*The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.*

and how would we solve this problem: What is 20% of 45? 40% means that 40 will replace percent in our proportion.

The phrase of what number represents the whole and is the unknown quantity.

20% means that 20 will replace percent in our proportion. Substitute: Now we can substitute these values into our proportion.

becomes Solve: Cross multiply and we get: 100x = 45(20) or 100x = 900 Divide both sides by 100 to solve for x and we get: x = 9 Solution: 9 is 20% of 45 In Problems 1, 2 and 3 we are given two numbers and asked to find the third by using a proportion.

In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.

## Using Proportions To Solve Problems

We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.For addition and subtraction, use the standard and - symbols respectively. A * symbol is not necessiary when multiplying a number by a variable. Similarly, 2 * (x 5) can also be entered as 2(x 5); 2x * (5) can be entered as 2x(5).The * is also optional when multiplying parentheses, example: (x 1)(x - 1).Thus, if you were asked to Find 15% of 120, you would multiply .15 by 120, to get an answer of 18.But what would you do if you given this problem: 8 is what percent of 20?This unknown quantity will be represented by x in our proportion. Substitute: Now we can substitute these values into our proportion.becomes Solve: Cross multiply and we get: 20x = 800 Divide both sides by 20 to solve for x and we get: x = 40 Solution: 8 is 40% of 20. Note that in Problem 1 we did not have to cross multiply to solve the proportion.Exponents may not be placed on numbers, brackets, or parentheses.Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.The calculator follows the standard order of operations taught by most algebra books - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.The only exception is that division is not supported; attempts to use the / symbol will result in an error. If either side of the proportion has a numerator and denominator that share a common factor with a variable, the calculator will report an erroneous solution.

## Comments Using Proportions To Solve Problems

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