Use a bar diagram to make equivalent ratios.
Understand the Problem
The question is asking to represent equivalent ratios using a bar diagram. This involves visually demonstrating how different ratios can represent the same proportion using bars to illustrate the relationship between the quantities.
Answer
The answer is a visual bar diagram showing equivalent ratios using bars of equal length, divided and shaded according to the ratios.
Answer for screen readers
The answer is a bar diagram showing two bars of equal length. The first bar is divided according to the initial ratio and shaded accordingly. The second bar is divided according to an equivalent ratio (obtained by multiplying each part of the initial ratio by the same number), and shaded accordingly. The proportion of shaded to unshaded should visually be the same in both bars.
Steps to Solve
- Draw a bar for the first ratio
Divide the bar into sections according to the ratio given. For example, if the ratio is 2:3, divide the bar into 5 equal sections (2 + 3 = 5).
- Shade the bar according to the first part of the ratio
Shade the number of sections corresponding to the first number in the ratio. In the 2:3 example, shade 2 sections.
- Leave the remaining sections unshaded
The unshaded portions represents the second part of the ratio. In the 2:3 example, 3 sections will remain unshaded.
- Draw another bar of the same length
This bar will represent the equivalent ratio.
- Divide and shade the second bar to show an equivalent ratio
Divide the second bar into a different number of sections, but ensure the proportion of shaded to unshaded remains the same as the first bar.
For example, to create an equivalent ratio for 2:3, we can multiply both numbers by 2 to get 4:6. Hence, divide the second bar into 10 sections (4+6 = 10), and shade 4 sections.
- Verify the equivalence
Visually check that the proportion of shaded area to the total length is the same for both bars. This confirms that the ratios are equivalent.
The answer is a bar diagram showing two bars of equal length. The first bar is divided according to the initial ratio and shaded accordingly. The second bar is divided according to an equivalent ratio (obtained by multiplying each part of the initial ratio by the same number), and shaded accordingly. The proportion of shaded to unshaded should visually be the same in both bars.
More Information
Bar diagrams are a great way to visually represent ratios and proportions, especially for learners who are more visual. They provide an intuitive understanding of equivalent ratios by showing that even when the numbers change, the relative amounts stay the same.
Tips
A common mistake would be to draw the second bar with a different total length than the first bar. The bars must have the same total length for a correct visual comparison of equivalent ratios. Another error is incorrectly calculating the equivalent ratio, which would lead to incorrect shading on the second bar, hence a false demonstration.
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