What is the ratio of green circles to black circles if 2/9 of the circles are black?
Understand the Problem
The question is asking for the ratio of green circles to black circles, given that 2/9 of the circles are black. To solve this, we need to determine the proportion of green circles based on the total number of circles.
Answer
The ratio of green circles to black circles is \( 7:2 \).
Answer for screen readers
The ratio of green circles to black circles is ( 7:2 ).
Steps to Solve
- Identify the fraction of black circles
Given that ( \frac{2}{9} ) of the circles are black, we can denote the total number of circles as ( T ) and the number of black circles as ( B ): $$ B = \frac{2}{9} T $$
- Calculate the number of green circles
Since the remaining circles are green, we have: $$ G = T - B $$ Substituting for ( B ): $$ G = T - \frac{2}{9} T $$ To combine the terms, express ( T ) as ( \frac{9}{9} T ): $$ G = \frac{9}{9} T - \frac{2}{9} T = \frac{7}{9} T $$
- Determine the ratio of green circles to black circles
The ratio of green circles ( G ) to black circles ( B ) is given by: $$ \text{Ratio} = \frac{G}{B} $$ Substituting in the values we found: $$ \text{Ratio} = \frac{\frac{7}{9} T}{\frac{2}{9} T} $$ The ( T ) and ( \frac{9}{9} ) terms cancel out: $$ \text{Ratio} = \frac{7}{2} $$
- Express the final ratio
Thus, the ratio of green circles to black circles simplifies to: $$ \text{Ratio} = 7:2 $$
The ratio of green circles to black circles is ( 7:2 ).
More Information
This ratio means that for every 7 green circles, there are 2 black circles. It's a useful way to understand the composition of the circles based on the given fractions.
Tips
- Confusing the fraction of black circles with the total number of circles. Ensure to distinguish between parts and the whole.
- Not simplifying the ratio properly. Always reduce fraction forms to their simplest terms.
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