How to add reasons
One reason is a comparison of two numbers . They take the form of two numbers side by side, separated by a semicolon. The number on the left is the amount you have of one thing, and the right is the amount you have of another. The addition of relationships is a simple process. The most important steps are the conversion of relationships into common fractions, and the search for their common denominator. When the fractions have a common denominator the numbers below are the same. Let's add the reasons of 1: 3 and 2: 4 to illustrate how it is done.
- Pencil and paper
- Calculator
one
Convert relations with fractions . For example, the ratio 1: 3 means that there is one of something, three of something else, and four units in total. A fraction is a relation of a part of a whole. So the ratio 1: 3 becomes the fraction 1 / (1 +3), or 1/4. Using the same methodology, the ratio 2: 4 becomes the fraction 2/6.
two
Multiply each number in the first fraction by the denominator in the second. The numerator is the number in the upper part, and the denominator is the number that appears in the lower part. Multiplying by that number allows the first fraction to have a common denominator with the second fraction. In the example, we multiply 1 * 6 = 6, and 4 * 6 = 24. The new relation is 6/24, which has the same value as 1/4.
3
Multiply each number in the second relation, with the denominator of the first relation. This step is handled in the same way as the first step. In our example, we multiply 6.2 by 4. 2 * 4 = 8, and 6 * 4 = 24. The new fraction is 8 / 24. The two fractions now have a common denominator and can be added together.
4
Add the two numerators. Do not add the denominators. In our example, to add 6/24 to 8/24, we find the sum of the numerators (6 + 8 = 14) and keep the same denominator, the result is 14/24.
5
Simplify the fraction . Perform this task to find the largest number that uniformly divides both the numerator and the denominator. For fraction 14/24, the largest number is 2. Divide both numbers by 2 and you get 7/12.
6
Check your answer by connecting the values in a calculator. In our example, the decimal value of our final fraction is 0.583, with the repetition of three. If you get the same number, you know that they add up correctly.
7
Turn the fraction back into relation . A fraction becomes a ratio by subtracting the numerator from the denominator and using that value for the other half of the proportion. In our example, 7/12 becomes the ratio of 7: (12-7) = 7: 5. Verify your answer by converting the ratio back to a fraction: 7 / (5 + 7) = 7/12.
