Primary 5 Foundation Mathematics revision reference

Use the section you need, then follow its lesson link for a fuller explanation. This reference belongs to Primary 5 Foundation Mathematics.

Whole-number methods

Read place value before comparing numbers. A zero can hold an empty place.
A factor divides a number exactly; a multiple is a whole-number multiple.
≈ means approximately equal. Round to the requested place, not after every calculation step.
Do brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
In column methods, align place values and exchange a higher unit for 10 of the next smaller unit when needed.

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.

The products in this course include a proper fraction multiplied by a proper or improper fraction, and a fraction multiplied by a whole number.

Decimal methods

Tenths, hundredths and thousandths name the places after the decimal point. 0.6 = 0.60, so compare values rather than the number of digits.

Align decimal points to add and subtract. Multiplication by 10, 100 or 1000 scales every place value; division reverses that scaling. For example, 0.36 × 100 = 36.

Rates and time

total = rate × number of units.

A rate of 4 pages per minute gives 12 pages in 3 minutes if that rate stays constant. Average rates describe a whole interval and need not be the rate at every instant.

For time, find the starting time, finishing time or duration from the other two. Use 60 minutes per hour, including when crossing an hour boundary. In 24-hour time, 14:05 is 2:05 pm.

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.

Area and perimeter

Perimeter is the distance around the outside. Area measures the surface inside.

For a rectangle with length l and width w:

P = 2(l + w), A = lw.

For a square with side s:

P = 4s, A = s².

Use matching length units before multiplying. A rectangle 6 cm by 4 cm has perimeter 20 cm and area 24 cm².

For a composite figure, split the area into rectangles without overlaps or gaps. For its perimeter, count only the outside edges; an internal dividing line is not part of the perimeter.

Angles and data

In ∠ABC, B is the vertex. Angles on a straight line add to 180°; angles at a point add to 360°; vertically opposite angles are equal. Use stated properties and measurements when finding an unknown angle.

Parallel lines stay the same distance apart and do not meet; perpendicular lines meet at a right angle.

For a table or graph, read the headings, labels, units and scale. Equal spaces on a numerical scale represent equal increases.

Read more: Measurement and geometry and Data.