Setting up and solving ratio and proportion problems, including unit rates and scale factors, for middle school math.
34 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a ratio?
- A comparison of two quantities using division.
- Write three ways to express the ratio of 3 to 5.
- 3:5, 3/5, or 'three to five'.
- What are equivalent ratios?
- Ratios that represent the same comparison, like 2:3 and 4:6.
- To simplify a ratio, what do you do?
- Divide both numbers by their greatest common factor (GCF).
- Simplify the ratio 8:12.
- 2:3 (divide both by 4, the GCF).
- What is a unit rate?
- A ratio that compares a quantity to one unit of another quantity.
- If 5 apples cost 10 dollars, what is the unit rate?
- 2 dollars per apple (divide 10 by 5).
- If you travel 150 miles in 3 hours, what is your unit rate?
- 50 miles per hour.
- What is a proportion?
- An equation that states two ratios are equal.
- What is cross multiplication?
- A method for solving proportions: multiply the numerator of each fraction by the denominator of the other.
- Solve: 3/5 = x/10. Find x.
- x = 6 (cross multiply: 3 times 10 = 5 times x, so 30 = 5x).
- Solve: 2/3 = 8/x. Find x.
- x = 12 (cross multiply: 2 times x = 3 times 8, so 2x = 24).
- What is a scale factor?
- A multiplier that describes how much a figure is enlarged or reduced.
- If a scale factor is 3, how does the figure change?
- The figure is enlarged; all dimensions are multiplied by 3.
- If a scale factor is 1/2, how does the figure change?
- The figure is reduced; all dimensions are multiplied by 1/2.