Primary 6 Foundation Mathematics revision reference

Use this reference beside the Primary 6 Foundation lessons. It brings together selected formulas, words and checks for this course.

Dividing fractions

Dividing asks how many groups of the stated size fit, or how much is in each equal share.

a/b÷ c = a/(bc), a/b÷c/d = a/b × d/c.

Denominators and divisors are never zero. On this page they are positive whole numbers.

Example: 3/4÷1/2 = 3/4 × 2 = 3/2. One and a half half-unit groups fit into three quarters. The answer can be larger than the starting number when dividing by a number smaller than one.

Turn a whole number into a fraction over 1 when needed. Keep the first fraction unchanged and take the reciprocal of the divisor only.

A fraction can also express a quotient: 3÷4 = 3/4 = 0.75. Divide the numerator by the denominator to change a fraction to a decimal.

Decimals and rounding

Estimate before calculating. For multiplication, track place values; for division, scaling both dividend and divisor by the same power of ten leaves the quotient unchanged.

For example, 1.8÷0.3 = 18÷3 = 6. Multiplying only one of the two numbers by 10 would change the answer.

Keep enough digits during working, then round the final answer to the requested accuracy. ≈ means approximately equal.

Percentages

Percent (%) 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 given percentage of the principal.

For example, 20% off $50 is a $10 discount, giving a price of $40.

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.

Angles and composite figures

A triangle’s interior angles add to 180°. Equal sides of an isosceles triangle have equal opposite angles. Every angle of an equilateral triangle is 60°. A right-angled triangle has one 90° angle.

Rectangles and squares have four right angles; a square also has four equal sides. For a composite figure, split it into squares, rectangles or triangles and mark the given lengths. Add areas of separate parts; for perimeter, follow the outside boundary only.

Pie charts and average

A pie chart shows parts of one whole. Compare the sector sizes and read any labels before finding an amount.

average = (total value)/(number of data values).

For a positive number of values, total = average × number of values. If 5 values have average 8, their total is 40.