $ 18 ÷ 3 = 6 $

✔ Answer: $ 6 $

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##### h) $ \frac{17}{4} $

- $ 17 ÷ 4 = 4 $ remainder $ 1 $
- $ \frac{17}{4} = 4\frac{1}{4} $

✔ Answer: $ 4\frac{1}{4} $

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##### i) $ \frac{22}{5} $

- $ 22 ÷ 5 = 4 $ remainder $ 2 $
- $ \frac{22}{5} = 4\frac{2}{5} $

✔ Answer: $ 4\frac{2}{5} $

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##### j) $ \frac{27}{4} $

- $ 27 ÷ 4 = 6 $ remainder $ 3 $
- $ \frac{27}{4} = 6\frac{3}{4} $

✔ Answer: $ 6\frac{3}{4} $

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##### k) $ \frac{23}{10} $

- $ 23 ÷ 10 = 2 $ remainder $ 3 $
- $ \frac{23}{10} = 2\frac{3}{10} $

✔ Answer: $ 2\frac{3}{10} $

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##### l) $ \frac{19}{10} $

- $ 19 ÷ 10 = 1 $ remainder $ 9 $
- $ \frac{19}{10} = 1\frac{9}{10} $

✔ Answer: $ 1\frac{9}{10} $

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##### m) $ \frac{31}{5} $

- $ 31 ÷ 5 = 6 $ remainder $ 1 $
- $ \frac{31}{5} = 6\frac{1}{5} $

✔ Answer: $ 6\frac{1}{5} $

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##### n) $ \frac{27}{3} $

- $ 27 ÷ 3 = 9 $

✔ Answer: $ 9 $

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##### o) $ \frac{30}{10} $

- $ 30 ÷ 10 = 3 $

✔ Answer: $ 3 $

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🔚 Final Summary

#### Key Concepts Used:
- Improper Fraction: Numerator ≥ Denominator
- Mixed Number: Whole number + proper fraction
- To convert: Divide numerator by denominator → quotient = whole number, remainder = new numerator

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✔ Answers Recap:

#### Section 1: Shapes
| Shape | Improper Fraction | Mixed Number |
|-------|-------------------|--------------|
| a) | $ \frac{19}{4} $ | $ 4\frac{3}{4} $ |
| b) | $ \frac{21}{4} $ | $ 5\frac{1}{4} $ |
| c) | $ \frac{13}{2} $ | $ 6\frac{1}{2} $ |
| d) | $ \frac{31}{10} $ | $ 3\frac{1}{10} $ |
| e) | $ \frac{27}{8} $ | $ 3\frac{3}{8} $ |
| f) | $ \frac{23}{5} $ | $ 4\frac{3}{5} $ |

#### Section 2: Problem 2 – Convert Improper Fractions
| Fraction | Mixed Number |
|---------|---------------|
| a) $ \frac{22}{3} $ | $ 7\frac{1}{3} $ |
| b) $ \frac{18}{2} $ | $ 9 $ |
| c) $ \frac{21}{4} $ | $ 5\frac{1}{4} $ |
| d) $ \frac{24}{10} $ | $ 2\frac{2}{5} $ |
| e) $ \frac{22}{10} $ | $ 2\frac{1}{5} $ |
| f) $ \frac{14}{3} $ | $ 4\frac{2}{3} $ |
| g) $ \frac{18}{3} $ | $ 6 $ |
| h) $ \frac{17}{4} $ | $ 4\frac{1}{4} $ |
| i) $ \frac{22}{5} $ | $ 4\frac{2}{5} $ |
| j) $ \frac{27}{4} $ | $ 6\frac{3}{4} $ |
| k) $ \frac{23}{10} $ | $ 2\frac{3}{10} $ |
| l) $ \frac{19}{10} $ | $ 1\frac{9}{10} $ |
| m) $ \frac{31}{5} $ | $ 6\frac{1}{5} $ |
| n) $ \frac{27}{3} $ | $ 9 $ |
| o) $ \frac{30}{10} $ | $ 3 $ |

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