Math Tests - mathematics practice questions

All operations 1-20

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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

Copy link to this topic. expand learning text

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

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Basic arithmetic operations


Sum - outcome of adding two or more numbers
summand + summand = addend + addend = sum
Related expressions: addition, more than, total, plus, increase, altogether
Examples:
Calculate the sum of 12 and 3.
Answer: 12+3=15
What is ten more than twelve?
Answer: 10+12=22

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.
Answer: 12−3=9
What number is ten less then twelve?
Answer: 12−10=2
What is 10 fewer than 50?
Answer: 50−10=40

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



   
   

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