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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today we're learning about ratios! Can anyone tell me what a ratio means?
Is it like comparing two numbers?
Exactly! A ratio compares two quantities. For instance, if we have 20 apples and 5 oranges, we can say the ratio of oranges to apples is 5:20, which simplifies to 1:4. Who can express this as a fraction?
That would be \frac{5}{20} = \frac{1}{4}!
Great job! Remember, this means for every 4 apples, there is 1 orange.
Now, let's connect ratios to percentages. If I have 5 oranges in a basket of 25 fruits, how do we find the percentage of oranges?
We can take 5 divided by 25 and multiply it by 100!
That's correct! So, we have: . What about apples?
The apples would be 100% - 20%, which is 80%!
Right! Always remember that the total percentage must add up to 100.
Imagine we're planning a picnic, and 60% of the total students are girls. If there are 18 girls, how do we figure out the total number of students?
We can set up an equation! If 60% of students are 18, then .
Exactly! Now, how many boys are there?
30 total students minus 18 girls means there are 12 boys.
Great work! The ratio of girls to boys is 18:12 or simplified to 3:2.
To find the percentage, take part of the whole, then multiply by 100 – that’s your goal!
Imagine a fruit basket filled with fruits. Counting apples and oranges teaches us how to compare using ratios and percentages.
For Ratios: Remember R for Relation and P for Percentage, you calculate based on total counts.
RAP: Ratios And Percentages, remember to RAP your calculations with care!
Term
What is a ratio?
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Term
How do you convert a ratio to a percentage?
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A comparison of two quantities indicating how many times one value contains the other.
A proportion or fraction out of 100, representing a part of a whole.
An amount or number of a particular item or substance.
A technique used to find the value of one unit based on the known value of multiple units.
This section focuses on understanding ratios and percentages through comparisons of quantities.
In this section, students learn how to express the relationship between two quantities using ratios and percentages. Examples highlight the practical application of these concepts in real-life scenarios, emphasizing how to convert between ratios and percentages and solve related problems.
In Section 7.1, we explore the fundamental concepts of ratios and percentages as tools for comparing quantities. A ratio is defined as a relationship between two numbers that indicates how many times the first number contains the second. For example, if you have 20 apples and 5 oranges, the ratios of oranges to apples is given as 5:20, which can be simplified to 1:4. This relationship can also be represented as a fraction:
Conversions from ratios to percentages help to visualize relationships better. For instance, in a basket containing only apples and oranges, if 5 out of 25 fruits are oranges, then:
Conversely, the percentage of apples will be 100% - 20% = 80%. The concept is practical, illustrated with examples including calculating the ratio of girls to boys in a class and determining transport costs for an upcoming school picnic. Exercises reinforce these ideas, inviting students to convert ratios to percentages and explore various contextual problems. By understanding these concepts, students gain essential skills for mathematical and everyday problem solving.