Which proportion has a solution of 8

Now, 2 is two thirds of 3. What number is two thirds of 12? In the next lesson we will see how to solve a proportion that looks like this:. At this point, please "turn" the page and do some Problems. Continue on to the next Section. E-mail: teacher themathpage. A statement that two ratios are the same. A proportion involves four numbers called the terms. Example 2. Why is this a proportion? Example 3. Example 4. Complete this proportion: 8 is to 32 as 9 is to?

The 1st term is to the 2nd as the 3rd is to the 4th. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks. Quick-Start Guide The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods.

Use the following as a guide: Variables Any lowercase letter may be used as a variable. Parentheses and Brackets Parentheses and brackets [ ] may be used to group terms as in a standard equation or expression. Order of Operations The calculator follows the standard order of operations taught by most algebra books — Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Example 5. Therefore, 6 also must be multiplied by 4 :. Four times 6 is Example 6. Solve this proportion:. Six times 3 is In fact, consider these columns of the multiples of 2 and 3 :. Now, 2 is two thirds of 3. Lesson And each multiple of 2 is two thirds of that same multiple of 3 :. And so on. In fact, those are the only natural numbers where the first will be two thirds of the second. Note that each pair have a common divisor. And upon dividing by that divisor, the quotients in every case are 2 and 3.

That is the theorem of the common divisor. They are the smallest numbers which have the ratio "two thirds. Example 7. Name three pairs of numbers such that the first is three fifths of the second. The elementary pair are 3 and 5. To generate others, take the same multiple of both: 6 and 10, 9 and 15, 12 and 20, and so on.

Example 8. Only a multiple of 3 can be three fourths of another number, which must be that same multiple of 4. Example Common divisor. Alternately, we see that has been divided by 2. Therefore 12 also must be divided by 2. Instead of dividing 12 and by 2, we could take half. Half of is Half of 12 is 6. We see that if we know three terms of a proportion, then we can always solve for the fourth. That is called The Rule of Three. We can summarize it as follows.