# CLASS-7DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION

DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION -

The distributive property of multiplication over addition is a fundamental property of numbers that combines both addition and multiplication. It states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Mathematically, for any numbers a, b, and c:-

a x (b + c) = (a x b) + (a x c)

Explanation -

• Left Side:-   a x (b + c) means you first add b and c and then multiply the result by a.
• Right Side:-  (a x b) + (a x c) means you multiply a by b and aaa by c separately, and then add the two products.

For any three rational number

a         c             e

------, ------, and -----, we have:-

b         d             f

a           c          e           a         c          a         e

------ x (------ + ------) = (----- x -----) + (----- x -----)

b           d          f           b         d          b         f

Example:-

- 2            3            5

Let, a = -----, b = -----, c = ------

3           4          - 6

Let prove,  a x (b + c) = (a x b) + (a x c)

- 2          3           5

Left side :- a x (b + c) = ------ x (------ + ------)

3           4        - 6

- 2           3          5

= ------- x (------ - ------)

3           4           6

- 2          (3 x 3) - (5 x 2)

= ------ x {-----------------}

3                 12

- 2         (9 - 10)

= ------ x -----------

3             12

- 2        - 1         (-) (-) 2

= ------ x ------ = --------------

3          12               36

1

=  -------

18

- 2          3         - 2          5

Right Side :- (a x b) + (a x c) = (------ x ------) + (------ x ------)

3          4            3       - 6

- 1        - 5

= ------ - -------

2           9

{(-1) x 9} - {(-5) x 2}

= ------------------------

18

(-9) + 10         1

= ------------ = ------

18             18