Fraction ReviewFraction Review

Addition/subtraction:Addition/subtraction:Adding/subtractingAdding/subtracting: is combining “like terms”: is combining “like terms”

3

Combining “like terms” is the Combining “like terms” is the reverse of the distributive propertyreverse of the distributive property..

3432

What number/variable is common to both terms?What number/variable is common to both terms?

Factor out the common term (reverse distributive property)Factor out the common term (reverse distributive property)

)42(3 )6(*3 36

Addition/subtraction:Addition/subtraction:Adding/subtractingAdding/subtracting: is combining “like terms”: is combining “like terms”

7

1

Combining “like terms” is the Combining “like terms” is the reverse of the distributive propertyreverse of the distributive property..

7

3

7

2

What number/variable is common to both terms?What number/variable is common to both terms?

Factor out the common term (reverse distributive property)Factor out the common term (reverse distributive property)

)32(7

1 )5(

7

1

7

5

Combining “like terms”Combining “like terms”1.1.Factor out the common termFactor out the common term

2. Add the integers inside the parentheses2. Add the integers inside the parentheses

3. Multiply the result3. Multiply the result

33 42 xx

)42(3 x

)6(3x

36x

Your turn:Your turn:

1. 1.

15

3

15

2

33 7275

11

2

11

5

Combinie “like terms” by showing each step:Combinie “like terms” by showing each step:1.1.Factor out the common termFactor out the common term2.2.Add the integers inside the parenthesesAdd the integers inside the parentheses3. Multiply the result3. Multiply the result

2. 2.

3. 3.

4. 4.

55 315 xx

MultiplicationMultiplication

4

1

2

1*2

1 What is one half of one half?What is one half of one half?

Multiply “straight across” Multiply “straight across” (numerators times numerators and(numerators times numerators and denominators times denominators)denominators times denominators)

Multiplication is Multiplication is repeated repeated additionaddition

2 used as an addend 4 times2 used as an addend 4 times2222

3

1*1

4

3

1

3

1

3

1

3

1

3

4

2*4

1/3 used as an addend 4 times1/3 used as an addend 4 times3

1*4

Multiplication of fractionsMultiplication of fractions3

1*4

3

4

Multiply “straight across” (numerators times numerators andMultiply “straight across” (numerators times numerators and denominators times denominators)denominators times denominators)

Your turn:Your turn:

5. 5.

9

6*5

45

3*7

2

7

2*8

x

Multiply the following. Do not simplify,Multiply the following. Do not simplify, we’ll do that later.we’ll do that later.

6. 6.

7. 7.

8. 8. 4

6*

5

3 xx

Adding FractionsAdding FractionsAre these “like fractions”?Are these “like fractions”?

7

3

5

2

What do “like fractions” look like?What do “like fractions” look like?

7

3*5

5

5

2*7

7

““like fractions” have a common denominator!!!like fractions” have a common denominator!!!

7

3

5

2

How can get a common denominator without changing theHow can get a common denominator without changing the value of the fraction?value of the fraction?

Identity property of multiplicationIdentity property of multiplication: if you multiply a number by ‘1’: if you multiply a number by ‘1’ the value of the number does not change.the value of the number does not change.

35

15

35

14 )1514(

35

1

Adding FractionsAdding Fractions

7

3*5

5

5

2*7

7

7

3

5

2

Identity property of multiplicationIdentity property of multiplication: if you multiply a number by ‘1’: if you multiply a number by ‘1’ the value of the number does not change.the value of the number does not change.

35

15

35

14

)1514(35

1 )29(

35

1

35

29

Do I want you to show the last 3 steps or can you just add theDo 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?

35

1514 For now, For now, no credit if you don’t show the last 3 steps,no credit if you don’t show the last 3 steps, because too many of you can’t remember how tobecause 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:Your turn:

9. 9.

3

6

5

4

4

3

3

2

4

2

2x

Add the following “unlike” fractions. Do notAdd the following “unlike” fractions. Do not simplify, we’ll do that later.simplify, we’ll do that later.

10. 10.

11. 11.

12. 12. 9

6

2

2 2 xx

Finding the Finding the leastleast common common denominatordenominator

What is the What is the quickest wayquickest way to find the common denominator? to find the common denominator?

10

3*6

1

Multiply each fraction’s numerator and denominator withMultiply each fraction’s numerator and denominator with the denominator of the other fraction.the denominator of the other fraction.

10

3*

6

6

6

1*

10

10

60

18

60

10 )1810(

60

1

60

28

This fraction must now be ‘reduced’.This fraction must now be ‘reduced’.

Finding the Finding the leastleast common common denominatordenominator

How can you find the How can you find the leastleast common denominator? common denominator?

