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Flashcards by Carlos Rozas, updated more than 1 year ago
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| Question | Answer |
| Ratios | A ratio is a comparison of two quantities e.g., the ratio of red squares to blue triangles is 3 squares to 4 triangles or 3 to 4 or 3:4 or \(\frac{3}{4}\) |
| Ratios #2 | Ratios can compare part to part 3:4 or \(\frac{3}{4}\) or part to whole 3:7 or \(\frac{3}{7}\). |
| Equivalent Ratios | equivalent ratios that can be simplified to exactly the same value e.g. \(\frac{6}{9}\) and \(\frac{8}{12}\) to \(\frac{2}{3}\) |
| How to Check if Two Ratios Form a Proportion (or are Equivalent): | Check if the cross products are equal. \(\begin{align}3*35&=105 \\ 5*21&=105\\ \end{align}\) |
| If Two Ratios are Equivalent: | 1) They have the same simplified value. 2) The cross products are equal. |
| Rates | a rate is comparison by division of two quantities with different units e.g. 2 oranges costs 3 dollars for a rate of \(\frac{\text{2 oranges}}{\text{3 dollars}}\) |
| Unit Rate | a unit rate is a rate in which in the second quantity is one. For example, if we payed $90 for 6 classes, the unit rate is $15 per class. |
| Unit Rate #2 | The denominator is always 1. \(\frac{\text{32 miles}}{\text{1 hour}}\) \(\frac{\text{5 cents}}{\text{1 minute}}\) \(\frac{\text{32 students}}{\text{1 class}}\) |
| Unit Rate #3 | Unit rates make it easy to compare two rates as they have the same denominator. |
| Equivalent Rates | rates that represent the same value and therefore the same unit rate. In the above example, the unit rate is \(\frac{\text{8 campers}}{\text{1 cabin}}\) |
| Proportion | A proportion is a statement that two ratios or rates are equal. \(\frac{6}{9} =\frac{8}{12}\) \(\frac{\text{16 campers}}{\text{2 cabins}}= \frac{\text{80 campers}}{\text{5 cabins}}\) |
| Rate Table | table of equivalent rates |
| Rate Table #2 | Since all the rates in a rate table are equivalent, the rate table represents a proportional (multiplicative) relationship. |
| Percents | a ratio of a number to 100 |
| Percent Proportion | The ratio of part to the whole is equivalent to the ratio of the percent value to 100. |
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