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Math 40 Chapter 1 Study Guide Name: Date: Must show work for credit. 1. Translate the following statement into symbols. (a) The product of 7 and y is 21. (b) Three times the sum of x and y is less than 13. 2. Use the rule for order of operations to simplify each expression. (a) 12 − 3(2 · 5 + 7) + 4 (b) 23 − 10[4 − 3(−2 + 18)] 3. Fill in the missing numerator so the fractions are equal. (a) 5 = 8 24 (b) −3 = 4 16 4. For each number, name the opposite, reciprocal, and absolute value. (a) −6 (b) 5 7 5. Place on of the symbols < or > between each of the following to make the resulting statement true. 2 1 (a) −9 −11 (b) − − 3 3 6. Perform the indicated operations and, if possible, simplify. 1 (a) | − 9 + (−6)| + | − 3 + 5| (b) 8 − 4 (c) 5(−6)2 − 3(−2)3 (e) 4(−7) − 3(9) −9 − (−9) (d) 4 − 2[−3(−1 + 5) + 4(−3)] (f) 2(−3 − 1) + 4(−5 + 2) −3(2) − 4 7. State the property or properties that justify the following. (a) 9(3y) = (9 · 3)y (b) (4 + y) + 2 = (y + 4) + 2 (c) −3(x − 5) = −3x + 15 (d) (1 + s) + r = (r + 1) + s √ 1 8. For −9, −2.5, 3, , 0, 2.6, 5 list all the elements of the set that are named in each 5 of the following subsets. (a) Whole Numbers (b) Integers (c) Rational Numbers (d) Irrational numbers 9. Factor into the product of primes. (a) 90 10. Combine. 11 5 (a) + 42 42 (b) 840 (b) 1 3 + 42 70 11. Find the next number in each sequence. (a) 8, 4, 0, ... (c) 1 5 , 1, , ... 3 3 (b) 8, −4, 2, −1, ... (d) 1, 1 1 , , ... 5 25