A comparison is a mathematical expression that represents the relationship between two numbers, indicating the number of times one value contains or is contained within another value. One example of comparison is the comparison of apples to oranges in a fruit basket. Knowing how to make comparisons can help us understand various concepts, such as how many ingredients to add in a recipe if we want to double the portion size, or how many snacks need to be served to a certain number of guests. To find out how to make a comparison, follow these steps.
Step
Method 1 of 2: Making a Comparison
Step 1. Use symbols to represent comparisons
To indicate that we are using a comparison, use a divide (/), colon (:), or for. For example, if you want to say, "For every five boys at the party, there are three girls," you can use one of the two symbols to indicate this. Like this:
- 5 boys / 3 girls
- 5 boys: 3 girls
- 5 boys to 3 girls
Step 2. Write the quantity of the first object to be compared to the left of the symbol
Write the quantity of the first object before the symbol. You will also need to state the unit, be it male or female, chicken or goat, kilometers or centimeters.
Example: 20 g flour
Step 3. Write the quantity of the second object to the right of the symbol
After you have written the quantity of the first object followed by the symbol, write the quantity of the second object, followed by the unit.
Example: 20 g flour/8 g sugar
Step 4. Simplify your comparison (optional)
You may want to simplify your comparisons to create a scale like in the recipe. If you use 20g of flour for a recipe, you know you need 8g of sugar, done. However, if you want to keep your comparisons as simple as possible, you need to write these comparisons in the lowest possible form. You will use the same process as simplifying fractions. The trick is to find the GCF (Largest Common Factor) of the two quantities first, then divide each quantity by the GCF.
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To find the GCF of 20 and 8, write down all the factors of these two numbers (numbers that can be multiplied to produce these numbers and divide them equally) and find the largest number that is divisible by both. Here's how:
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20: 1, 2,
Step 4., 5, 10, 20
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8: 1, 2,
Step 4., 8
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- 4 is the GCF of 20 and 8, the largest number that divides these two numbers equally. To simplify your comparison, divide both numbers by 4:
- 20/4 = 5
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8/4 = 2
Your new ratio now is 5 g flour/2 g sugar
Step 5. Convert the ratio to percent (optional)
If you want to convert the ratio to percent, follow these steps:
- Divide the first number by the second number. Example: 5/2 = 2, 5.
- Multiply the result by 100. Example: 2, 5 * 100 = 250.
- Add a percent symbol. 250 + % = 250%.
- This shows that for every one unit of sugar, there are 2.5 units of flour, or there is 250% flour in sugar.
Method 2 of 2: Additional Information Regarding Comparison
Step 1. The order of the quantities is not important
The comparison shows the relationship between the two quantities. "5 apples for 3 pears" equals "3 pears for 5 apples". So, 5 apples/3 pears = 3 pears/5 apples.
Step 2. Comparisons can also be used to explain probabilities
For example, the probability of getting a 2 on rolling the dice is 1/6, or one possible six events. Note: if you use comparisons to express probabilities, the order of the quantities matters.
Step 3. You can zoom in on the comparison as you zoom out
While you may get used to simplifying it, zooming in on the comparison can also be helpful. For example, if you need 2 cups of water for every one cup of pasta you boil (2 cups of water/1 cup of pasta), and you want to boil 2 cups of pasta, you will need to enlarge the ratio to see how much water is needed. To enlarge the comparison, multiply the first and second quantities by the same number.
