SAT Mc Graw Hill 2011

Adding and Subtracting Fractions

Just as 2 apples +3 apples =5 apples, so 2 sevenths + 3
sevenths =5 sevenths! So it’s easy to add fractions if the
denominators are the same. But if the denominators are
different, just “convert” them so that they arethe same.

When “converting” a fraction, always multiply

(or divide) the numerator and denominator by

the same number.

Example:

If the denominator of one fraction is a multi-

ple of the other denominator, “convert” only

the fraction with the smaller denominator.

Example:

One easy way to add fractions is with “zip-zap-

zup”: cross-multiply for the numerators, and

multiply denominators for the new denomina-

tor. You may have to simplify as the last step.

Example:

Multiplying and Dividing Fractions

To multiply two fractions, just multiply

straight across. Don’tcross-multiply (we’ll dis-

cuss that in the next lesson), and don’tworry

about getting a common denominator (that’s

just for adding and subtracting).

Example:

To multiply a fraction and an integer, just mul-

tiply the integer to the numerator (because an

integer such as 5 can be thought of as 5/1).

y

x

y

x

y

5 x

33

5

3

5

×=

×

×

=

5

6

7

8

5

6

7

8

40

48

42

48

82

48

41

24

+=+= + = =

xx x x

3

2

53

2

5

5

15

6

15

56

15

+=+= + =

+

5

18

4

9

5

18

42

92

5

18

8

18

13

18

+= +

×

×

=+=

12

18

12 6

18 6

2

3

=

÷

÷

=

2

5

25

55

10

25

=

×

×

=

Example:

To divide a number by a fraction, remember

that dividing by a number is the same as multi-

plying by its reciprocal.So just “flip” the second

fraction and multiply.

Example:

Simplifying Fractions

Always try to simplify complicated-looking frac-

tions. To simplify, just multiply or divide top and

bottom by a convenient number or expression. If

the numerator and the denominator have a

common factor, dividetop and bottom by that

common factor. If there are fractions within the

fraction, multiplytop and bottom by the com-

mon denominator of the “little” fractions.

Example:

(Notice that, in the second example, 60 is the common

multiple of all of the “little denominators”: 5, 3, and 4.)

Be careful when “canceling” in fractions. Don’t

“cancel” anything that is not a common factor.

To avoid the common canceling mistakes, be

sure to factor before canceling.

Example:

Right:

x

x

xx

x

x

(^21)
1

11

1

1

−

−

=

()+ ()−

()−

=+

Wrong:

x

x

x

x

x

(^221)
1

−

−

==

2

5

2

3

1

4

60

2

5

2

3

60

1

4

24 40

15

+ 6

=

×+

⎛

⎝⎜

⎞

⎠⎟

×

⎛

⎝⎜

⎞

⎠⎟

=

+

=

44

15

42

2

22 1

2

21

xx

x

+

=

()+

=+

3

7

5

2

3

7

2

5

6

35

m^2

m

mm m

÷=×=

4

7

5

4

7

5

1

45

7

20

7

×= × =

×

=

Lesson 3: Fractions

278 MCGRAW-HILL’S SAT

15

5 x^6

48

40 42