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Substitute into algebraic expressions II



By using an expression, or rule, with a variable, we can allow for different circumstances, or changes. Let's suppose you're ordering your school books for the year, and you're told to order some extra books. The amount you need to order (let's call this y) will be different to someone else, so we can use an expression such as this to calculate your total:

y + $5$5

In Video 1, we'll see what happens when we substitute some numbers in place of our variable, and then what happens when we have to reduce the number of books we need to order. We also look at working with a thermometer, where we may need to add or subtract to numbers below zero. These are called negative numbers.

Working with directed numbers

Sometimes we need to add or subtract a directed number, or a number that has a positive (+) or negative (-) sign. It helps to think about what that actually means, in order to remember some special rules we use in some cases.

In Video 2, let's take a look at adding and subtracting, and see what happens when we try to subtract a negative number!

vanilla with toppings

When our expression contains more than one variable, we use exactly the same process we've used so far, but we just have more steps. Here's a quick video where we need to substitute two variables with numbers. As well as that, we need to add or subtract decimals or fractions. So where does 'vanilla' come into it? Watch Video 3 and all will be revealed.


Substituting a variable for a value means we can solve our expressions. If we have more than one variable, we just use the same process, with more steps. The order of operations is the same when we have variables, so we can follow those rules as well!


Worked Examples

Question 1

Find the value of $v+9$v+9 when $v=-8$v=8.

Question 2

Find the value of $2-r$2r when $r=-3$r=3.

Question 3

Find the value of $u+v+27$u+v+27 if $u$u is $-36$36 and $v$v is $48$48.

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