Content

• Steps

Ratios are mathematical expressions for comparing two or more numbers. Ratios can be used to compare quantities and absolute quantities or Compare sections with a sum. Ratios can be calculated and written in different formats, however, the principles guiding how to use them are the same.

Steps

Part 1 of 3: Understanding What Ratio is

1. 

   Notice how ratios are used. Ratios are used both academically and in life to compare multiple quantities or quantities. The simplest ratio is to compare two values, there are also ratios that compare three or more values. In any case where two or more different numbers and quantities are to be compared, the proportions apply. By describing the relationship in quantity, ratios indicate whether a chemical recipe can be doubled or a recipe can be added. Once you understand the problem, you will often use ratios in your life.

2. 

   
   
   Understand what a ratio is. As noted above, ratios represent the quantity relationship of at least two objects. For example, if baking requires two cups of flour and one cup of sugar, you would say a flour-to-sugar ratio is 2/1.
   • Ratios are used to determine the relationship between quantities, even if they are not directly bound (such as in a recipe). For example, if there are 5 girls and 10 boys in the class, the ratio of girls to boys is 5/10. These two quantities are not dependent or tied together, and will change if the number of students is removed or added. The ratio is simply to compare quantities.

3. 

   
   
   Notice the ways ratios are written. Ratios can be written in words or in mathematical symbols.
   • You will often see ratios written in words (as above). Since ratios are often used in many different ways, if you're not working in science or math, then you'll find it the most common way of writing ratios.
   • Ratios are often used with a colon. When comparing two quantities, you use a colon (like 7: 13) and when comparing two or more quantities, you add a colon between each successive quantity pair (like 10: 2: 23). . In the classroom example, we can compare the number of boys to the number of girls by the ratio: 5 girls: 10 boys. We can also write it simply: 5: 10.
   • Ratios are sometimes written as fractions. In the classroom example, the ratio of 5 girls to 10 boys could simply be written as 5/10. However, you should not understand the ratio as a fraction and remember that these numbers do not represent the ratio of a part to a sum.
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Part 2 of 3: Using Ratios

1. 

   
   
   Bring the ratio back to its minimal form. Ratios can be minimized like fractions by removing the common divisor of the terms in the ratio. To minimize the ratio, divide the terms in the ratio by the common divisors until no further division can be made. However, when working on it, it's important not to forget the original quantity to get that ratio.
   • In the class example above, the ratio of 5 girls to 10 boys (5: 10), both terms have a common divisor of 5. Divide two terms by 5 (large common divisor Best) to get the ratio of 1 girl to 2 boys (or 1: 2). However, one must keep in mind the original quantity even when using the minimized ratio. A class has a student population of 15 rather than 3. The minimum ratio compares the relationship between the number of boys and girls. There are 1 out of 2 male students, not just 2 boys and 1 girl.
   • Some ratios cannot be simplified. For example, 3: 56 cannot be simplified because two numbers have no common divisor - 3 is prime, and 56 is not divisible by 3.

2. 

   Use multiplication or division to "balance" ratios. One common type of problem that uses ratios is to use ratios to balance increasing or decreasing two numbers in proportion to each other. Multiply or divide the terms in a ratio by the same number to get a new ratio proportional to the original ratio, so to balance the ratio, multiply or divide the ratio by the proportional factor.
   • For example, a baker needs to triple a baker's recipe. If the ratio of flour to regular sugar is 2/1 (2: 1), both numbers would be multiplied by 3. The corresponding amount would be 6 cups of flour and 3 cups of sugar (6: 3).
   • The same process can be reversed. If the baker needs only half of the ingredients for a regular recipe, both quantities multiply by 1/2 (or divide by 2). The result will be 1 cup of flour versus 1/2 (0.5) cup of sugar.

3. 

   Find unknown numbers that know two equal ratios. Another form of the problem of ratios requires finding an unknown in the ratio, given another number in the ratio, and the second being equal to the first. The principle of cross multiplication can solve this problem quite easily. Write down the ratio as a fraction, set the ratios equal, and cross multiply to get the result.
   • For example, let's say we have a student group of 2 boys and 5 girls. If we calculate the ratio of boys to girls, how many male students will there be in a class with 20 girls? To solve this problem, first, we have two ratios, one with unknown numbers: 2 men: 5 women = x men: 20 women. Converting to a fraction, we have 2/5 and x / 20. If cross-multiplied, we get 5x = 40, solve the problem by dividing the two sides of the equation by 5. The final result is x = 8.
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Part 3 of 3: Error Detection

1. 

   Avoid addition or subtraction in ratio word problems. Many word problems look like this: "A recipe requires 4 potatoes and 5 carrots. If you need to use 8 potatoes, what number of carrots must have to keep the proportions. ? " Many students add the same amount to each quantity. You actually need to use multiplication, not addition, to keep the ratio the same. Here is an example of how to do it right and wrong when solving this problem:
   • Wrong way: "8 - 4 = 4, I add 4 potatoes and a recipe. That means I will also add 4 carrots to the 5 given ones ... Wait! That's not the right way. I will try again.
   • Correct way: "8 ÷ 4 = 2, we multiply the number of potatoes by 2. That means we also multiply 5 carrots by 2.5 x 2 = 10, so we need a total of 10 carrots. for new recipes ".

2. 

   Convert to the same unit. Some problems are more complicated by using many different units of calculation. Convert to the same unit before finding the ratio. Here is an example of a problem and its solution:
   • A treasurer has 500 g of gold and 10 kg of silver. What is the ratio of gold to silver in the treasury?
   • Grams and kilograms are not the same, so we have to change the units. 1 kg = 1,000 g, so 10 kg = 10 kg x = 10 x 1,000 g = 10,000 g.
   • The treasurer has 500 g of gold and 10,000 g of silver.
   • The gold to silver ratio is.

3. 

   
   
   Write the unit in the problem. In proportional word problems, it is easier to make mistakes when writing the unit after each value. Remember, the same units will not be listed on the score. After minimizing the ratio, add the units to the final result.
   • Example: If you have 6 boxes, and for every 3 boxes there are 9 marbles, how many marbles total?
   • Wrong way: Wait, nothing is crossed out, the result will be "box x box / marble". That is not reasonable
   • Correct way:
     
     
     18 marbles.
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