**1.1.1. Order of operations**

**B**= Brackets, **O**=Orders and operations, **DM**= division/multiplication, **AS **= addition/subtraction.

You should be able to

- interpret, evaluate and express correctly mathematical expressions using the correct order of operations.
- simplify, add, subtract, multiply and divide fractions and use cross-multiplication
- understand percentages, and be able to convert between fractions, percentages and decimals; you should be able to calculate a percentage change and compute what percentage of a quantity will produce another
- use the laws of exponents to simplify and compute expressions involving powers

Our recommendation is to:

**Test your ability by trying the diagnostic quiz**. You can reattempt it as many times as you want and can leave it part-way through.**Identify which topics need more work.**Make a note of any areas that you are unable to complete in the diagnostic quiz, or areas that you don't feel comfortable with.**Watch the tutorials for these topics,**you can find these below. Then try some practice questions from the mini quiz for that specific topic. If you have questions, please ask on the forum.**Re-try the diagnostic quiz.**And repeat the above steps as necessary until you can pass the diagnostic test. A pass grade is 80%.

Optionally, also see if you can **apply these skills to an economic application **or look at the **additional resources** and **advanced quizzes **at the bottom of the page,

**B**= Brackets, **O**=Orders and operations, **DM**= division/multiplication, **AS **= addition/subtraction.

\(\frac{a}{b}+\frac{c}{b}= \frac{a+c}{b}\), \(c\frac{a}{b}= \frac{ca}{b}\),

\(\frac{a}{b}\times\frac{c}{d}= \frac{ac}{bd}\), \(\frac{a}{b}\div\frac{c}{b}= \frac{a}{b}\frac{d}{c}\)

\(x\% = \frac{x}{100}\),

\(``y\% \text{ of } z" = \frac{y}{100}\times z\)

\(a^nb^n = a^{n+m}\), \(\frac{a^n}{a^m} = a^{n-m}\), \(\frac{a^n}{b^n} = \left(\frac{a}{b}\right)^{n}\),

\(a^nb^n = (ab)^n\), \((a^n)^m = a^{nm}\), \(a^0=1\),
\(a^1=a\), \(a^{-n}= \frac{1}{a^n}\)

You can find **practice quizzes on each topic **in the links above the tutorial videos, or you can take the **diagnostic quiz** as many times as you like to. The **additional resources **gives links to external sources of information and some of these may also have further exercises to try.