Primary 5 Mathematics

The number being multiplied.

The number you multiply by.

The answer.

Product per part.

Ones, tens, hundreds...

Carry over when sum ≥ 10.

Vertical layout.

Rough check.

The number being divided, e.g. 864 in 864 ÷ 24.

The number you divide by, e.g. 24 in 864 ÷ 24.

The answer of a division, e.g. 36 in 864 ÷ 24 = 36.

What is left over, e.g. 18 in 738 ÷ 24 = 30 remainder 18.

The step-by-step vertical division layout.

Estimating how many times the divisor fits, e.g. 24 fits into 86 about 3 times (24×3=72).

Bring the next digit down to keep dividing, e.g. bring the 4 down after dividing 86.

Quotient × divisor (+ remainder) must equal the dividend: 36 × 24 = 864 ✓.

The answer after multiplying, e.g. 16 in 12 × 13 = 16.

The top number; numerators multiply together.

The bottom number; denominators multiply together.

Cancel diagonally before multiplying, e.g. cancel 2 and 4 in 23 × 14.

"12 of 13" means 12 × 13.

A fraction with numerator 1, e.g. 16.

Divide one numerator and one denominator by a common factor, e.g. 2 and 4 both by 2.

A fraction smaller than 1; multiplying two proper fractions gives an even smaller one.

A price reduction; "20% off" means you pay 80% of the original price.

The price before the discount, e.g. $100.

The price actually paid after discounting.

A fraction of 100, e.g. 80% = 80100 = 0.8.

Original price − selling price, e.g. 100 − 80 = $20.

Paying 50%, e.g. half of $60 is $30.

Turn the percentage into a decimal before multiplying: 80% = 0.8.

Discounting twice — multiply in turn, e.g. 20% off then 10% off = ×0.8 then ×0.9.

A number with a decimal point, e.g. 0.3, 1.25.

The dot between the whole and decimal parts.

How many digits after the point: 0.3 has 1, 0.15 has 2.

The answer after multiplying, e.g. 0.06 in 0.2 × 0.3.

Rough check: 0.2 × 0.3 must be less than 0.2.

Step one ignores the point: multiply as whole numbers, 2 × 3 = 6.

Count total decimal places from the right, then place the point.

A zero at the end, e.g. 0.180 can be written 0.18.

The fraction flipped, e.g. the reciprocal of 34 is 43.

Swap top and bottom, e.g. 13 becomes 31.

Dividing by a fraction = multiplying by its reciprocal.

Mnemonic: Keep the first fraction, Change ÷ to ×, Flip the second.

Numerator bigger than denominator, e.g. 32.

A whole plus a proper fraction, e.g. 32 = 1½.

What division asks: 1 ÷ 14 counts the quarters in one whole → 4.

Check backwards: answer × divisor = dividend.

The number you divide by, e.g. 0.2 in 0.6 ÷ 0.2.

The number being divided, e.g. 0.6 in 0.6 ÷ 0.2.

The answer of the division.

Move both decimal points together so the divisor becomes whole.

Multiply both numbers by 10 (or 100); the quotient is unchanged.

The goal of decimal division: make the divisor whole like 2 or 4 first.

Scaling both numbers equally keeps the quotient: 62 = 6020 = 3.

Answer × original divisor = dividend: 3 × 0.2 = 0.6 ✓.

1,000,000 — where seven-digit numbers begin.

A number with seven digits, e.g. 1,234,567.

Each digit's value: millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, ones.

A single symbol 0–9 used to build numbers.

Split by place value: 1,234,567 = 1,000,000 + 200,000 + 30,000 + …

Commas every three digits from the right: 1,234,567.

Zeros hold empty places: the 0s in 4,050,600 cannot be dropped.

Compare digit counts first, then digits from the left.

A number with exactly two factors, 1 and itself, e.g. 7.

A number with more than two factors, e.g. 12.

A number that divides another exactly: 3 is a factor of 12.

A factor that is itself prime: 12 = 2 × 2 × 3.

A diagram splitting step by step: 12 → 4 × 3 → 2 × 2 × 3.

Divides with no remainder: 15 is divisible by 3 and 5.

Repeated prime factors as powers: 12 = 2² × 3.

1 has only one factor — neither prime nor composite.

The reward a bank pays you, or the charge for borrowing.

The starting amount saved or borrowed, e.g. $1000.

The yearly interest as a percent of the principal, e.g. 5% p.a.

Meaning "each year", written p.a.

How many years (periods), e.g. 2 years.

Each year uses the original principal: I = P × r × t.

Principal plus interest: $1000 + $100 = $1100.

Turn the percent into a decimal first: 5% = 0.05.

A letter standing for an unknown number, e.g. a, x.

