lesson 1-3: mult/div real #s the first slides here review adding, subtracting, multiplying, and...
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Lesson 1-3: Mult/Div Real #sThe first slides here review
adding, subtracting, multiplying, and dividing fractions. You do not have to take notes on these slides. We will do a few practice problems in class.
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Add & Subtract FractionsAdd & Subtract Fractions
1. Find the common denominator.2. Make equivalent fractions using
the new common denominator.3. Add/sub the numerators.
Denominator stays the same.4. Simplify/reduce.5. Leave improper fractions as is.
Hooray!
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ExamplesExamples
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1
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Multiply Fractions & Mixed Multiply Fractions & Mixed #s#s1. Change any mixed #s into
improper fractions.2. Multiply numerators.3. Multiply denominators.4. Simplify. (You can also simplify
before you multiply.)5. Leave improper fractions as is.
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ExamplesExamples
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42
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2111
10
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Divide Fractions & Mixed Divide Fractions & Mixed #s#s1. Change any mixed #s into
improper fractions.2. Find the reciprocal of the 2nd
fraction (the divisor), rewriting the problem as a multiplication problem.
3. Multiply.4. Simplify. (You can also simplify
before you multiply.)5. Leave improper fractions as is.
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ExamplesExamples
20
9
2
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1611
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Decimal Operations - Decimal Operations - RemindersRemindersMultiplication
◦Line up digits as in whole # mult.◦After multiplying as usual, count up
total places behind decimal point, and move decimal that number of places.
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Decimal Operations - Decimal Operations - RemindersRemindersDivision:
◦Shift decimal in the divisor (outside #) to the right so that you are dividing by a whole #. Shift the decimal in the dividend the same # of places. Now divide as usual.
◦Keep dividing until it ends or repeats.
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Now in your Know It Now in your Know It Notes:Notes:Reciprocal: numerator and
denominator change place (fraction flipped over)
Multiplicative inverse: a number and its reciprocal are called multiplicative inverses
A number times its reciprocal = 1
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Inverse Prop. Of Inverse Prop. Of MultiplicationMultiplicationThe product of a real # (but not
zero) and its reciprocal is 1.Algebraically: For a≠0,
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Integer RulesInteger RulesPositive # • Positive # = Positive # Negative # • Negative # = Positive
# (Same signs = positive answer)
Positive # • Negative # = Negative #
Negative # • Positive # = Negative # (Opposite signs = neg answer)
Same rules for division.
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Important Stuff about Important Stuff about ZeroZero
Zero times a number = zeroZero divided by a number = zeroA number divided by zero =
undefined◦How could you make zero groups of
something? It is not possible, so we get “undefined” instead.