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.

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!

ExamplesExamples

24

29

24

20

24

96

5

8

3

1

9

24

9

63

9

87

3

23

9

87

2

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.

ExamplesExamples

16

5

3

3

48

15

6

5

8

3

11

42

11

10

5

2111

10

5

14

1

2

1

2

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.

ExamplesExamples

20

9

2

2

40

18

5

6

8

3

6

5

8

3

25

88

10

11

5

1611

10

5

13

8

5

1

2

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.

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.

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

Inverse Prop. Of Inverse Prop. Of MultiplicationMultiplicationThe product of a real # (but not

zero) and its reciprocal is 1.Algebraically: For a≠0,

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.

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.