Solving Proportions
Proportion
A proportion is an equation that states that two ratios (fractions) are equivalent (look different but have the same value).
How do you check if the ratios are proportional by checking through cross products?
Multiply the extremes and multiply the means. If the products are equivalent, the ratios are proportional. If the products are not equivalent, the ratios are not proportional.
Cross product
Multiply the extremes, multiply the means, and then set them equal to each other.
How do you solve 1-step proportions by cross product?
Multiply the extremes, multiply the means, and then set them equal to each other. Then, isolate the variable by cancelling the coefficient with inverse operations.
What should you do if you are trying to solve a proportion but the numerator or the denominator has more than 1 term?
Remember to put the whole numerator or the denominator with more than 1 term into a grouping symbol such as parentheses.
How do you check if the ratios are proportional by checking through quotients?
Since fraction bar means divide, divide numerator by denominator in both fractions to get a quotient. If the quotients are equivalent, the ratios are proportional. If the quotients are not equivalent, the ratios are not proportional.
How do you check if you solved the 1-step proportional equation correctly?
Substitute the value for the variable into the ratio. Then, get both quotients and compare values. If the values match, you solved it correctly. If the values do not match, something went wrong.
How do you check if you solved the multi-step proportional equation correctly?
Substitute the value for the variable into the ratios. Then, use order of operations to simplify. Calculate both quotients and compare values. If the values match, you solved it correctly. If the values do not match, something went wrong.
Extremes
The extremes are the first and last numbers in a proportion.
What are the four methods to check if the ratios are proportional?
The four methods are: 1) Reduce both fractions to simplest terms 2) Use logic to check by inspection 3) Check through cross products 4) Check through quotient
Means
The means are the middle terms of a proportion.
What are the two methods to set up proportional equations from word problems?
The two methods are: 1)Same variable type straight across from each other 2) Same variable type in on top of each other
Substituion
To substitute is to replace.
What is the method to solve multi-step proportions?
We solve multi-step proportions by using the cross product, then simplifying both sides, and isolating the variable through inverse operations.
Reduce to simplest terms
When you reduce to simplest terms, you get a fraction with both numerator and denominator having their smallest possible values, but retaining the original fraction's value
How do you check if the ratios are proportional by reducing both fractions to simplest terms?
Work with one fraction at a time. Take each fraction and reduce it as much as you can by dividing the numerator and the denominator by the same number. If the fractions are equivalent, the ratios are proportional. If the ratios are not equivalent, the ratios are not proportional.
What are the two methods to solve 1-step proportions?
You can solve 1-step proportions by 1) Inspection (works sometimes) 2) Cross product (works always)
Quotient
A quotient is the result of division.
Ratio
A ratio is a comparison of two quantities by division.
How do you check if the ratios are proportional by using logic to check by inspection?
Ask yourself if there is a consistent pattern between both numerators and both denominators? If yes, the ratios are proportional. If not, the ratios are not proportional.
How do you solve 1-step proportions by inspection?
Ask yourself if there is a consistent pattern between both numerators or both denominators? If yes, apply the pattern to the line where the variable is.
Equivalent fractions
Equivalent fractions are two or more fractions that name the same amount.
Equivalent
Equivalent is to look different but to have the same value.
