NZ Level 5
Lesson

## Working with fractions and decimals

Decimals and fractions are just different ways to name numbersWhen we work with number problems that have fractions and/or decimals in them, place value is one of the most important things to remember. Not only does it tell us the value of our digits, it helps us change from fractions to decimals, or vice-versa.

## From fractions to decimals

We have seen how we can add and subtract fractions but sometimes, we need to work with fractions and show our answer in decimals. If the denominator of our fraction is tenths, hundredths or thousandths, we can readily change our answer to a decimal. If not, we may need an extra step where we think of an equivalent fraction in tenths, hundredths or thousandths. Let's work through some examples in Video 1.

#### Worked example

##### Question 1

Evaluate $\frac{4}{5}+\frac{3}{100}+\frac{1}{500}$45+3100+1500, expressing your answer as a decimal.

## Whole numbers

Sometimes our problems include whole numbers and in this short video, you can see how it can be worked out. Just like the first video, you can see there are different ways to solve these problems, so you might find one way easier than the other.

## From decimals to fractions

Working in the other direction, our work on how to add decimals up to the thousandths, as well as how to subtract decimals up to thousandths, can help when we need to work with decimals but express an answer in fractions. However, again there are a few different ways to solve these kinds of questions.

We can express our answer as a mixed number, such as $2\frac{1}{2}$212, or an improper fraction, such as $\frac{5}{2}$52. Both are correct. We also make sure that our fraction is in its simplest form. Let's work through some different examples in Video 3.

Remember!

Writing a fraction in its simplest form means there are no common factors between the numerator and the denominator.

If the numerator and denominator are both even, then they will at least have $2$2 as a factor. However, there may be more, so make sure you check!

#### Worked Examples

##### Question 2

Evaluate $0.313+0.185$0.313+0.185 expressing your answer as a fraction

##### Question 3

Evaluate $0.72-0.18$0.720.18 expressing your answer as a fraction

### Outcomes

#### NA5-3

Understand operations on fractions, decimals, percentages, and integers