Multiplication & Division of Algebra Fractions

Examples; Simplify the following:

Solution

Step 1

 Note; Each of the values above are single digit;

 Step 2

Cancellation Process; 6 goes in 18 and 24 to give 3 and 4 respectively while 5 goes in 20 and 15 to give 4 and 3 respectively;

Step 3

Cancellation Process; 3 cancels 3, b cancels b, c cancels c, 4 cancels 4 and d cancels d respectively;

Step 1

Note; When dividing any form of fractions be algebra or others, sign must change first to multiplication and when that happens the values to the right becomes inverse. It’s a rule!

Step 2           

Cancellation Process; 3 goes in 12 and 9 to give 4 and 3 while 5 goes in 10 and 15 to give 2 and 3 respectively;

Step 3

Multiply them together;

Step 4

Cancellation Process; c² goes in c⁴ to give c², d³ cancels each other while n goes in n³ to give n²;

Step 1

Note; 3m + 3n is a two digit value which means according to the rule you’ll have to look for common factors;

3m + 3n   ----the common factor will be 3;

3(m + n)

Step 2

Combine them together;

Step 3

Cancellation Process; m + n cancels each other while m cancels m;

Step 1

Note; 4u – 8v and 3u – 6v are two digit values.

Step 2

NUMERATOR (RIGHT)

4u – 8v   ---the common factor will be 4;

4(u – 2v)

Step 3

DENOMINATOR (LEFT)

3u – 6v   ---the common factor will be 3;

3(u – 2v)

Step 4

Combine them together;

Step 5

Cancellation Process; (v – 2u) cancels each other, v cancels each other while u goes in u² to give u;

Step 1

Note; m² – 9 and m² + 2m are two digit values while m² – m – 6 is a three digit value;

Step 2

NUMERATOR (LEFT)

m² – 9   ---actually there’s no common factor here but this can be written thus to derive the common factor;

m² - 3²

(m – 3)²

(m – 3)(m + 3)

Step 3

NUMERATOR (RIGHT)

m² + 2m   ---the common factor of this will be m;

m(m + 2)

Step 4

DENOMINATOR (LEFT)

m² – m – 6        -6m² (x)      (-3m & +2m)

                              -m (+)

m² – 3m + 2m – 6

m(m – 3) + 2(m – 3)

(m – 3)(m + 2)

Step 5

Combine them together;

Step 6

Cancellation Process; (m – 3) cancels each other, (m + 2) cancels each other while m goes in m² to give m;