Primary 6 Mathematics revision reference

Use this beside the Primary 6 lessons. Keep diagrams, quantities and units visible when choosing a method.

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.

Percentages and ratio

If a part P is p% of a whole W, then W = P÷p/100, with p nonzero. Choose the whole before calculating.

percentage change = change/(original value) × 100%.

The ratio a:b compares quantities in the same unit. It describes a + b equal ratio units in total. A share is its number of ratio units multiplied by the value of one unit.

Example: divide 60 in the ratio 2:3. There are 5 units, each worth 12, so the shares are 24 and 36. A ratio of 2:3 makes the first share 2/5 of the total, not 2/3.

This course writes ratios using whole-number terms. Simplify by dividing all terms by their common factor.

Algebra notation and equations

3a means 3 × a; a/3 means a÷3.
Combine like terms: 3a + 2a = 5a. Unlike terms such as a + 2 stay separate.
Substitution replaces a letter with its given value. Write the replacement before calculating.
To solve an equation, keep both sides equal by applying the same operation to each side. Check the answer in the original equation.

For 3a + 2 = 17, subtract 2 from each side, then divide each side by 3: a = 5. This course uses simple linear expressions without brackets and equations with whole-number coefficients.

Circles, composite figures and volume

For radius r and diameter d = 2r:

C = 2π r = π d, A = π r².

Use the value of π specified in the question. A semicircle has area (1/2)π r² and perimeter π r + 2r; the straight diameter counts. A quarter circle has area (1/4)π r² and perimeter (1/2)π r + 2r.

For a cuboid, V = lwh, so h = V÷(lw). For a cube, V = s³, so s = cube root of V. √ means square root and ∛ means cube root. An area uses square units; a volume uses cubic units.

Split a composite figure into familiar shapes without overlaps or gaps. Count only its outer boundary for perimeter. Angle sums and stated shape properties help recover missing dimensions.

Average

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

The number of values must be positive. If 4 numbers have average 7, their total is 28. Combining two groups requires combining their totals and their numbers of values; averaging their averages works only when the groups have equal sizes.