Hong Kong
Stage 1 - Stage 3

# Number Problems

Lesson

## Number Sentences

I own $2$2 adult dogs, and they had a litter of $5$5 puppies. How many dogs do I have in total?

We know we could write this using maths:

$2$2 (dogs that I started with) + $5$5 (new cute puppies)

And, we could solve this by completing the operation:

$2+5=7$2+5=7

So I have seven dogs in total.

This is an example of a number sentence. We used the numbers in the worded statement to form a mathematical statement.

We can also write expressions and equations from worded statements even if we don't have all the numbers we need.

## Writing Equations

#### Example

I had some pocket money saved. Then my mother gave me $\$25$$25, for cleaning the car and now I have a total of \62$$62.

Let's call the starting amount $p$p. (In fact if you are not told what to call it you can call it anything you like!)

The key to writing equations like this is to be able to identify key words in the sentences.

### Is it addition or subtraction?

more, sum, add, join, altogether, in total, both, combined, increase are all words that would indicate the operation of addition.

left, subtract, minus, remain, decrease, use, less than, difference, take away, fewer, shorter are all words that would indicate the operation of subtraction.

### Is it multiplication or division?

product of, multiplied by, times, of, double, triple, groups are all words that would indicate the operation of multiplication.

quotient of, divided by, per, into, out of , ratio of, unit price, cut up, separated , share equally, split, half, parts are all words that would indicate the operation of division.

is, are, was,were, will be, gives, yields, sold for are all words that would indicate an equals sign.

Mathematising (the idea of turning words into maths) is a bit like translating into another language! But it does get easier with practice.

Let's have a look at some.

#### Examples

##### Question 1

Firstly we need to identify the key words in the statement:

And then we write the statement using mathematical symbols:

Here are a few more to watch before you attempt the exercise.

##### Question 2

The sum of $x$x and $10$10 is $25$25. Construct an equation and solve for the value of $x$x.

##### Question 3

The product of $5$5 with the difference of $5$5 from $x$x equals $-15$15. Construct an equation and solve for the value of $x$x.