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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)
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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
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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
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Richard Goldman