Lesson 1-3: Mult/Div Real #s The 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 Fractions Find the common denominator. Make equivalent fractions using the new common denominator. Add/sub the numerators. Denominator stays the same. Simplify/reduce. Leave improper fractions as is. Hooray!

Examples 1

2

Multiply Fractions & Mixed #s Change any mixed #s into improper fractions. Multiply numerators. Multiply denominators. Simplify. (You can also simplify before you multiply.) Leave improper fractions as is.

Examples 1 2 2 1

Divide Fractions & Mixed #s Change any mixed #s into improper fractions. Find the reciprocal of the 2nd fraction (the divisor), rewriting the problem as a multiplication problem. Multiply. Simplify. (You can also simplify before you multiply.) Leave improper fractions as is.

Examples 1 2 8 5

Decimal Operations - Reminders Multiplication 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 - Reminders Division: 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 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 Multiplication The product of a real # (but not zero) and its reciprocal is 1. Algebraically: For a≠0,

Integer Rules Positive # • 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 Zero Zero times a number = zero Zero divided by a number = zero A number divided by zero = undefined How could you make zero groups of something? It is not possible, so we get “undefined” instead.