  Math Tests - mathematics practice questions

All operations 1-20 ## Order of operations

When calculations have more than one operation, we have to follow rules for the order of operations:

Step 1:
From left to right, do all multiplication and division.

\$\$100−20×3+5 = 100−60+5\$\$

Step 2:
From left to right, do all addition and subtraction.
\$\$100−60+5 = 45\$\$

However, if there are parentheses or other types of brackets, do all operations that lie inside them first:
\$\$70+36÷(8−2)+1 = 70+36÷6+1=\$\$
\$\$ 70+6+1 = 77\$\$

The order of operations also applies while working inside parentheses:
\$\$8+(3+3×4) = 8+(3+12) \$\$
\$\$= 8+15 = 23\$\$

When you have parentheses inside brackets and braces (sometimes referred as nested parentheses), always work from the inside out. There are multiple types of brackets. The innermost parentheses/round brackets () are calculated first, followed by the brackets/box brackets [] that normally form the next layer, followed by braces/curly brackets {} that form a third layer outwards:
\$\${1+[4×(2+3)+1]}÷11=\$\$
\$\$={1+[4×5+1]}÷11=\$\$
\$\$={1+[20+1]}÷11=\$\$
\$\$={1+21}÷11=22÷11=2\$\$

All operations 1-100 ## Order of operations

When calculations have more than one operation, we have to follow rules for the order of operations:

Step 1:
From left to right, do all multiplication and division.

\$\$100−20×3+5 = 100−60+5\$\$

Step 2:
From left to right, do all addition and subtraction.
\$\$100−60+5 = 45\$\$

However, if there are parentheses or other types of brackets, do all operations that lie inside them first:
\$\$70+36÷(8−2)+1 = 70+36÷6+1=\$\$
\$\$ 70+6+1 = 77\$\$

The order of operations also applies while working inside parentheses:
\$\$8+(3+3×4) = 8+(3+12) \$\$
\$\$= 8+15 = 23\$\$

When you have parentheses inside brackets and braces (sometimes referred as nested parentheses), always work from the inside out. There are multiple types of brackets. The innermost parentheses/round brackets () are calculated first, followed by the brackets/box brackets [] that normally form the next layer, followed by braces/curly brackets {} that form a third layer outwards:
\$\${1+[4×(2+3)+1]}÷11=\$\$
\$\$={1+[4×5+1]}÷11=\$\$
\$\$={1+[20+1]}÷11=\$\$
\$\$={1+21}÷11=22÷11=2\$\$

Translating verbal expressions into equations ## Basic arithmetic operations

Sum - outcome of adding two or more numbers
Related expressions: addition, more than, total, plus, increase, altogether
Examples:
Calculate the sum of 12 and 3.
What is ten more than twelve?

Difference - outcome of subtracting two numbers
minuend – subtrahend = difference
Related expressions: minus, decrease, difference, deduct, less than, fewer than, take away
Examples:
Calculate the difference of 12 and 3.
What number is ten less then twelve?
What is 10 fewer than 50?

The parts you subtract or add are also called terms.

Product - outcome of multiplying two or more numbers.
factor × factor = product
Example: Calculate the product of 12 and 3.
Answer: 12 × 3 = 36

Quotient - outcome of division of two numbers
dividend ÷ divisor = quotient
Example: Calculate the quotient of 12 and 3.
Answer: 12 ÷ 3 = 4