## Number sentences

Like we saw earlier, we can use symbols and variables to turn wordy number problems into **number sentences** or **equations**. Most of the time, replacing words with symbols gives us a clearer and more succinct expression.

What if I know that the sum of a number and $3$3is $16$16? In words, I would say:

The sum of a number and $3$3 is $16$16

Or I could assign a variable (or variable) to this unknown number, calling it $x$`x`, and use maths to rewrite the expression as a **number sentence**:

$x+3=16$`x`+3=16

## Key words

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 indicate the operation of **addition.**

**left, subtract, minus, remain, decrease, use, less than, difference, take away, fewer, shorter** are all words that 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 sentences (turning words into maths) is a bit like translating them into another language! But it does get easier with practice.

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#### Example

##### Making maths out of cricket balls

What if we knew that cricket balls cost $99$99 cents more that rugby balls? We could call the cost of a cricket ball $c$`c` and the cost of a rugby ball $r$`r`, and use maths to write:

$c=r+0.99$`c`=`r`+0.99

Then, if we knew that a cricket ball costs $\$2.25$$2.25 we can write our equation like this:

$2.25=r+0.99$2.25=`r`+0.99

If we want to find the cost of the rugby ball then we will need solve the equation.

$2.25$2.25 |
$=$= |
$r+0.99$`r`+0.99 |

$2.25-0.99$2.25−0.99 |
$=$= |
$r$`r` |

$r$`r` |
$=$= |
$1.26$1.26 |

So a rugby ball costs $\$1.26$$1.26

#### Examples

##### Question 1

$x$`x` divided by $20$20 equals $5$5. Construct an equation and solve for $x$`x`.

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##### Question 2

The product of $5$5 with the sum of $x$`x` and $7$7 is $50$50. Construct an equation and solve for $x$`x`.

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##### Question 3

The sum of four consecutive odd numbers is $64$64.

a) Let $x$`x` be the smallest of the numbers. Form an equation and solve for $x$`x`.

b) Find all 4 numbers.