Rate | Ratio | Grade 8 Rate Mathematics | Grade 9 Rate Mathematics

Summary

In this video, the concept of rate is explored, particularly in relation to speed and cost calculations. Through engaging examples, the video demonstrates how to find average speed using distance and time, as well as how to apply ratios to solve rate questions involving cost per kilogram. From calculating speed in kilometers per hour to determining costs for different weights of chicken breasts, viewers learn the practical application of rates in everyday scenarios, with a focus on using ratios for accuracy in cost calculations.

Takeaways

• 😀 Rate is defined as the relationship between one quantity and another, such as speed, cost, or weight.
• 😀 In speed-related rate questions, we often calculate the average speed by dividing the distance by the time taken.
• 😀 Example: If John travels 1400 kilometers in 12 hours, his average speed is 116.66 km/h (calculated as 1400 ÷ 12).
• 😀 When working with kilograms and cost, rates can help determine the cost for different quantities based on a known rate per unit.
• 😀 Example: If chicken costs 65 Rand per kilogram, you can calculate the cost for 4 kilograms by multiplying 65 by 4, which gives 260 Rand.
• 😀 Ratios are a helpful tool for solving rate questions. By setting up a ratio, you can scale the known rate to the required quantity.
• 😀 Example: To find the cost for 2.5 kilograms, divide 4 by 1.5, which gives 2.66, and multiply this by the price to get 173.33 Rand.
• 😀 When dealing with multiple quantities, the same method of finding the relationship between them through division or multiplication can be applied.
• 😀 More complex rate problems can involve working with fractional values. For example, dividing 4 by 1.5 to get a ratio of 2.66.
• 😀 You can solve rate questions more efficiently by using unit conversions and applying the same multiplication/division method for consistent results.

Q & A

What is the definition of rate in the context of this video?

Rate is defined as the relationship between one quantity and another quantity. It describes how one unit changes in relation to another.

How is speed related to rate in this video?

Speed is a common example of rate, where the relationship between distance (in kilometers) and time (in hours) is examined to calculate average speed, measured in kilometers per hour.

What is the formula for calculating average speed from the given example?

The formula for calculating average speed is: average speed = distance (in kilometers) ÷ time (in hours). For example, if someone travels 1400 kilometers in 12 hours, their average speed is 1400 ÷ 12 = 116.67 kilometers per hour.

How is the cost of buying chicken breasts calculated in the video?

The cost is calculated using a ratio. If 1 kilogram of chicken costs 65 Rand, the cost for any amount of kilograms can be found by multiplying 65 by the number of kilograms. For example, the cost for 4 kilograms is 65 × 4 = 260 Rand.

What is the benefit of using a ratio in rate problems?

Using a ratio helps to organize and simplify the calculation by showing the relationship between two quantities, allowing for easy scaling when calculating costs, speeds, or other values.

What calculation is done to find the cost of 2.5 kilograms of chicken at 65 Rand per kilogram?

To find the cost of 2.5 kilograms, you multiply 65 Rand by 2.5, resulting in a cost of 162.50 Rand.

How can a fraction like 5/3 be used in rate calculations?

A fraction like 5/3 can be used to find the relationship between two quantities, such as converting between different amounts of kilograms and their respective costs. In the video, multiplying by 5/3 helped calculate the cost for various quantities of chicken.

How did the speaker calculate the cost of 4 kilograms using a ratio?

To calculate the cost of 4 kilograms, the speaker set up a ratio (1 kilogram = 65 Rand) and multiplied by 4, resulting in 260 Rand for 4 kilograms.

What would happen if the cost per kilogram was changed in this type of problem?

If the cost per kilogram changes, the multiplication factor would also change accordingly. The cost for different amounts would be recalculated by multiplying the new cost per kilogram by the desired number of kilograms.

What is the method used for calculating the cost of 3.86 kilograms of chicken?

The cost of 3.86 kilograms is calculated by first finding the ratio between 1.5 kilograms and 3.86 kilograms, which gives a multiplier of 193/75. This multiplier is then used to calculate the cost by multiplying it by 65 Rand, resulting in a cost of 167.26 Rand.