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Lecture 8 Notes: Section 4.1, 4.2, 4.3, & 4.4 – Richard Goldman MAT116 Algebra I Basic Mathematics for College Students – 3e Review Convert Mixed 3¾ - Add 3 to ¾ = 3/1 + ¾ = 12/4 + ¾ = 15/4 number to improper Fraction (Multiply whole number by denominator then add numerator to it.) Convert Improper 15/4 – Divide numerator by denominator - the result is the whole number – Put the Fraction to Mixed remainder over the denominator to form a fraction number 15/4 = 3 R3 = 3 ¾ Graphing Demonstrate on number line Fractions Multiply and Convert to improper fractions then process as usual Divide Mixed Fractions Adding and Find LCD of fractions then add or subtract (carry and borrow as needed) Subtracting Mixed Numbers Order of Groups ( Parenthesis, Complex Fractions, Absolute Values) Operation Powers Multiply & Divide (Left to Right) Add & Subtract (Left to Right) Complex (Fraction over Fraction – write out horizontal and process) Fractions 4.1 An Introduction to Decimals Decimal 1/10 = 0.1 Decimal Places 0.1 1 Tenth 0.01 1 Hundredth 0.001 1 Thousandth 0.0001 1 Ten Thousandth 0.00001 1 Hundred Thousandth 0.000001 1 Millionth 0.0000001 1 Ten Millionth Leading 0 0.1 = .1 (Leading zero is a general convention used to help eliminate error) Trailing 0 0.10 = 0.1 (Trailing zero is an engineering/scientific convention use to display accuracy) Reading 123.45 Is read as One hundred, twenty-three and 45 hundredths 0.45 Is read as Forty-five hundredths (also – point Four, Five) Comparing The number with the biggest different number in the column closest to decimal is the largest value. Rounding Round from the right just like with whole numbers. 4.2 Adding and Subtracting Decimals Adding & 1. Line up Decimal points Subtracting 2. Add trailing zeros to match longest decimal Decimals 3. Add or subtract as you would whole numbers 4.3 Multiplying Decimals Multiplying 1. Multiply as you would whole numbers Decimals 2. Count total decimal places in both factors and add to product (add leading 0’s if necessary) 493700926 Page 1 of 2 Richard Goldman Multiplying by powers of 10’s Order of Operation 4.4 Dividing Decimals Rounding Dividing by powers of 10’s Order of Operation 493700926 Move the decimal place to the right for each 0 in the power. 10 x 123.456 = 1,234.56 100 X 123.456 = 12,345.6 Same Dividing Decimals 1. Move the decimal place in the devisor to make it a whole number 2. Move the decimal place in the dividend the same number places 3. Divide until there is no remainder or the desired precision is reached (add trailing zeros to the dividend as necessary) Carry out division one digit past desired accuracy and then round back Move the decimal place to the Left for each 0 in the power. 123.456 ÷ 10 = 12.3456 123.456 ÷ 100 = 1.23456 Same Page 2 of 2 Richard Goldman