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Day 5: Writing and combining expressionsDescription: Combining expressions
Objective: The purpose of this exercise is to learn how to write an expression with variable values and then to combine expresssions together
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Creating and using Expressions

An expression is a combination of variable and constant values.

Example Expressions

Using the variable ‘n’ to represent how many hours John works for on a given day, create an expression for how much he earns if he is paid 10 euro per day plus 9 euro per hour.

10 + 9 times how many hours he works

= 10 + 9n

Example Expressions

If a toy weighs ‘w’ grams and 12 toys are contained in a box which itself weighs 20 grams, how much does the box of toys weigh?

20 grams (for the box) + 12 times by the weight of each toy

= 20 + 12w

Multiples of expressions

If a teddy bear weighs ‘w’ grams and a doll weighs 15 grams more than the bear, how much do 12 dolls weigh?

Each doll weighs (‘w’ + 15) grams, so 12 dolls weigh:

12 times by (‘w’ + 15) grams.

To work this out we times the 12 by EACH term in the expression (‘w’ + 15)

12 times ‘w’ + 12 times by +15 grams

= 12w + 180

Multiples of expressions

If a teddy bear weighs ‘w’ grams and a doll weighs 15 grams less than the bear, how much do 12 dolls weigh?

Each doll weighs (‘w’ - 15) grams, so 12 dolls weigh:

12 times by (‘w’ - 15) grams.

To work this out we times the 12 by EACH term in the expression (‘w’ - 15)

12 times ‘w’ + 12 times by -15 grams

= 12w - 180

Combining expressions

If a teddy bear weighs ‘w’ grams and a doll weighs 15 grams less than the bear, how much do 10 bears and 12 dolls weigh?

Each doll weighs (‘w’ - 15) grams, so 12 dolls weigh:

12 times by (‘w’ - 15) grams.

= 12w – 180

Each bear weighs ‘w’ grams, so 10 bears weigh:

10 times by ‘w’ grams.

= 10w

In total this is 12w - 180 + 10w

= 22w - 180

Combining expressions in one step

If a teddy bear weighs ‘w’ grams and a doll weighs 15 grams less than the bear, how much do 10 bears and 12 dolls weigh?

= 10(w) + 12(w-15)

remember that +12(w-15)

+12w - 180

= 10w + 12w – 180

= 22w - 180

Combining Expressions

A crate of toys weighs 2000grams.

The crate contains boxes which weigh 50 grams (without contents).

Each box contains 20 dolls which weigh ‘w’ grams.

Write an expression for the weight of the crate when 2 of these boxes are removed

Ans. Each box weighs (50 + 20w)

The crate now weighs 2000 grams less 2(50 + 20w)

= 2000 – 2(50+20w)

= 2000 – 100 -40w

= 1900 – 40w

Combining Expressions with negative values

a) If a teddy bear weighs ‘w’ grams and a doll weighs 15 grams less than the bear, how much do 10 bears and 12 dolls weigh?

= 22w – 180

b) A box weighing 50 grams has 10 bears and 12 dolls in it. How much does the box weigh in total.

Answer: 50 + 22w – 180

= 22w -130

c) A crate weighing 3000 grams has two of these boxes removed from it. How much does the crate weigh now?

Answer: 3000 – 2 (22w – 130)

= 3000 – 44w + 260

= 3260 – 44w

Example question

If a teddy bear weighs  ‘w’ grams and a doll weighs 15 grams morethan the bear, and a box which contains the dolls weighs 120grams when empty.

Write a (simplified) expression for how much a box containing 12 dolls weigh.

Each doll weighs (w+15) grams, so 12 dolls weigh 12 (w+15)

= 12w + 180

Plus the box which weighs 120 grams

= 12w + 180 + 120

= 12w + 300

Simplified means writing in its most simple form.