Simplifying and upscaling ratios is a process to change how a ratio looks using multiplying and dividing. Whatever we do to one part of a ratio we need to do the same thing to the other parts.

When asked to split something in a given ratio we need to divide by the total number of parts first. We can then upscale our ratio by this amount for our final answer. They may use language like "split", "share" or "divide" to indicate that this is what we need to do.

This module is converting ratios to fractions, and also back the other way. This skill is very useful with more difficult ratio problems.

This is a less common aspect of ratio problems. We will know to use this when the language is comparative. For example: "more than", "less than", "older than" etc. Ratio is all about finding what one part is worth.

When given more than one ratio to work with we need to convert our ratios until we have one ratio involving all variables. We do this by finding a common multiple between the given ratios and upscaling accordingly.

More advanced ratio problems is about understanding the relationship between one part of a ratio and the others. Once we find that we can form an equation that we can solve. It is also common to use the ratio to fraction conversions we practiced earlier in the block.

Without a calculator we tend to use common percentages and then multiply and divide if necessary. The ones that we use the most are 50%, 25% and 10%. When using a calculator we use decimal multipliers as this translates well to the rest of our percentage work.

In non calculator questions we will use the previous module to help us find a percentage before adding or subtracting this from the original amount. With a calculator we will use our multiplier work from before, remembering that we always start from 100%.

Reverse percentages are used when we are not starting from 100%. We may be at a lower percentage, or a percentage change may have already taken place. With a calculator we will always go to 1%, without a calculator it is usually easiest to go to 10% first.

When finding the percentage change we always do what we are talking about divided by what we started with, then multiplied by 100. This may be called the loss, gain, increase, decrease, increase etc. They can word it in many different ways, but the process is always the same.

We use compound interest when we have a repeated percentage change. We use our percentage multipliers from before and raise them to the power of how many times we repeat the increase/decrease.

Venn diagrams are used to represent information and help us understand overlaps between particular groups. We always need to make sure we start from the middle and work out so that the data does not get counted more than once!

Probability trees are a great tool to help when more than one event occurs. When we go along branches we multiply, when we have more than one option at the end we add the probabilities together. We need to be particularly careful when one event has a direct effect on the other. For example once a counter is taken from a bag this will mean there are less counters in the bag to choose from.

This video is about converting recurring decimals to fractions, and also going back the other way. The important part here is getting the recurring part directly next to the decimal point in two separate ways. We can then subtract these from eachother to cancel the recurring part out.

The following worksheet will revisit all of the skills you have practiced throughout this block. This is a good chance to see where your ratio and probability is at and to get feedback on what may be worth recapping! Try and answer each question to the best of your ability, and if you need reminding you can watch the videos above. Good luck!