Primary 5 Mathematics revision reference

Use this lookup beside the Primary 5 lessons. It collects selected relationships and method reminders; use the lesson links to revisit the reasoning.

Whole numbers and decimals

Do brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.

Multiplying by 10, 100 or 1000 changes the value of every digit by that factor. Dividing reverses that change. For example, 0.47 × 100 = 47 and 47÷100 = 0.47.

Read more: Numbers and relationships and Decimals.

Fraction methods

In a/b, the denominator b names the equal parts in one whole. The numerator a counts those parts; b is positive.

Equivalent fractions have the same value: multiply or divide the top and bottom numbers by the same whole number (not zero).
To add or subtract, first express both fractions in the same fractional unit. Add or subtract the numerators and keep that denominator.
To multiply, multiply numerators and multiply denominators. Simplify common factors before multiplying when this makes the arithmetic easier.

a/b × c/d = ac/(bd).

Convert a mixed number to an improper fraction before multiplying: 2 1/3 = 7/3. To add mixed numbers, either work with improper fractions or combine whole parts and fractional parts, exchanging one whole when needed.

Check: 1 1/2 + 3/4 = 6/4 + 3/4 = 9/4 = 2 1/4. Adding the denominators would change the size of the parts.

A fraction also represents division: a÷ b = a/b for positive b. Divide the numerator by the denominator to obtain a decimal.

Percentages and rates

Percent, written %, means out of 100.

p% of W = p/100 × W.

For a discount, subtract the discount from the original price. For GST, add the tax to the price before tax; use the rate stated in the question. Simple annual interest for one year is the stated percentage of the principal.

Rate is an amount per unit of another quantity:

total amount = rate × number of units.

At $3 per notebook, 4 notebooks cost $12. Keep both units visible when a rate is unfamiliar.

Measurement units

1 km = 1000 m; 1 m = 100 cm.
1 kg = 1000 g; 1 ℓ = 1000 ml.

Larger unit to smaller unit: multiply by the number of smaller units in one larger unit. Reverse the conversion by dividing.

For example, 2 m 35 cm = 235 cm. Keep the unit beside the answer.

Triangles and cuboids

For a triangle, choose a base b and its perpendicular height h:

A = (1/2)bh.

The sloping side is not the height unless it is perpendicular to the chosen base. A triangle with base 8 cm and perpendicular height 5 cm has area 20 cm².

For a cuboid with length l, width w and height h:

V = lwh = base area × h.

A cube of side s has volume s³. Volume uses cubic units. For liquid in a rectangular tank, use the liquid’s height, rather than the tank’s full height.

1 ml = 1 cm³, 1 ℓ = 1000 cm³.

Use internal dimensions when a question gives them for the space holding the liquid.

Angle facts

Angles on a straight line add to 180°.
Angles at a point add to 360°.
Vertically opposite angles are equal.
The interior angles of a triangle add to 180°.
An isosceles triangle has two equal sides and equal angles opposite those sides. An equilateral triangle has three equal sides and three 60° angles.
A parallelogram has opposite sides parallel and equal, and opposite angles equal. A rhombus is a parallelogram with all sides equal. A trapezium has a pair of parallel sides.

Identify a reason for each angle step; a diagram’s appearance alone is not a measurement.