Number And Algebra - Chapter 7 Applying Ratios And Rates - Nelson Think Math Page 3
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Applying ratios and rates
At a fruit and vegetable shop, the prices are usually displayed as rates. The quantities of tomatoes
Maths clip
that different customers buy may be different, but the price per kilogram is the same. Most
Why do we have
products where the amount that we can buy varies are priced in this way. There are many other
ratios?
situations where a quantity may vary, but the rate or ratio relative to something else remains the
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same, such as scale drawings, electric currents, force and acceleration. We use rates, ratios and
proportions to perform calculations in circumstances like these.
n
Mathematical literacy
The mathematical words below have special meanings that you will learn in this chapter. It is
Maths dictionary
important that you learn to spell them and gradually learn what they mean in mathematics. You
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may find the glossary or online mathematical dictionary useful for this purpose.
cross-product
kilowatt
reduction
speed
enlargement
rate
scale
equivalent
ratio
scale factor
7.1
Rates
Video tutorial
A rate compares related measurements. The measurements that are compared within a rate are
Rates problems
usually referred to as quantities.
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Important!
Rates
A rate is obtained by dividing one quantity by a different, related quantity. A rate can be
written as a fraction.
The measurement units for the quantities in a rate are separated by the word ‘per’ or the
symbol /, with the second unit being the denominator.
Prices, pay rates and speeds are the most common rates.
distance
For example,
Average speed ¼
Quantity 1
time
Rates can be used to calculate one quantity from the other.
Rate
Quantity 2
A triangle of the rate can be used to remember the operation:
quantity 1
quantity 1
Rate ¼
or Quantity 1 ¼ rate 3 quantity 2 or Quantity 2 ¼
quantity 2
rate
Example
1
Teacher notes
Elena earned $66.80 working for 5 hours.
Triangle method
a
What was her rate of pay?
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1
b
What would she earn by working for 3
hours?
2
Puzzle sheet
Solution
Rates problems
pay
a
Write the rate equation.
Rate of pay ¼
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time
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