Mental Shortcuts - Basic

Mathematics is much more than the tedious, boring memorization of formulas. A mathematician plays around with the equation, recognizes facts and principles seen previously, and builds up on what he/she already knows in order to tackle the great unknown. By simply playing, we are becoming a Mathematician.

You are never too young (or old) to start learning the fundamentals of being a mathematician. Even if all you have is basic knowledge of the order of operations, you can still brainstorm different ideas and suggestions for dealing with potentially nasty calculations. Play around with the numbers, move them about, and tweak them slightly. By identifying patterns, we are able to create new methods to solve problems that have never been seen before!

Here are some tips to get you started:

1. If you are adding and subtracting many numbers, find a nice way to pair them up.
2. If you are multiplying and dividing many numbers, look for common factors.
3. Apply the distributive property in creative ways.
4. When you learn a new formula, think about why it works and explain it to someone else.
5. When you spot a pattern, figure out why it exists.

When calculating $100-36$ by hand, we have to do a lot of "borrowing." It would be much easier to subtract from $99$ instead. Which of the following is equivalent to $100-36$?

$$A) \, 99 - 37 \quad B) \, 99 - 36 \quad C) \, 99 - 35 \quad D) \, 99 + 36$$

If you are subtracting numbers, find a nice way to pair them up:
Since $100 = 1+ 99$, we can rewrite the problem as $1+ 99-36= 99-36+1 = 99-35$. This removed the need for pesky borrowing!

Hence, the answer is $C) \, 99 - 35$.

Back to Quiz: Mental Shortcuts - Basic

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In Basic Mathematics, you will learn about:

• Recognizing Patterns: This is the bread and butter of being a mathematician. A quick recognition of patterns allows you to form hypothesis and ideas, paving a route to attacking the problem.
• Order of Operations: Basic arithmetic skills that shouldn't be forgotten. Doing this quickly will speed up your thought processes on harder problems.
• Fractions, Decimals and Percentages: Relating these concepts with each other allows you to gain a deeper understanding of each of them. Drawing linkages between "different" areas is at the heart of mathematics.
• Angles: An introduction to geometry, that helps you recognize patterns in shapes.