Download Section 4.1 – Mental Math, Estimation and Calculators

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