Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 4. Section 1 Page 1 Section 4.1 – Mental Math, Estimation and Calculators Homework (pages 148-149) problems 1-24 Mental Estimation Techniques: • When trying to compute mentally, you can use the laws of commutative, associativity, and distribution to simplify your task • Example, page 150 number 1 a) 52 ⋅14 − 52 ⋅ 4 = 52(14 − 4) = 52(10) = 520 b) (5 ⋅ 37) ⋅ 20 = (5 ⋅ 20) ⋅ 37 = 100 ⋅ 37 = 3700 c) (56 + 37 ) + 44 = (56 + 44) + 37 = 137 d) 23 ⋅ 4 + 23 ⋅ 5 + 7 ⋅ 9 = 23( 4 + 5) + 7 ⋅ 9 = 30 ⋅ 9 = 270 • Additive compensation is when you have an addition or subtraction problem and you add a value to one, and subtract it from the other (to compensate) • Example, page 150 number 4a 359 + 596 = 355 + 600 = 955 • When you have a subtraction problem (a - b) you can add a value to both numbers. Why? This is known as the equal additions method • Example, page150 number 2b 83 − 37 = 86 − 40 = 46 • Multiplicative compensation is when you have a multiplication or division problem, and you multiply a value to one, and divide it from the other • Example, page 150 number 4b 76 76 × 25 = × ( 25⋅ 4) = 19 × 100 = 1900 4 • The number 5, 25 and 99 can be regarded as special factors because 10 100 5 = , 25 = and 99 = 100 − 1 2 4 • Example, page 150 number 4d 1240 ÷ 5 = 1240 ÷ (10 ÷ 2) = 124 × 2 = 248 • Example, page 141 4.3f 100 45600 456 × 25 = 456 × = = 11400 4 4 • When multiplying powers of 10, you can use standard or exponential form (count the total number of zeros) • Example, page 150 number 5a 32000 × 400 = (32 × 4) 105 = 12,800,000 • Example, page 150 number 5d 5 × 104 × 30 × 105 = (5 ⋅ 30) (104 ⋅ 105 ) = 150,000,000,000 • Range estimation is finding a low and high estimate for an answer • Example, page 151 number 7a 57 × 1924. Low: 50 × 1900 = 95000 High: 60 × 2000 = 120000 Chapter 4. Section 1 Page 2 Using a Calculator: • A calculator computes operations in the order they are entered. Parenthesis are done first, then exponents, then multiplication and division, finally addition and subtraction • For example, if you want to compute (5 + 3) 2 you must enter the parenthesis, or compute the 5+3 first, and then raise it to a power • What would be the result if you enter (12 + 7 × 2) ÷ 2 ⋅ 4 ? • It is often useful to determine the remainder for a quotient. For example how can we find the quotient and remainder for 640 ÷ 23 ? 640 ÷ 23 ≈ 27.8 19 640 − 23 × 27 = 19 so 640 ÷ 23 = 27 + 23