## Problem solving

When we solve written problems, first we need to identify what it is we are being asked. Once we understand the problem, we can write it out in numbers. With decimals, we follow the same approach, and then use what we have seen in adding and subtracting decimals to solve the number problem.

Some words that help us understand what mathematical operations we need to perform include:

- less
- more
- altogether
- additional
- as well as
- reduced by, and
- fewer

Knowing what to do can depend on how it is written in the number problem though, so watch this introduction video to see how the word more means we need to use addition in one problem, but subtraction in another.

## Problem solving with tenths

Lana and Tom are trying to figure out who has the most cake. This means we are comparing Lana's cakes to Tom's cakes, or working out the difference between the two. Can you work out where we need to use addition and where we need to use subtraction to solve this problem?

Have a look to see how we solve their dilemma, adding decimals up to tenths. They have two cakes each, so we add the mass together for each of them.

## Problem solving with hundredths

Lana and Tom are now comparing the distance they walked to the school fair. To find out who walked the furthest, we add decimals to the hundredths.

## Problem solving with subtraction

Let's use subtraction to find out whether the bus or train covers less distance when it travels to the city. We also work out which order to subtract in, which is an extra thing to consider compared to addition.

Remember!

Order is important when subtracting numbers, including decimals.

Generally we start with the largest number first.

#### Worked examples

##### Question 1

Caitlin was measuring how much she and her brother Bill grew over two years.

In the first year Caitlin grew $6.5$6.5 cm and Bill grew $3.5$3.5 cm. In the second year Caitlin grew $4.4$4.4 cm and Bill grew $7.4$7.4 cm.

How much did Bill grow over the two years?

##### Question 2

Fred is baking a large chocolate cake. The recipe calls for $1.25$1.25 kg of sugar. If Fred has added $0.81$0.81 kg of sugar so far, how much more does he need to add?

##### Question 3

A farmer measured the rainfall her property received in the months of February, March, and April. The amounts are shown in the table.

How much rain did her property receive in total in March and April?

Month |
Rainfall (mm) |

February |
$91.5$91.5 |

March |
$87.9$87.9 |

April |
$74.9$74.9 |