Ratios and Proportions Flashcards
Free ratios and proportions flashcards covering ratios, rates, unit rates, equivalent ratios, solving proportions, scale and percent problems. Flip each card, say the answer first, then mark what you know and drill what you miss.
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Ratios and rates
| Question | Answer |
|---|---|
| What is a ratio | A comparison of two quantities, written a:b, a to b, or a/b. |
| Write 3 apples to 5 oranges as a ratio | 3:5. |
| How do you simplify a ratio | Divide both parts by their greatest common factor. 12:18 = 2:3. |
| What is a part-to-part ratio | Compares one part to another, such as boys to girls. |
| What is a part-to-whole ratio | Compares one part to the total, such as boys to all students. |
| What is a rate | A ratio comparing quantities with different units, such as 60 miles per 2 hours. |
| What is a unit rate | A rate with 1 in the denominator, such as 30 miles per hour. |
| How do you find a unit rate | Divide the first quantity by the second. 150 miles / 3 hours = 50 miles per hour. |
| What is unit price | The cost of one item or one unit, found by dividing price by quantity. |
| Which is the better buy, 3 for $4.50 or 5 for $7 | 5 for $7. That is $1.40 each, versus $1.50 each for 3 for $4.50. |
| What are equivalent ratios | Ratios that simplify to the same ratio, made by multiplying or dividing both parts by the same number. 2:3 = 4:6. |
Proportions
| Question | Answer |
|---|---|
| What is a proportion | An equation stating that two ratios are equal, such as 2/3 = 4/6. |
| How do you check if two ratios form a proportion | Cross multiply. If the cross products are equal, it is a proportion. |
| What is cross multiplication | For a/b = c/d, a × d = b × c. |
| Solve 3/4 = x/12 | x = 9 (3 × 12 / 4). |
| Solve 5/x = 15/6 | x = 2 (5 × 6 / 15). |
| If 4 pens cost $6, what do 10 pens cost | $15 (unit price $1.50 × 10). |
| What is a constant of proportionality | The constant ratio k in y = kx, equal to y/x. |
| What is the graph of a proportional relationship | A straight line through the origin (0, 0). |
| If y = 2.5x, what is y when x = 8 | 20. |
| How does a table show a proportional relationship | The ratio y/x is the same in every row. |
Scale, percent and applications
| Question | Answer |
|---|---|
| What is a scale factor | The ratio between corresponding lengths in a scaled drawing and the real object or original figure. |
| A map scale is 1 in = 20 mi. What distance is 3.5 in | 70 miles. |
| What is the percent proportion | part/whole = percent/100. |
| What is 20% of 85 using a proportion | 17 (x/85 = 20/100). |
| What is percent change | (new − old) / old × 100. |
| A price rises from $40 to $50. What is the percent change | 25% increase. |
| Two similar triangles have sides 3 and 9. What is the scale factor | 3 (the larger is 3 times the smaller). |
| If the scale factor is 2, how does area change | Area is multiplied by 2² = 4. |
| How do you convert speed 60 mph to miles per minute | 60 / 60 = 1 mile per minute. |
| A recipe uses 2 cups flour for 12 cookies. How much for 30 cookies | 5 cups. |
Frequently asked questions
What is the difference between a ratio and a rate?
A rate is a ratio that compares different units, such as miles per hour. A ratio can compare quantities with the same units.
How do you solve a proportion?
Cross multiply and divide. For 3/4 = x/12, multiply 3 × 12 = 36 and divide by 4 to get x = 9.
When are ratios taught?
Ratios and proportional relationships appear in Grades 6 and 7 in the Common Core standards.
Sources
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