Percents

A ratio is a way of comparing two values.

A part-part ratio compares two parts that are both in the same whole. A part-whole ratio compares a part to the whole.

A part-whole ratio can be represented as a fraction. Part-part ratios must be converted to part-whole ratios before the information can be written as a fraction.

You use a part-part ratio when the relationship between the parts is the most relevant aspect of the comparison. For example, if you are baking, the ratio of flour to sugar is more relevant than the ratio of flour to batter. You can adjust the amount of sugar proportionally to the amount of flour to increase or decrease the size of the batch.

You use a part-whole ratio when the relationship between a part and the whole is the most relevant aspect of the comparison. For example, if you are reporting your score on a quiz, it is more relevant to compare the number of correct answers (part) to the total number of questions (whole), than it is to compare the number of correct answers (part) to the number of incorrect answers (part).

A percent is a special part-whole ratio where the whole is 100.

Percent means per 100, so 60 percent means 60 per 100. So 60% of 100 is 60.

I can answer this by reasoning about equivalent ratios. I know that 60% of 100 is 60. I also know that half of 100 is 50. To keep the ratios equivalent I need to multiply or divide both the numerator and denominator of my ratio by the same value. Since 50 is half of 100, and 30 is half of 60, 60% of 50 must be 30.

I know that 28% means I have 28 out of 100. This also means I have 28 hundredths. I write 28 hundredths as 0.28, so 0.28 is the decimal value of 28%.

First I need to set up an equation [ggfrac]20/n[/ggfrac]=[ggfrac]80/100[/ggfrac] and then use proportional reasoning. I know that 20×4=80, and to keep my ratios equivalent, I need to multiply the numerator and denominator by the same value. This means [i[]n[/i]×4=100, so since 25×4=100 there must be 25 logs in the whole pile.