Mathematics revealed by Elizabeth Berman

By Elizabeth Berman

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The fractions ! and t look different, but they name the same number. It is easier to work with t than ! When you write a fraction with the smallest possible numerator and denominator, you are re­ ducing it to lowest terms. EXAMPLE Reduce -ff to lowest terms. First write the prime factorization of the nu9 merator and denominator. 24 = 2 . 2 · 2 · 3 and 36 = 2 . 3 36 2 . 2 . 3 . 3 2 2 = 1 ·- = - 24 3 3 EXAMPLE Reduce 165 to lowest terms. Cancel the common factors. 3 2 .

12 = _ _ _ _ C. {Sample) 4 = D. 5 = 2 2·2 L. 13 = M. 14 = N. 15 = 0. 16 = P. 17 = Q. 18 = R. 19 = 5'l EXERCISES 2-1 NUMBERS AS PRODUCTS NAME In Exercises 9 through 1 7 make a tree diagram. Write the prime fac­ torization, with factors in order from smallest to largest. 9. (Sample) 100 = (2)(2)(5)(5) 10. 30 = --- 1 1 . 76 = 13. 31 = 16. 99 = ___ _ _ _ --- 14. 2 15 = 17. 75 = 12. 45 = ___ _ _ _ --- 15. 64 = --- 58 FRACTIONS 18. Complete Table 2-3, finding the least common multiple of each pair of numbers.

You can make only one rectangle if the number of squares is a prime, like two or three. You can make more than one rec­ tangle if the number of squares is a composite, like six. Zero and one are not classified as either prime or composite. I will explain the reason later. · · The word prime is from the Latin primus, first. Composite is from the Latin com, together; and ponere, to put. PRIME FACTORIZATION Any number n can be factored: n ( l)(n). However, a composite number has factors other than itself and one.

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