Mathematics exam 5 pdf

Multiplying Fractions

a

b

× d

c

=

a

b

×

×

c

d

Multiplying fractions is one of the easiest operations to

perform. To multiply fractions, simply multiply the

numerators and the denominators, writing each in the

respective place over or under the fraction bar.

Example

4

5

×

6

7

=

2

3

4

5

Dividing Fractions

a

b

÷ d

c

=

a

b

×

d

c

=

a

b

×

×

d

c

Dividing fractions is the same thing as multiplying frac￾tions by their reciprocals. To find the reciprocal of any

number, switch its numerator and denominator.

For example, the reciprocals of the following numbers

are:

1

3

=

3

1

= 3 x =

1

x

4

5

=

5

4

5 =

1

5

When dividing fractions, simply multiply the divi￾dend by the divisor’s reciprocal to get the answer.

Example

1

2

2

1

÷

3

4

=

1

2

2

1

×

4

3

=

4

6

8

3

=

1

2

6

1

Adding and Subtracting Fractions

a

b

× d

c

=

a

b

×

×

c

d

a

b

+ d

c

=

ad

b

+

d

bc

■ To add or subtract fractions with like denomina￾tors, just add or subtract the numerators and

leave the denominator as it is.

Example

1

7

+

5

7

=

6

7

and

5

8

−

2

8

=

3

8

■ To add or subtract fractions with unlike denomi￾nators, you must find the least common denom￾inator, or LCD.

For example, for the denominators 8 and 12,

24 would be the LCD because 8 × 3 = 24, and

12 × 2 = 24. In other words, the LCD is the

smallest number divisible by each of the

denominators.

Once you know the LCD, convert each fraction

to its new form by multiplying both the numera￾tor and denominator by the necessary number to

get the LCD, and then add or subtract the new

numerators.

Example

1

3

+

2

5

=

5

5

(

(

1

3

)

)

+

3

3

(

(

2

5

)

)

= 1

5

5

+ 1

6

5

=

1

1

1

5

–NUMBER OPERATIONS AND NUMBER SENSE–

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