Fraction Review

Addition/subtraction: Adding/subtracting: is combining “like terms” Combining “like terms” is the reverse of the distributive property. What number/variable is common to both terms? Factor out the common term (reverse distributive property)

Addition/subtraction: Adding/subtracting: is combining “like terms” Combining “like terms” is the reverse of the distributive property. What number/variable is common to both terms? Factor out the common term (reverse distributive property)

Combining “like terms” 1.Factor out the common term 2. Add the integers inside the parentheses 3. Multiply the result

Your turn: 1. Combinie “like terms” by showing each step: 1.Factor out the common term 2.Add the integers inside the parentheses 3. Multiply the result

Multiplication What is one half of one half? Multiply “straight across” (numerators times numerators and denominators times denominators) denominators times denominators)

Multiplication is repeated addition 2 used as an addend 4 times 2 used as an addend 4 times 1/3 used as an addend 4 times Multiplication of fractions Multiply “straight across” (numerators times numerators and denominators times denominators) denominators times denominators)

Your turn: 5. Multiply the following. Do not simplify, we’ll do that later. we’ll do that later

Adding Fractions Are these “like fractions”? What do “like fractions” look like? “like fractions” have a common denominator!!! How can get a common denominator without changing the value of the fraction? value of the fraction? Identity property of multiplication: if you multiply a number by ‘1’ the value of the number does not change. the value of the number does not change.

Adding Fractions Identity property of multiplication: if you multiply a number by ‘1’ the value of the number does not change. the value of the number does not change. Do I want you to show the last 3 steps or can you just add the numerators over the common denominator? numerators over the common denominator? For now, no credit if you don’t show the last 3 steps, because too many of you can’t remember how to because too many of you can’t remember how to add fractions unless I link combining “like terms” add fractions unless I link combining “like terms” with the addition of fractions. with the addition of fractions.

Your turn: 9. Add the following “unlike” fractions. Do not simplify, we’ll do that later. simplify, we’ll do that later

Finding the least common denominator What is the quickest way to find the common denominator? Multiply each fraction’s numerator and denominator with the denominator of the other fraction. the denominator of the other fraction. This fraction must now be ‘reduced’.

Finding the least common denominator How can you find the least common denominator? Factor, factor, factor “2” is already a common factor of both denominators. denominators. Multiply the other fraction by the factors of the denominator that are not common. of the denominator that are not common.

Finding the least common denominator How can you find the least common denominator? Factor, factor, factor “3” is missing from the right side denominator. Multiply the right side fraction by 3/3. Multiply the right side fraction by 3/3. Multiply the other fraction by the factors of the denominator that are not common. of the denominator that are not common.

Finding the least common denominator How can you find the least common denominator? Factor, factor, factor “5” is missing from the left side denominator. Multiply the left side fraction by 5/5. Multiply the left side fraction by 5/5. Multiply the other fraction by the factors of the denominator that are not common. of the denominator that are not common.

Your turn: 13. Add the following “unlike” fractions. Do not simplify, we’ll do that later. simplify, we’ll do that later

Division Division by ‘3’ is the same as mulitiplication by ___? Multiplication by the reciprocal of ‘3’ Why is that?

Division Division by ‘2/3’ is the same as mulitiplication by ___? Multiplication by the reciprocal of ‘2/3’

Your turn: Rewrite the expression as multiplication

Divide Fractions I don’t know how to divide fractions. divide fractions. What do I do? Multiply by the reciprocal Can this fraction be reduced?

Your turn: Divide the following. Don’t simplify the result (we’ll do that later) (we’ll do that later)

Simplifying Fractions Yuck!

Simplifying fractions Factor, then “cancel out” common factors from the numerator and denominator from the numerator and denominator

Your turn: Simplify the following fractions by first factoring then by cancelling out common factors between the numerator cancelling out common factors between the numerator and denominator and denominator

Another example Simplify: Name one factor in the expression above.

Your Turn:

Another Example Look for common factors in numerator and denominator in numerator and denominator

Your Turn: 29. Simplify (hint: look for common factors)

BE CAREFUL!!!!! Addition and Subtraction mean: Combine the terms into one term (if you can) No, no, no, no, no!!! If you can’t (unlike terms) they still are connected to each other. Put it into a parentheses.