Distributive Law

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Expanding Equations:

Example One - Fruit Face

This fruit face has 2 oranges, 1 apple and 1 banana.

(a) Write this algebraically using variables such as a for apple, b for banana and o for orange.
(b) How many of each type of fruit would be in 10 fruit faces? Write this in algebra.

Answer:
(a) 1a + 1b + 2o
(b) 10 × (1a + 1b + 2o) = 10a + 10b + 20o

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Example Two - Bumper Cars

A bumper car manufacturer produces carnival sets, each with 5 white and 4 yellow bumper cars.

(a) Write this algebraically using variables such as w for a white car and y for a yellow car.
(b) How many of each colour would be in 3 carnival sets? Write this in algebra.

Answer:
(a) 5w + 4y
(b) 3 × (5w + 4y) = 15w + 12y

Factorizing Equations:

Factorizing is grouping terms by their greatest common factor. It is the reverse of expanding equations.

Example Three - Rock Concert

Each band at a gig has 3 guitars and 1 drum kit.

(a) Write this algebraically using variables such as g for guitar and d for drum kit.
(b) A mix-up has occurred with the storage of music equipment. There are 15 guitars and 5 drum kits in a van. How many bands are playing? Write this in algebra.

Answer:
(a) 3g + 1d
(b) 15g + 5d = 5 × (3g + 1d)
There are 5 bands playing.

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Example Four - Lego Monkey

Each Lego monkey uses 300 orange, 20 grey and 10 black blocks.

(a) Write this algebraically using variables such as b for black, g for grey and o for orange.
(b) How many Lego monkeys can be made from 1800 orange, 180 grey and 60 black blocks? Write this in algebra.

Answer:
(a) 300 o + 20 g + 10 b
(b) 1800 o + 20 g + 10 b = 6 × (300 o + 20 g + 10 b)
Six monkeys can be made.