5*2

7*3*2

1

Factor, factor, factorFactor, factor, factor

““2” is already a common factor of both2” is already a common factor of both denominators.denominators.

Multiply the other fraction by the factorsMultiply the other fraction by the factors of the denominator that are of the denominator that are not common.not common.

Finding the Finding the leastleast common common denominatordenominator

How can you find the How can you find the leastleast common denominator? common denominator?

5*2

7*3*2

1

Factor, factor, factorFactor, factor, factor

10

7*

3

3

6

1

““3” is missing from the right side denominator.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 factorsMultiply the other fraction by the factors of the denominator that are of the denominator that are not common.not common.

Finding the Finding the leastleast common common denominatordenominator

How can you find the How can you find the leastleast common denominator? common denominator?

5*2

7*3*2

1

Factor, factor, factorFactor, factor, factor

10

7

3

3

6

1

““5” is missing from the left side denominator.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 factorsMultiply the other fraction by the factors of the denominator that are of the denominator that are not common.not common.

30

21

30

5

10

7

3

3

6

1

5

5

)215(30

1

30

26

Your turn:Your turn:

13. 13.

3

6

5

4

4

3

3

2

4

2

2x

Add the following “unlike” fractions. Do notAdd the following “unlike” fractions. Do not simplify, we’ll do that later.simplify, we’ll do that later.

14. 14.

15. 15.

16. 16. 7

6

2

2 2 xx

DivisionDivision

Division by ‘3’ is the same as mulitiplication by ___?Division by ‘3’ is the same as mulitiplication by ___?

Multiplication by the reciprocal of ‘3’Multiplication by the reciprocal of ‘3’

Why is that?Why is that?

3

x

x*3

1

1*3

1 x

3

x

DivisionDivision

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

Multiplication by the reciprocal of ‘2/3’Multiplication by the reciprocal of ‘2/3’

32x

x*2

3

Your turn:Your turn:

7

x

Rewrite the expression as multiplicationRewrite the expression as multiplication

18.18.5

2

17. 17. 19.19.352

7*12

1

12

7

Divide FractionsDivide Fractions

?7

5

3

2 I I don’t knowdon’t know how to how to

divide fractions.divide fractions.

What do I do?What do I do?

Multiply by the reciprocalMultiply by the reciprocal

15

14

5

7*3

2

Can this fraction be reduced?Can this fraction be reduced?

Your turn:Your turn:

5

4

3x

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

22.22.5

2

20. 20. 21.21.352

2*3*2*3

7*5*

5*3

3*2*2

Simplifying FractionsSimplifying Fractions

36

35*

15

12540

420 Yuck!Yuck!

2*3*2*3

7*5*

5*3

3*2*2

9

7

3*3

7*5

5*3

3*2

2*2

2

9

7

Simplifying fractionsSimplifying fractions

Factor, then “cancel out” common factorsFactor, then “cancel out” common factors from the numerator and denominatorfrom the numerator and denominator72

24

6*6*2

3*2*2*2*1

36*2

3*8*1

3*2*3*2*2

3*2*2*2*1

3

1

Your turn:Your turn:

105

30

Simplify the following fractions by first factoring then bySimplify the following fractions by first factoring then by cancelling out common factors between the numeratorcancelling out common factors between the numerator and denominatorand denominator

25.25. 105

23. 23. 24.24.36

168

26.26.xyz

zyx

18

9 32

Another exampleAnother exampleSimplify:Simplify:

)2)(4(5

)4)(2)(1(

xx

xxx

)2)(4(5

)4)(2)(1(

xx

xxx

Name one Name one factorfactor in the expression above. in the expression above.

)2(*)4(*5

)4(*)2(*)1(

xx

xxx

5

)1( x

Your Turn:Your Turn:

)12)(2(

)3)(12(

xx

xx27.27.

28.28. )1)(23(6

)23)(1)(5(3 2

xxx

xxxx

Another ExampleAnother Example

9

342

2

x

xx Look for common factorsLook for common factors in numerator and denominatorin numerator and denominator

)3)(3(

)1)(3(

xx

xx)3(

)1(

x

x

Your Turn:Your Turn:

29. 29. Simplify (Simplify (hinthint: look for common factors): look for common factors)

)3(

1223

xx

xxx

BE CAREFUL!!!!!BE CAREFUL!!!!!

)9(7

7

x

x

Addition and Subtraction mean:Addition and Subtraction mean:

Combine the terms into Combine the terms into one termone term (if you can) (if you can)

No, no, no, no, no!!!No, no, no, no, no!!!

If you can’t (unlike terms) If you can’t (unlike terms) they still are connected to each other.they still are connected to each other.

Put it into a parentheses.Put it into a parentheses.

)9(7

)7(

x

x