Instructions
- Read the definitions and examples provided in each section carefully.
- Complete all tables and fill-in-the-blank questions using clear, numerical answers.
- Show your work in the Real-World Application section.
- Aim for accuracy and neatness, as this sheet will help you master the building blocks of fractions!
Section 1: Fraction Fundamentals
A fraction represents a part of a whole. Remember the key vocabulary:
- Numerator: The top number (how many parts you have).
- Denominator: The bottom number (how many parts make up the whole).
1. Identify the Parts
For the fraction $\frac{4}{9}$, identify the following parts:
- Numerator: _____
- Denominator: _____
2. Representing Fractions
Complete the table below. If the visual is missing, write the fraction. If the fraction is given, draw a simple shape (circle or rectangle) and shade the correct amount.
| Fraction | Shaded Visual Representation (Example) |
|---|---|
| 3/8 | Draw 8 equal boxes and shade 3 |
| 1/4 | |
| Draw a circle divided into 6 pieces and shade 5 | |
| 5/10 | |
| Draw a rectangle divided into 3 pieces and shade 1 |
Section 2: Equivalent Fractions
Equivalent fractions name the same amount, even though they look different. To find equivalent fractions, multiply or divide the numerator and the denominator by the same non-zero number.
3. Complete the Equivalence Chart
Find the missing numerator, denominator, or the operation required to make the fractions equal.
| Start Fraction | Operation (What did you multiply/divide by?) | Equivalent Fraction |
|---|---|---|
| 1/3 | Multiply by 4/4 | 4/12 |
| 2/5 | Multiply by 2/2 | |
| 10/16 | Divide by 2/2 | |
| 3/4 | 9/12 | |
| 1/8 | 4/32 | |
| 25/30 | 5/6 |
4. Comparing Fractions
Use the symbols >, <, or = to correctly compare the pairs of fractions.
- 1/2 ___ 3/8
- 4/5 ___ 8/10
- 7/10 ___ 7/9
Section 3: Conversions (Mixed Numbers and Improper Fractions)
An Improper Fraction has a numerator larger than the denominator (e.g., 5/3). A Mixed Number is a whole number and a fraction (e.g., $1\frac{2}{3}$).
5. Convert Improper Fractions to Mixed Numbers
Example: 7/3 $\rightarrow$ Divide 7 by 3. You get 2 with a remainder of 1. Answer: $2\frac{1}{3}$
- 9/4 = ___
- 11/5 = ___
- 15/6 = ___
6. Convert Mixed Numbers to Improper Fractions
Example: $1\frac{2}{3}$ $\rightarrow$ (1 3) + 2 = 5. Answer: 5/3*
- $3\frac{1}{2}$ = ___
- $2\frac{3}{10}$ = ___
- $4\frac{1}{5}$ = ___
Section 4: Real-World Application
Solve the following word problems. Show your work.
7. The Pizza Party
Liam and his friends ordered a large pizza cut into 8 slices. Liam ate 3 slices, and his friend Maya ate 2 slices.
a) What fraction of the pizza did Liam eat?
____________________________________b) What fraction of the pizza did they eat in total? (Show addition or explanation.)
Work/Explanation:
____________________________________
Total Fraction Eaten: _________________c) What fraction of the pizza was left over?
Fraction Left Over: ___________________8. The Race Track
Sarah runs laps around a track. She has completed 5/6 of her workout goal. Her brother, Alex, has only completed 1/2 of his workout goal.
Who has completed a greater fraction of their workout? (Hint: Convert 1/2 to sixths to compare.)
Work/Explanation:
____________________________________
Answer: ___________________Challenge Zone (Optional)
9. Sorting Fractions
Order the following four fractions from least to greatest:
$$\frac{1}{2}, \quad \frac{1}{10}, \quad \frac{3}{5}, \quad \frac{7}{10}$$
(Hint: Convert all fractions to tenths to make them easier to compare.)
Order:
Answer Key
Section 1: Fraction Fundamentals
1. Identify the Parts
- Numerator: 4
- Denominator: 9
| 2. Representing Fractions | Fraction | Shaded Visual Representation |
|---|---|---|
| 1/4 | Draw 4 equal boxes and shade 1 | |
| 5/6 | Draw a circle divided into 6 pieces and shade 5 | |
| 5/10 | Draw 10 equal boxes and shade 5 (or 1/2 shaded) | |
| 1/3 | Draw a rectangle divided into 3 pieces and shade 1 |
Section 2: Equivalent Fractions
| 3. Complete the Equivalence Chart | Start Fraction | Operation (What did you multiply/divide by?) | Equivalent Fraction |
|---|---|---|---|
| 2/5 | Multiply by 2/2 | 4/10 | |
| 10/16 | Divide by 2/2 | 5/8 | |
| 3/4 | Multiply by 3/3 | 9/12 | |
| 1/8 | Multiply by 4/4 | 4/32 | |
| 25/30 | Divide by 5/5 | 5/6 |
4. Comparing Fractions
- 1/2 > 3/8 (because 1/2 = 4/8)
- 4/5 = 8/10 (because 4/5 = 8/10)
- 7/10 < 7/9 (When numerators are the same, the fraction with the smaller denominator is larger)
Section 3: Conversions
5. Convert Improper Fractions to Mixed Numbers
- 9/4 = $2\frac{1}{4}$
- 11/5 = $2\frac{1}{5}$
- 15/6 = $2\frac{3}{6}$ (or $2\frac{1}{2}$)
6. Convert Mixed Numbers to Improper Fractions
- $3\frac{1}{2}$ = 7/2
- $2\frac{3}{10}$ = 23/10
- $4\frac{1}{5}$ = 21/5
Section 4: Real-World Application
7. The Pizza Party
a) What fraction of the pizza did Liam eat? 3/8
b) What fraction of the pizza did they eat in total? (3/8 + 2/8 = 5/8). Total Fraction Eaten: 5/8
c) What fraction of the pizza was left over? (8/8 - 5/8 = 3/8). Fraction Left Over: 3/8
8. The Race Track
Alex (1/2) is equal to 3/6. Sarah completed 5/6.
Answer: Sarah (5/6 > 3/6)
Challenge Zone (Optional)
9. Sorting Fractions
Conversion to tenths: 1/2 = 5/10 1/10 = 1/10 3/5 = 6/10 7/10 = 7/10
Order: 1/10, 1/2, 3/5, 7/10