*A common question students ask teachers is: “When will I ever use Maths after high school?” It may come as a surprise, but actually you apply mathematical concepts everyday of your life in some way or another. Keep reading to find out how Maths is already making your life easier! *

## 1. Saving time

It might seem obvious that to walk the shortest distance possible across a train station, park or road, you should walk in the straightest, most direct line possible. However, most people intuitively know this isn’t the fastest route to take. When given a choice, people often choose to walk diagonally instead to get to the other side faster. This mathematical concept is called the triangle inequality, and it has many applications in geometry and for complex numbers, some of which are even discussed in the HSC Extension 2 course. The triangle inequality says that the length of a side of a triangle is always shorter than or equal to the sum of the other two sides.

Next time you’re running to catch the bus, you may very well be applying the triangle inequality without even knowing it.

## 2. Cooking

No cooking recipe can predict exactly how much food every user wants to make. For example, a curry paste may specify: “Use 1kg of curry paste for 5L of water,” but you only want to use 500mL of water to share between two people. To cook a good curry, you must be able to work out the right amount of curry paste for the amount of water you want to use. The key here is to apply your knowledge of ratios. Ratios are usually taught during Year 7 or Year 8 Mathematics, and a good understanding of this topic will help you cook up the right amount of cookies, pancakes, pies, or whatever food you love to eat, without having to resort to a calculator.

Here’s an example to test your mental arithmetic powers and your curry-cooking ability. Find X if the following is true:

1000 g : 5000 mL = X g : 500 mL

## 3. Saving money

When you want to buy something, you try to buy the best value item for the lowest cost, so that you still have money left over to buy other things. Packaging sizes, however, normally vary between different brands. You may encounter a packet of 12 pencils which are identical to a different brand that sells packets of 8 pencils. If the packet of 12 was $7 and the packet of 8 was $4, you should think about which purchase will give you the most value for your money. This is another application of ratios, as in order to compare the two different prices, you should only compare them for items which are the same size. Which of the packets above should you buy?

## 4. Winning games

Imagine you are at a fair and one stall is offering a coin tossing game. The game costs $2 to play, and it goes like this: Two coins are tossed. If they are both heads, you win $5! If they are not both heads, you get a sticker for trying. Would you play this game?

The answer, in terms of probability concepts, should be no. If people keep playing the game, the owner of the stall will end up making a lot of money, and the people who play the game again and again will be losing their money.

Statistics and probability have a huge range of applications in modern life. The topic of probability is usually introduced in High School in Year 10, and continues to be important in the HSC Mathematics, Extension 1, and Extension 2 courses. Most games designed at a fair or game centre are designed such that the owners always win in the long run. In order to spend your time wisely, you should always consider the probability of winning, and whether or not the game is worth it.

Imagine another situation where you are playing a card game with your friend, and spades are the best cards. You both have five cards each, nine spades have already been played, and there are 14 cards left in the deck. If you have two spades, you can work out that it’s very likely that the other player has less spades than you, and come up with your winning strategy accordingly.

The next time you challenge someone to a card game, see if you can use your knowledge of probability to help you win.

## 5. Organising your schedule

Planning how you use your time is one of the best ways to improve your productivity and a great example of how you use simple arithmetic in your everyday life. Correctly applying rules of addition, subtraction, multiplication or division when planning your time can lead you to make the best decisions now, in order to get the most out of the rest of the week.

For example, a famous author is coming to visit your school from 3:30pm – 4:30pm, and you would really love to go and see her. However it takes 35 mins to get home from school, and you have soccer practice at 7:00pm. It takes 15 mins to get to soccer practice, and after soccer practice you will be exhausted and need to sleep. If you go to see the author, you must plan how much time you will have left to do your homework, and eat dinner. Will there be enough time for you to finish that Maths assignment?

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