Math ICoursework # 1Sections:1.1 Operations in Fractions and decimals1.2 Conversions of fraction to decimal and vice versa1.3 Percentage and common math shortcuts1.4 Operations in Polynomials

1.1 Operations in Fractions and decimals

A. Fractions

B. Decimals

Addition and SubtractionAlign the decimal places then add or subtract

Add or Subtract3.24 4.801.26 2.654.50 2.15

MultiplicationCase 1: Multiplying non zeros

Count the number of decimal places2.34 x 0.136 = 0.31824 (5 decimal places)35.6 x 3.2 = 113.92 (2 decimal places)

Case 2: Multiplying with zeros

Move decimal places to the right1. 65.68 x 100 = 6,5682. 25.318 x 10 = 253.18Move decimal places to the left1. 65.68 x 0.01= 0.65682. 25.318 x 0.1 = 2.53183. 1689 x 0.001 = 1.689

DivisionCase 1: Dividing non zeros

Make the divisor a whole number by moving its decimal to the rightMove also the decimal point in the dividend 1. 68.96 1.33 6896 133 2. 68.96 0.133 6896 133 3. 16.5 120 165 120

Case 2: Dividing with zeros

Move decimal places to the right1. 15 0.0001 = 150,0002. 8 0.1 = 80Move decimal places to the left1. 15 1000 = 0.0152. 8 10 = 0.83. 8,112.5 100 = 81.125

1.2 Conversions of fraction to decimal and vice versa

Place Value: 0.18769 Hundred thousands Ten thousands Thousands Hundredths Tenths

To convert fraction into decimal, divide the numerator from denominator1. 2/7 2 7 = 0.2862. 34 = 0.753. 5/6 5 6 = 0.83To convert decimal into fraction, read first the decimal places to determine of what denominator to use.1. Change 0.124 to a fractionSince 0.124 is 124 thousandths, use 1000 as the denominator, so

2. 0.56 But for the repeating decimals use 99 and so on for the denominator3. 0.131313.. = 4. 0.287287287 =

1.3 Percentage and common math shortcuts

Percent-means per hundred

30 % means there are 30 per 100 or 30: 100100% means 100/100 or 1 whole400% means 400/100 or 4

Changing fraction to percentDivide the numerator by the denominator and multiply the product by 1002/5 = 0.4 x 100 = 40%6/5 = 1.2 x 100 = 120%

Changing percent to fractionMove the decimal places to the left, read the place value and determine the denominator35% 0.35 = 160% 1.6 1 + 0.6 1 +

Shortcuts

Common fractions to percentages conversion

= 0.5 = 50%2/3 = 0.667 = 66.67% = 0.75 = 75%2/5 = 0.4 = 40%4/5 = 0.8 = 80%3/10 = 0.3 = 30%3/8 = 0.375 = 37.5%1/3 = 0.3333 = 33.33% = 0.25 = 25%1/5 = 0.20 = 20%3/5 = 0.6 = 60%1/10 = 0.1 = 10%7/8 = 0.875 = 87.5%1/8 = 0.125 =12.5%5/8 = 0.525 = 52.5%

Multiplying fractions cancel, cancel and cancel1. 2.

3.

Turn questions into equationsOf to xIs to =What to N

1. What is 25% of 200? N = 25% x 200 N = x 200 = 502. What percent of 50 is 10? N x 50 = 10 N = 3. Fifteen is 50% of what number? 15 = 50% x N 15 = N Divide 15 by 1/2 N = 30

1.4 Operations in Polynomials

Addition and SubtractionCombine like terms then add or subtract1. (2x3 + 6x2 + 9x +8) + (3x4 + x3 + 6x +2)= 3x4 + 2x3 +x3 +6x2 + 9x +6x +8+2= 3x4 +3x3+6x2+15x + 102. (2x3+6x2+9x+8) (3x4+x3+6x+2)= 2x3+6x2+9x+8 3x4 x3- 6x 2= -3x4+ 2x3-x3+6x2+9x-6x+8-2= -3x4+x3+6x2+3x-6

Multiplication2x4+3x2+6x+4x 2x3+2x +3 6x4 +9x2+18x+12 4x5+ 6x3 +12x2+8x 4x7+6x5+ 8x3 +12x4 = 4x7+ 10x5+14x3+18x4+21x2+26x+12 = 4x7+10x5+18x4+14x3+21x2+26x +12

DivisionCase 1: Use Traditional Dividing

x2- 2x +1 x-1 x3 3x2+3x 1 -x3 + x2 - 2x2 + 3x +2x2 2x x 1 -x + 1 0Case 2: Use synthetic division

x3-3x2+3x-1 divided by x-1

x-1 x r x (-1) = x +1

1 3 +3 1 + 1 - 2 1 2 + 1

x3-1 so , x2

x2 2x +1

Solve the following problems:Note: Dont use calculators

1. 0.02% x 0.22 =2. 0.374 x 0.49 x 0.667 x 0.76 x 0.33 is approximately equal to3. Divide 72 by 4. Convert 4.05 into fraction5. Twelve is 150% of what number?6. What Is? 7. If then y =8. If, what is b expressed in terms of a?9. 10. A car dealer sells an SUV for $ 39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer?