Ratio, rate and proportion

REFLECTION

You have covered many of the concepts in this chapter earlier in your study of mathematics. • Which concepts did you remember really well? • Why do you think you remembered these so well? • Did you find any new ways of doing things or better ways of explaining things as you worked through this chapter? Share your ideas with a partner. Other indices and roots You have seen that square numbers are all raised to the power of two (5 squared = 5 × 5 = 52) and that cube numbers are all raised to the power of three (5 cubed = 5 × 5 × 5 = 53). You can raise a number to any power. For example, 5 × 5 × 5 × 5 = 54. You read this as ‘5 to the power of 4’. The same principle applies to finding roots of numbers. 52 = 25 √_ 25 = 5 53 = 125 3 √_ 125 = 5 54 = 625 4 √_ 625 = 5 You can use your calculator to perform operations using any roots or squares. The yx key calculates any power. So, to find 75, you enter 7 yx 5 and get a result of 16 807. The x key calculates any root. So, to find 4 √_ 81, you enter 4 x 81 and get a result of 3. Make sure that you know which key is used for each function on your calculator and that you know how to use it. On some calculators these keys might be second functions. MATHEMATICAL CONNECTIONS You will work with higher powers and roots again when you deal with indices in algebra in Chapter 2, standard form in Chapter 5 and rates of growth and decay in Chapters 17 and 18. Index notation and products of prime factors Index notation is very useful when you have to express a number as a product of its prime factors because it allows you to write the factors in a short form. SAMPLE 21