Arithmetic practice and the order of operations

The order of operations

Example: $12 + 3 \times 4 = 12 + 12 = 24$, but $(12 + 3) \times 4 = 15 \times 4 = 60$.

With nested brackets, start with the innermost ( ), then the braces { }.

Multiplying and dividing decimals

To multiply, ignore the decimal points, multiply the whole numbers, then count the total number of decimal places in both factors.

Example: for $2.4 \times 0.35$, $24 \times 35 = 840$ and there are $1 + 2 = 3$ decimal places, so the answer is $0.84$.

To divide, multiply both numbers by 10 or 100 so that the divisor becomes a whole number: $7.56 \div 1.8 = 75.6 \div 18 = 4.2$.

Calculation shortcuts

• $37 \times 25 + 63 \times 25 = 100 \times 25 = 2500$
• $25 \times 37 \times 4 = 37 \times 100 = 3700$ (remember $25 \times 4 = 100$ and $125 \times 8 = 1000$)
• $99 \times 46 = (100 - 1) \times 46 = 4600 - 46 = 4554$
• $1 + 2 + \cdots + 100$: pair the first and last terms to get $50$ pairs of $101$, so the sum is $5050$.