Alberta Grade 8 Math — Unit: Rational & Irrational Numbers
Organizing IdeaNumber — Number sense is developed through understanding the ways numbers describe the world.
Guiding QuestionHow can the density of the number line contribute to a sense of number?
Learning OutcomeStudents interpret rational and irrational numbers.
This lesson covers: adding, subtracting, multiplying, and dividing any two rational numbers (positive or negative, fractions or decimals);
applying the conventional order of operations to expressions involving rational numbers;
using estimation to assess the reasonableness of a sum, difference, product, or quotient.
One Set of Rules, Two New Wrinkles
A rational number is any number that can be written as
ab,
where a and b are integers and b isn’t zero. So
34, −0.5,
−72,
and 6 are all rational.
Adding, subtracting, multiplying, and dividing rationals follows the same logic as on whole numbers,
with two added wrinkles: signs (positive and negative) and mixed forms
(a fraction and a decimal in the same problem). This lesson works through the four operations,
then applies the conventional order of operations, then shows how
estimation catches errors.
Quick recap: a fraction is rational. A terminating decimal is rational. A repeating decimal
is rational. Any integer is rational. Numbers like √2 and π are not rational
— they’re irrational, and these operations don’t simplify them the same way.
Add and Subtract
Pick a problem. Click Next step to walk through the calculation one move at a time.
Subtracting a number is the same as adding its opposite. So 0.7 − 1.2 = 0.7 + (−1.2).
With a fraction or decimal in front of a minus sign, that flip can simplify the work.
Multiply and Divide
The sign rules are short. Once the sign is figured out, the rest is just arithmetic.
positive × / ÷ positive→positive
negative × / ÷ negative→positive
positive × / ÷ negative→negative
negative × / ÷ positive→negative
Dividing by a fraction is the same as multiplying by its reciprocal. So
12 ÷
14 becomes
12 ×
41. Some teachers call this
“keep, change, flip.”
Order of Operations
When an expression mixes operations, the order matters. BEDMAS tells you which
to evaluate first.
Bbrackets
Eexponents
DMdivide / multiply
ASadd / subtract
D and M happen left-to-right at the same level; same for A and S. Pick a problem and step through.
Estimation Catches Mistakes
Before you compute, round each number to something friendly and estimate the answer in your head.
Then compare your exact answer to the estimate. If they’re far apart, recheck your work.
Estimation is fast, the exact calculation is slow. Use the fast check on every problem —
a sign error or a misplaced decimal point will jump out.
Round 1 of 3
Single-Operation Sprint
Pick the correct answer.
Pick the correct answer to start.
What You Now Know
The four operations on rationals work just like on whole numbers, with two extras: track the sign
(the sign rules are short and worth memorising), and match the form when one operand is a fraction
and the other a decimal — convert one to match the other before computing.
For expressions with multiple operations, follow BEDMAS: brackets first, then exponents, then
division and multiplication left-to-right, then addition and subtraction left-to-right. And on every calculation,
a quick mental estimate tells you whether the exact answer is in the right ballpark.
These same operations and rules extend to real-world problems — money, measurement, recipes,
sports stats. The computation is the same; only the units change.