Instructions
Follow these steps to complete the worksheet. This activity is designed to help you master adding proper fractions with different denominators using a practical, real-world design perspective.
- Find the Least Common Denominator (LCD): Identify the smallest multiple that the denominators share.
- Convert the Fractions: Rewrite each fraction so they both share the LCD.
- Add the Numerators: Add the top numbers together. Keep the denominator the same.
- Simplify your Answer: Reduce the fraction to its simplest form, if possible.
Scaffolding Example
Before starting, review this step-by-step example:
Problem: Add $\frac{1}{4} + \frac{3}{8}$
- Step 1: The LCD for 4 and 8 is 8.
- Step 2: Convert $\frac{1}{4}$ to have a denominator of 8: $\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$. (The second fraction, $\frac{3}{8}$, already has a denominator of 8).
- Step 3: Add the numerators: $\frac{2}{8} + \frac{3}{8} = rac{5}{8}$.
- Step 4: $\frac{5}{8}$ cannot be simplified further. This is your final answer!
Section 1: The Dimension Table
You are working as an apprentice at an architectural design studio. Complete the table below to determine the combined thicknesses of different materials for a building model.
| Material A Thickness | Material B Thickness | Least Common Denominator (LCD) | Converted Addition Expression | Simplified Sum |
|---|---|---|---|---|
| Example: $\frac{1}{3}$ in | $\frac{1}{6}$ in | 6 | $\frac{2}{6} + \frac{1}{6}$ | $\frac{3}{6} = \frac{1}{2}$ in |
| 1. $\frac{1}{4}$ in | $\frac{3}{10}$ in | |||
| 2. $\frac{2}{5}$ in | $\frac{1}{3}$ in | |||
| 3. $\frac{3}{8}$ in | $\frac{5}{12}$ in | |||
| 4. $\frac{1}{6}$ in | $\frac{3}{8}$ in | |||
| 5. $\frac{2}{7}$ in | $\frac{1}{3}$ in |
Section 2: Real-World Design Scenarios
Solve the following practical problems. Show your work clearly in the spaces provided.
6. The Custom Skateboard Ramp
An engineer is layering plywood sheets to make a durable skateboard ramp. The base sheet is $\frac{3}{8}$ inches thick, and the top protective sheet is $\frac{5}{16}$ inches thick. What is the total thickness of the plywood layout?
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Show your LCD and conversion steps:
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Final simplified answer:
7. The Paint Mixture
A graphic designer is mixing custom acrylic paint colors for a poster. They mix $\frac{1}{3}$ cup of cyan paint with $\frac{2}{5}$ cup of magenta paint. What is the total volume of the custom mixture in cups?
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Show your LCD and conversion steps:
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Final simplified answer:
8. Magazine Layout Borders
In a magazine page design, the left margin takes up $\frac{1}{12}$ of the page width, and the right margin takes up $\frac{3}{16}$ of the page width. What combined fraction of the page width is dedicated solely to these two margins?
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Show your LCD and conversion steps:
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Final simplified answer:
Section 3: The Master Designer Challenge
Ready to test your skills? Try adding three proper fractions together by finding a common denominator for all three numbers.
9. Challenge Problem:
A designer is layering three ultra-thin sheets of colored acrylic film for a lighting installation. The sheet thicknesses are $\frac{1}{4}$ mm, $\frac{1}{6}$ mm, and $\frac{2}{5}$ mm. What is the total combined thickness of the film layer?
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Show your work:
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Final simplified answer:
Answer Key
Section 1: The Dimension Table
- LCD: 20 | Converted: $\frac{5}{20} + \frac{6}{20}$ | Sum: $\frac{11}{20}$ in
- LCD: 15 | Converted: $\frac{6}{15} + \frac{5}{15}$ | Sum: $\frac{11}{15}$ in
- LCD: 24 | Converted: $\frac{9}{24} + \frac{10}{24}$ | Sum: $\frac{19}{24}$ in
- LCD: 24 | Converted: $\frac{4}{24} + \frac{9}{24}$ | Sum: $\frac{13}{24}$ in
- LCD: 21 | Converted: $\frac{6}{21} + \frac{7}{21}$ | Sum: $\frac{13}{21}$ in
Section 2: Real-World Design Scenarios
- Skateboard Ramp:
- LCD of 8 and 16 is 16.
- $\frac{3}{8} \rightarrow \frac{6}{16}$
- $\frac{6}{16} + \frac{5}{16} = \frac{11}{16}$ inches.
- Paint Mixture:
- LCD of 3 and 5 is 15.
- $\frac{1}{3} \rightarrow \frac{5}{15}$, $\frac{2}{5} \rightarrow \frac{6}{15}$
- $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$ cups.
- Magazine Layout Borders:
- LCD of 12 and 16 is 48.
- $\frac{1}{12} \rightarrow \frac{4}{48}$, $\frac{3}{16} \rightarrow \frac{9}{48}$
- $\frac{4}{48} + \frac{9}{48} = \frac{13}{48}$ of the page width.
Section 3: The Master Designer Challenge
- Challenge Problem:
- LCD of 4, 6, and 5 is 60.
- Conversions: $\frac{1}{4} \rightarrow \frac{15}{60}$, $\frac{1}{6} \rightarrow \frac{10}{60}$, $\frac{2}{5} \rightarrow \frac{24}{60}$
- Sum: $\frac{15}{60} + \frac{10}{60} + \frac{24}{60} = \frac{49}{60}$ mm.