This subject includes 3 connected topics that deal with representing relationships using division: ratios, rates and proportions.
A ratio is a comparison of two numbers, represented by a division of their amounts. The ratio between a and b can be represented using a colon as a:b or as a fraction a/b. For example: The number of girls in the class is 22 and the number of boys in the class is 11. The ratio of boys to girls in the class is 11:22, reducing 11:22 gives 1:2. The ratio of girls to boys is 22:11, reducing 22:11 gives 2:1=2.
Equivalent ratios are ratios that express the same relationship between numbers. Two ratios are equivalent if we can reduce or expand one ratio and get the other ratio.
Complementary ratios are ratios that add up to a whole that is 1.
There are 2 types of ratios: a part to part ratio and a part to whole ratio.
A rate is a quantity compared to another related quantity, where the quantities have different units. For example: The speed per hour is the rate measured by the number of miles per a unit of time of 1 hour.
A unit rate is a rate compared to a single unit quantity (the denominator is 1).
To calculate the unit rate, divide the total of one quantity (the numerator) by the number of units of the other quantity (the denominator).
A proportion is an equality between 2 or more equivalent ratios. The proportion between a, b, c and d can be represented using a colon as a:b=c:d or as a fraction a/b=c/d. For example: A carrot cake recipe is composed of 3 cups of flour and 1 cup of sugar, if we put 3 cups of sugar in the bowl, we need to add 9 cups of flour: 3/1=9/3 or 3:1=9:3
We can write proportions in 2 ways: There are same units above the divisor line and below the division line or there are same units at the nominator and the denominator of each ratio.
Solving proportions is done using the cross product method which involves multiplying the numerator of one fraction by the denominator of another fraction and then equaling the multiplications.
Since ratios, rates and proportions are written as fractions, before learning this topic you should learn solving fractions topic.
Continue reading this page for detailed explanations and examples.