Here are some important concepts you'll need to know to solve our "musical" math exercises!

- ♪ For the "bonus operation" problems, you will need to remember your order of operations.
- ♪ The following device can help you memorize: "Please excuse my dear Aunt Sally," or PEMDAS!
- -This stands for the order:
- Parentheses
- Exponents
- Multiplication
- Division
- Addition
- Subtraction

- ♪ In our math problems, we won't see parentheses or exponents.
- -Let's explore some examples.
- 6 - 2 + 3 = 7. In this example, we have only subtraction and addition. The order between subtraction and addition does NOT matter. So we solve from left to right.
- 8 ÷ 4 × 5 = 10. In this example, we have only division and addition. The order between division and multiplication does NOT matter. So we solve from left to right.
- 12 ÷ 3 + 7 = 11. In this example, we have division and addition. Here, the order matters, but we can still solve from left to right.
- 15 - 6 × 2 = 3. In this example, we have subtraction and multiplication. Here, the order matters, so we do NOT solve left to right. First, multiply 6 by 2 (which equals 12). Then subtract that from 15. 15 - 12 = 3.

- ♪ Mixed number conversion: since our input currently supports improper fractions only, you will have to convert between these two forms.
- -Let's use 3 and 1/2 as an example.
- You take the whole number (3) and multiply that by the denominator of the fraction (2).
- Then add the numerator of the fraction (1) to that product (3 × 2 = 6 and 6 + 1 = 7).
- Put that number over the fraction denominator (7/2) and you're done!

- -3 and 1/2 = 7/2
- ♪ Dividing by Fractions
- -Dividing by a fraction is the same as multiplying by that fraction's reciprocal.
- -A
**reciprocal**is the opposite of a fraction. You flip the numerator and the denominator. For example: the reciprocal of 5/9 is 9/5. - -Let's use 1/2 ÷ 1/4 as an example.
- Find the reciprocal of the divisor (the second number) only. In this problem the divisor is 1/4
- Now our problem is 1/2 × 4/1
- Solve: 1 × 4 = 4 and 2 × 1 = 2. 4/2 = 2

- -1/2 ÷ 1/4 = 2

And that's it! Practice lots and have fun!