What's the ratio?
In mathematics, a ratio is the comparison of two or more numbers, indicating their relative size. The ratio compares two quantities by division, the dividend or dividend is called the front, and the divisor or dividend is called the back.
Example: You investigated a group of 20 people and found that 13 of them prefer cake to ice cream, and 7 people prefer ice cream to cake. The scale of this data set is 13:7, where 13 is the front part and 7 is the back part.
The ratio can be formatted as a comparison between parts or between parts and the whole. Part-to-part comparison focuses on two separate quantities within the ratio of two or more figures, such as the number of dogs and the number of cats in the pet type poll of the animal clinic. Part of the comparison of the whole measures a quantity and a total quantity, such as the number of dogs and the total number of pets in the clinic. Interest rates like this are much more common than you think.
Proportion in daily life
Ratios often appear in daily life and help simplify many of our interactions by looking at numbers. Ratios enable us to measure and express quantities by making them easier to understand.
Examples of proportion in life:
This car travels at a speed of 60 miles per hour, which means 1 hour 60 miles.
You have a one in 28 million chance of winning the lottery. Under all possible circumstances, only 1 out of 28,000,000 won the lottery.
Each student has enough biscuits to eat two, or two biscuits for every 78 students.
The ratio of children to adults is 3: 1, that is, the number of children is three times that of adults.
How to write a ratio
There are several different ways to express the ratio. One of the most common methods is to write a ratio with a colon as a comparison between this and that, such as the example of children and adults above. Because the ratio is a simple division problem, it can also be written as a fraction. Some people like to express ratios only in words, such as cookies.
In the context of mathematics, colon and fraction formats are the first choice. When comparing more than two quantities, please choose the colon format. For example, if the mixture you prepare needs 1 part oil, 1 part vinegar and1part water, you can express the ratio of oil, vinegar and water as1:10. When deciding how best to write your ratio, consider the background of comparison.
Simplified ratio
No matter how the ratio is written, it is important to reduce it to as small an integer as possible, just like any fraction. This can be achieved by finding the greatest common factor between numbers and dividing them accordingly. For example, by comparing the ratios of 12 and 16, you will find that both 12 and 16 can be divisible by 4. This simplifies your ratio to 3 to 4, or the quotient of 12 and 16 divided by 4. Your ratio can now be written as:
3:4
3/4
3 to 4
0.75 (sometimes decimals are allowed, but not commonly used)
Practice calculating the ratio of two quantities.
Practice identifying opportunities to express ratios in real life by finding the numbers you want to compare. Then, you can try to calculate these ratios and reduce them to the smallest integer. Here are a few examples of practicing calculating the real ratio.
There are 6 apples and 8 fruits in a bowl.
What is the proportion of apples in the total fruit? (Answer: 6:8, simplified to 3:4)
If two pieces of fruit that are not apples are oranges, what is the ratio of apples to oranges? (Answer: 6:2, simplified to 3: 1)
The ranch doctor is a country vet. He only treats two kinds of animals-cows and horses. Last week, she treated 12 cows and 16 horses.
How much does she treat cows and horses? (Answer: 12: 16, simplified to 3:4. For every 3 cows treated, 4 horses treated)
What is the proportion of cows in the total number of animals she treats? (Answer: 12+ 16 = 28, the total number of animals treated. The ratio of cows to the total number is 12:28, which is simplified to 3:7. For every 7 animals treated, 3 of them are cows)
Practice calculating the ratio of two or more quantities.
Use the following demographic information about military bands to complete the following exercises by comparing the ratios of two or more numbers.
gender
120 boys
180 girls
Instrument type
160 woodwind instrument
84 percussion
56 brass
class
127 freshmen
63 sophomores
55 teenagers
55 elderly people
1. What is the ratio of boys to girls? (Answer: 2:3)
2. What is the proportion of freshmen in the total number of bands? (Answer: 127:300)
3. What is the ratio of percussion instruments to woodwind instruments and brass instruments? (Answer: 84: 160:56, simplified as 2 1:40: 14)
4. What is the proportion of freshmen, sophomores and sophomores? (Answer: 127:55:63. Note: 127 is a prime number and cannot be scaled down by this ratio)
5. If 25 students leave the woodwind group and join the percussion group, what is the ratio of woodwind musicians to percussion group?
(Answer: 160 woodwind–25 woodwind = 135 woodwind;
84 percussion players +25 percussion players = 109 percussion players. The ratio of woodwind players to percussion players is 109: 135)