By H. Piaggio

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**Additional resources for An Elementary Treatise on Diff. Eqns. and Their Applns.**

**Example text**

7. 18. 24521 2. 1 is a natural number. 2 21 is a prime number. No prime number is an even number. 8ϾϪ2 6. Ϫ 3 Ͻ Ϫ 2 9 Յ 0 Ϫ9 0 8. 0 Ϫ11 0 Ն 10 Place an appropriate symbol in each box to make the statement true. 9. 3 ϩ 7 11. 0 Ϫ2 0 10 2 3 2 1 ϭ 7 7 7 12. 4 ϩ 8 11 10. VOCABULARY AND CONCEPTS Fill in the blanks. 13. The number above the bar in a fraction is called the . 14. The number below the bar in a fraction is called the . 2 Fractions 15. To a fraction, we divide its numerator and denominator by the same number.

53 ϩ 2(8 Ϫ 3 ؒ 2) ϭ 53 ϩ 2(8 Ϫ 6) ϭ 53 ϩ 2(2) ϭ 125 ϩ 2(2) ϭ 125 ϩ 4 ϭ 129 Self Check EXAM PLE 4 (4 ؒ 2)3 ϭ 83 ϭ 8 ؒ 8 ؒ 8 ϭ 512 Evaluate: 5 ϩ 4 ؒ 32. Evaluate: 3(3 ϩ 2) ϩ 5 . 17 Ϫ 3(4) Do the multiplication within the parentheses. Do the subtraction within the parentheses. Find the value of the exponential expression. Do the multiplication. Do the addition. 3 Exponents and Order of Operations Solution We simplify the numerator and denominator separately and then simplify the fraction. 3(3 ؉ 2) ϩ 5 3(5) ϩ 5 ϭ 17 Ϫ 3(4) 17 Ϫ 3(4) 15 ϩ 5 ϭ 17 Ϫ 12 20 ϭ 5 ϭ4 Self Check Evaluate: 4 ϩ 2(5 Ϫ 3) .

14. The number below the bar in a fraction is called the . 2 Fractions 15. To a fraction, we divide its numerator and denominator by the same number. 16. To write a number in prime-factored form, we write it as the product of numbers. 17. If the numerator of a fraction is less than the denominator, the fraction is called a fraction. 18. If the numerator of a fraction is greater than the denominator, the fraction is called an fraction. 19. If the product of two numbers is , the numbers are called reciprocals.