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Robbins Chandler
08/23/2024 · Middle School

\( 40 \% \) of \( 70=70 \% \) of 40 How can 9 prove it by diagran

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To prove that \( 40\% \) of \( 70 \) is equal to \( 70\% \) of \( 40 \) using a diagram, we can use a simple bar diagram to visually represent the percentages. ### Step 1: Calculate the Values First, let's calculate the values: 1. **Calculate \( 40\% \) of \( 70 \)**: \[ 40\% \text{ of } 70 = \frac{40}{100} \times 70 = 28 \] 2. **Calculate \( 70\% \) of \( 40 \)**: \[ 70\% \text{ of } 40 = \frac{70}{100} \times 40 = 28 \] Both calculations yield \( 28 \), confirming that \( 40\% \) of \( 70 \) is indeed equal to \( 70\% \) of \( 40 \). ### Step 2: Create a Bar Diagram Now, let's create a bar diagram to visualize this: 1. **Draw two bars**: One for \( 70 \) and one for \( 40 \). 2. **Label the bars**: - The first bar (for \( 70 \)) should be divided into \( 100 \) equal parts, where \( 40\% \) of it (which is \( 28 \)) is highlighted. - The second bar (for \( 40 \)) should also be divided into \( 100 \) equal parts, where \( 70\% \) of it (which is also \( 28 \)) is highlighted. ### Example Diagram ``` 70 |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| 0 10 20 30 40 50 60 70 |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| |--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------| 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Quick Answer

To prove \( 40\% \) of \( 70 \) equals \( 70\% \) of \( 40 \), calculate both percentages, which are both \( 28 \). Then, use a bar diagram to visually represent these percentages, dividing a bar for \( 70 \) into \( 40\% \) and a bar for \( 40 \) into \( 70\% \), both resulting in \( 28 \) units.
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