How to Write Ratios

How to Write Ratios. Guidelines on how to write ratios with examples and step by step explanations. What is a ratio? A ratio is two numbers that are in a specified relationship with each other. The simplest form of a ratio is in the format . Commonly used ratios are given names. These names makes them easier to remember. These ratios can be written in simple terms or expanded out into fractions

Ratios are a way to compare 2 different quantities, which makes them incredibly useful for doing everything from graphing to calculating volume. In this introduction to ratios you will learn ways to understand ratios and how to use ratios in everyday life.

A ratio is a mathematical means of comparing one value to another. You hear the term “ratio” used in relation to studies or analyses of various sets of data, such as in demographics or the performance ratings of products. Proportions and fractions are intertwined with ratios. Both proportions and fractions deal with the comparison of multiple values. You can use proportions and fractions as alternative means of writing ratios. You may have to perform this type of task in a middle school, high school or college math course.

Table of Contents

Characteristics of a Ratio

A ratio is a sort of mathematical metaphor, an analogy used to compare different amounts of the same measure. You could almost consider any type of measurement a ratio, since every measurement in the world has to have some sort of reference point. This fact alone makes measurement by ratio one of the most basic of all forms of quantification.

Units of Measure

A ratio compares two things in the same unit of measure. It doesn’t matter what that unit of measure is — pounds, cubic centimeters, gallons, newton-meters — it matters only that the two are measured in the same units. For instance, you can’t compare 1 part fuel to 14 parts of air if you’re measuring fuel in pounds and air in cubic feet.

Modes of Expression

You can express a ratio either in narrative form or in symbolic mathematical notation. You can express ratio as “the ratio of A to B,” “A is to B,” “A : B” or the quotient of A divided by B. For example, you can express a ratio of 1 to 4 as 1:4 or 0.25 (1 divided by 4).

Equality of Ratios

You can use ratios as direct analogies to compare one thing to another, notating it either with an “=” sign or verbally. For instance, you can say “A is to B as C is to D,” or you can say, “A:B = C:D.” In this instance, A and D are the “extremes” and B and C are called the “means.” For example, you can say, “1 is to 4 as 3 is to 12,” or you can say “1:4 = 3:12.”

Ratios as Fractions

In practice, ratios act something like fractions. You can replace the colon with a division sign and still arrive at the same result. As in the previous example, 1/4 (1 divided by 4) and 3/12 (3 divided by 12) both come out to 0.25. This is consistent with the last mode of expression. So any ratio may be expressed as A divided by B.

Continued Proportions

Any series of three or more ratios can string together to create a continued or serial proportion. As an example, “1 is to 4 as 3 is to 12 as 4 is to 16” and “1:4 = 3:12 = 4:16” are both continued proportions. Expressing them as decimal figures (dividing the first number by the second in each proportion), you indeed find that 0.25 = 0.25 = 0.25.

How to Make a Ratio

Method 1 Make a Ratio

  1. Use a symbol to denote the ratio. To indicate that you’re using a ratio, you can use the division sign ( / ), a colon ( : ), or the word to. For example, if you wanted to say, “For every five men at the party, there are three women,” then you could use any of the three symbols to state this.[1] Here’s how you would do it:
    • 5 men / 3 women
    • 5 men : 3 women
    • 5 men to 3 women
  2. Write the first given quantity to the left of the symbol. Write down the quantity of the first item before the symbol of your choice. You should also remember to state the units, or the number you’re working with, whether it’s men or women, chickens or goats, or miles or inches.
    • Example: 20 g of flour
  3. Write the second given quantity to the right of the symbol. After you’ve written the first given quantity followed by the symbol, you should write the second given quantity, along with its units.
    • Example: 20 g of flour/ 8g of sugar
  4. Simplify your ratio (optional). You may want to simplify your ratio to do something like scale down a recipe. If you’re using 20 g of flour for a recipe, then you know you’ll need 8 g of sugar, and you’re done. But if you’d like to scale down the ratio as much as possible, then you’ll need to simplify it by writing the ratio in its lowest possible terms. You should use the same process as you would use to simplify a fraction. To do this, you have to find the GCF, or the greatest common factor, of both quantities, and then see how many times that number fits into each given quantity.
    • To find the GCF of 20 and 8, write down all of the factors of both numbers (the numbers that can multiply to make those numbers and thus can be evenly divided into those numbers) and find the largest number that is evenly divisible into both. Here’s how you do it:
      • 20: 1, 2, 4, 5, 10, 20
      • 8: 1, 2, 4, 8
    • 4 is the GCF of 20 and 8 — it’s the largest number that evenly divides into both numbers. To get your simplified ratio, simply divide both numbers by 4:
    • 20/4 = 5
    • 8/4 = 2
      • Your new ratio is 5 g flour/ 2 g sugar.
  5. Turn the ratio into a percentage (optional). If you’d like to turn the ratio into a percentage, you just have to complete the following steps:
    • Divide the first number by the second number. Ex: 5/2 = 2.5.
    • Multiply the result by 100. Ex: 2.5 * 100 = 250.
    • Add a percentage sign. 250 + % = 250%.
    • This indicates that for every 1 unit of sugar, there is 2.5 units of flour; it also means that there is 250% as much flour as there is sugar.

Method 2 Additional Information About Ratios

  1. The order of the quantities doesn’t matter. The ratio simply represents the relationship between two quantities. “5 apples to 3 pears” is the same as “3 pears to 5 apples.” Therefore, 5 apples/ 3 pears = 3 pears/ 5 apples.
  2. A ratio can also be used to describe probability. For example, the probability of rolling a 2 on a die is 1/6, or one out of six. Note: if you’re using a ratio to denote probability, then the order of quantities does matter.
  3. You can scale a ratio up as well as down. Though you may be used to simplifying numbers whenever you can, it can benefit you to scale a ratio up. For example, if you know that you’ll need 2 cups of water for every 1 cup of pasta you boil (2 cups water/1 cup pasta), but you want to boil 2 cups of pasta, then you’ll need to scale up the ratio to know how much water to use. To scale up a ratio, simply multiply the top and bottom by the same number.
    • 2 cups water/ 1 cup pasta * 2/ 2 = 4 cups water/ 2 cups pasta. You’ll need 4 cups of water to boil 2 cups of pasta.

Conclusion

Ratio is defined as a relationship of one quantity to another quantity. It shows the relationship between two quantities, e.g., the number of students in a class is to the number of teachers in a school. Ratios compare two quantities with each other. When neither of the quantities is zero then it is called a proper ratio.

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