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Questions and Answers
What is a rate?
What is a rate?
- A ratio where both terms have the same units
- A fraction that represents the total change in quantity
- A special ratio where the two terms have different units (correct)
- A measure of speed in kilometers per hour
How do you increase a quantity in the ratio 4:3?
How do you increase a quantity in the ratio 4:3?
- Divide the quantity by 3
- Multiply the quantity by 3/4
- Multiply the quantity by 4/3 (correct)
- Add 4 to the quantity
What is the average rate of change?
What is the average rate of change?
- Rate of decrease in a circuit
- Difference between two quantities divided by their ratio
- Total change divided by time taken (correct)
- The same as a simple ratio
Which of the following represents the correct calculation to decrease 35 in the ratio 3:7?
Which of the following represents the correct calculation to decrease 35 in the ratio 3:7?
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If a lorry travels at an average speed of 100 km per hour, what does this represent?
If a lorry travels at an average speed of 100 km per hour, what does this represent?
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Study Notes
Rate
- Rate is a ratio with different unit types.
- Example is PKR 85 for 12 ounces of corn.
Average Rate
- Average rate is the change in one quantity relative to another.
- Example is a lorry's speed of 100 km per hour.
- Calculated as change in one object divided by change in another.
Increasing Ratios
- To increase a quantity in ratio a:b where b is greater than a, multiply the quantity by a/b.
- Example: Increase sugar quantity in the ratio 4:3, multiply quantity by 4/3.
Decreasing Ratios
- To decrease a quantity in ratio a:b where b is less than a, multiply quantity by a/b.
- Example: Decrease flour for 4 people to 3 people, use ratio 3:4, multiply flour amount by 3/4.
Worked Example 1 (a)
- Increase 40 in the ratio 4:40, which means a new quantity to old quantity ratio of 5:2
- This means solving the equation x/40 = 5/2.
- Solving for x, we get a new quantity of 100, so new quantity is 100.
Worked Example 1 (b)
- Decrease 35 in ratio 3:7.
- This means a new quantity to old quantity ratio of 3:7.
- Set up the equation as new quantity/35 = 3/7.
- Solving for new quantity, we get 15.
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