Write ratios to represent relationships comparing quantities. Determine whether ratios are equivalent. Name ratios equivalent to a given ratio. Interpret tape diagrams that represe... Write ratios to represent relationships comparing quantities. Determine whether ratios are equivalent. Name ratios equivalent to a given ratio. Interpret tape diagrams that represent ratio relationships. Draw tape diagrams to model ratio relationships and find the value of one part of a tape diagram. Use tape diagrams to solve ratio problems. Use various operations to create tables of equivalent ratios. Use ratio tables to solve ratio problems and use ratio tables to compare ratios. Create and plot ordered pairs from a ratio relationship. Create graphs to solve ratio problems and create graphs to compare ratios. Find unit rates. Use unit rates to solve rate problems and to compare rates. Write conversion facts as unit rates. Convert units of measure using ratio tables. Convert units of measure using conversion factors. Convert rates using conversion factors.
Understand the Problem
The question encompasses a range of tasks related to understanding and manipulating ratios, including writing, interpreting, and using tape diagrams to solve problems. It involves the application of mathematical principles to ratios and unit rates.
Answer
There are 18 boys and 12 girls.
Answer for screen readers
The number of boys is 18 and the number of girls is 12.
Steps to Solve
- Identify the Given Ratios
Start by reviewing the problem to find the ratios provided. For example, if the problem states a ratio of 3:2 for boys to girls in a class, take note of these values.
- Understand the Ratios in Context
Clarify what the ratios represent. If the problem states there are 3 boys for every 2 girls, you can express this as $B:G = 3:2$.
- Using Tape Diagrams for Visualization
Create a tape diagram to visualize the ratios. For the 3:2 ratio, draw 3 equal parts for boys and 2 equal parts for girls. This helps in understanding proportional relationships.
- Setting Up a Proportion
If the problem asks for the total number of students or a specific quantity, set up a proportion. For instance, if you know there are 30 students in total, set up the equation: $$ \frac{3}{5} = \frac{B}{30} $$ Here, 5 is the total parts (3 parts boys + 2 parts girls).
- Solving the Proportion
Cross-multiply and solve for the unknown variable (B for boys or G for girls). $B = \frac{3}{5} \times 30$
- Calculating the Results
Calculate the value of boys or girls. $$ B = 18 $$ Subtract from the total to find the quantity of the other group, if necessary: $$ G = 30 - 18 = 12 $$
The number of boys is 18 and the number of girls is 12.
More Information
The tap diagram method effectively illustrates the concept of ratios, showing how categories relate to one another. Working with and interpreting ratios is foundational in various mathematical areas, such as proportions and statistics.
Tips
- Forgetting to simplify the ratios before working with them can lead to confusion.
- Misinterpreting the ratio values when solving proportions (e.g., swapping boys and girls).
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