Ratios Flashcards
What are the 3 Ratio formulas?
1.- Multiplier = Data/Ratio
2.- Data = Multiplier * Ratio
3.- Ratio = Data / Multiplier
What is one unique condition of ratios?
- If you’re given one ratio and a certain number is added or subtracted to the ratio, the new ratio CANNOT be determined unless the original amount (total) is given.
- You CAN multiply a ratio, even if the total amount is not given.
Is there a way to know a ratio when adding or subtracting values?
Yes, you can figure out the multiplier if the total or another ratio is given. Just be careful, cause you will probably need more information.
If you’re doing a ratio problem and their asking you for the lowest (or smallest) possible number of a certain or group of ratios, what do you have to do?
You need to find the LCD of the ratio that is the same (or the common ratio) between two sets or ratios.
What is the only way of uniting two ratios?
Having a common term in different ratios allows you to:
- Combine the ratios into one, giving a complete picture of the system.
- Ensure consistency and direct comparability between ratios.
- Simplify calculations involving proportions.
In essence, a common term acts as an anchor, making it easier to analyze and work with the system as a whole.
What is the advantage of having ratios as fractions?
All fractions of the ratio have to equal one.
Example: There are three ratios, but they are only giving you two ratios in the form of fraction.
3/7
5/14
Then you know the last ratio will equal 3/14
How do you multiply a decimal by 100?
Simple, you just the decimal place to the right, depending of the number of zero, in the case of 100 its two zero
How do you divide a decimal by 100
When dividing a decimal number by 100, you shift the decimal point two places to the left. This is the opposite of what you do when multiplying by 100.
Halving of a part of a ratio is ….?
Doubling of the other. Think Shrinkflation
When doubling or halving ratios different parts of the same ratio, how do we unite them?
We look for which part of the new ratios could be made the same. Making the new ratio the same.
Example:
Gold : Silver : Copper
5 : 8 : 12
We are going to create a new alloy:
Double Gold to Silver
10 : 8 : —
Halving Gold to Copper
5 : — : 24
How if we have 8 kg of Silver, how much Copper for the new Alloy do we need?
What do we have in common in the new recipe? Gold, lets make it the same so both receips are balanced
2(5:—:24) = 10: — :24
Doubling the Gold to Copper receipe makes the gold amount the same for both receiped, making the new recipe balances.
10:8:24
We will need 24 kilos of copper for every 8 kilos of silver.
There is one way in which we can add or subtract to a ratio, but under what condition? And, if the conditions are met what formulas do we use?
If you have an original ratio, and then we add or subtract to that ratio and we get either and new ratio o total, we can play ball.
The formula for when a new ratio is added:
(Ratio 1) * X +/- whatever is the amount
divided
(Ratio 2) * X +/- whatever is the amount
All of that equalling the new ratio
How do you know when you reach the base in ratio problems?
When there aren’t any more factors in common that you can simplify, you have reached the base, which has a multiplier of one.
Example:
Suppose you have a ratio of red balls to blue balls as 8:12.
To find the simplest or base form of this ratio, we’ll look for common factors of both numbers and then simplify:
Both 8 and 12 are divisible by 4.
Dividing both numbers by 4, we get:
8 ÷ 4 = 2
12 ÷ 4 = 3
So, the simplified or base ratio of red balls to blue balls is 2:3.
In this base form, the ratio has a multiplier of one, meaning that for every 2 red balls, there are 3 blue balls. This is the simplest representation of the original ratio, and it cannot be simplified any further since 2 and 3 do not have any common factors other than 1.