A maths phrase with letters, e.g. a + 3, 5x.

Replace the letter with a number: if a = 5, then a + 3 = 5 + 3.

The number before the letter: 5 in 5x.

Terms with the same letter combine: 2a + 3a = 5a.

a × 5 is written 5a; a × b is ab — the × sign is dropped.

Find the letter's value: x + 2 = 7 → x = 5.

Substitute back to verify: 5 + 2 = 7 ✓.

Replacing a value with an approximation: 38 ≈ 40.

A quick rough calculation to sanity-check an answer.

Round to the tens place: 38 → 40, 23 → 20.

462 → 500 (tens digit 6 rounds up).

Check the digit AFTER the place kept: ≥5 rounds up, <5 rounds down.

Estimates use the ≈ sign, not =.

Round up on 8 (38→40); round down on 3 (23→20).

Estimates catch errors: 38 × 22 should be near 40 × 20 = 800.

The flat pattern made by cutting a solid open and laying it out.

A solid with six rectangular faces, like a tissue box.

A flat surface of a solid; a cuboid has 6.

Matching pairs facing each other, equal in size: top/bottom, front/back, left/right.

Folding the net along its lines rebuilds the solid.

The same cuboid can unfold into cross, T and other layouts.

A genuine net never folds two faces onto each other.

Adding all faces of the net gives the surface area.

A 3D shape: cuboid, cube, cylinder and so on.

The flat pattern of a cut-open solid.

Six identical square faces, like a die.

A prism with two triangular bases and three rectangular faces.

One square base plus four triangular faces.

Two circular bases plus one curved side (unrolled: a rectangle).

How many faces: cube 6, triangular prism 5.

A true net folds without gaps or overlaps.

The angle between a sector's two radii, measured in degrees.

One complete turn = 360°, like a clock hand going once round.

Angle unit: a circle is 360°, a right angle 90°.

The sector's share of the circle, e.g. 14, 512.

A quarter turn = 90°.

A half turn = 180°, a straight line.

A clock has 12 marks, each 360 ÷ 12 = 30° apart.

The tool for measuring angles, a semicircular scale 0–180°.

Turning a shape around a fixed point.

The way a clock turns: top → right → bottom → left.

Against the clock: top → left → bottom → right.

The fixed point that stays still while the shape turns.

A quarter turn.

Clockwise or anticlockwise — always state it.

Where the shape points after turning; the shape itself is unchanged.

90° is one quarter of a full turn.

The bottom edge of the parallelogram, e.g. the 6 cm side.

The perpendicular distance from the top edge to the base — must make a right angle.

Two lines meeting at a 90° right angle.

The amount of flat space a shape covers, in square units.

Area units, e.g. cm², m².

The two tilted sides — they are NOT the height.

Cut along the height and move the triangle to the other side, turning it into a rectangle.

Area = base × height, written A = b × h.

How much space a solid takes, e.g. how many 1 cm³ cubes fill a box.

The longest edge of the cuboid, e.g. 5 cm.

The sideways edge of the cuboid, e.g. 3 cm.

The vertical edge of the cuboid, e.g. 2 cm.

Volume units, e.g. cm³, m³.

A solid with six rectangular faces, like a tissue box.

A solid with six square faces, like a die; volume = edge × edge × edge.

Think of volume in layers: fill the base, then stack up.

A quadrilateral with four equal sides, like a tilted diamond.

A line joining opposite vertices; a rhombus has two.

The two diagonals of a rhombus cross at 90°.

The flat space covered, in cm².

Rhombus area = diagonal × diagonal ÷ 2.

Divide by 2 — always part of the rhombus formula.

One diagonal splits the rhombus into two congruent triangles.

A rhombus whose diagonals are equal is a square.

A shape whose points are all equidistant from the centre.

The middle point of the circle, usually called O.

The distance from centre to edge, e.g. 5 cm.

A chord through the centre touching both sides; d = 2r.

The distance all the way around the circle.

Circumference ÷ diameter for ANY circle, about 3.14.

Total boundary length; for a circle it is the circumference.

Half a circle; perimeter = πr + d (arc plus diameter).

A quadrilateral with exactly one pair of parallel sides, like a triangle with its top cut off.

The top parallel side, e.g. 3 cm.

The bottom parallel side, e.g. 5 cm.

The perpendicular distance between the two bases.

Sides that never meet; a trapezium has exactly one pair.

The two non-parallel sides on the sides.

Two identical trapeziums flipped together form a parallelogram.

Area = (upper base + lower base) × height ÷ 2.

The volume of a 1 m × 1 m × 1 m cube — very big.

A common capacity unit; a large soft drink bottle is about 1.5 L.

How much a container can hold.

m³ → L multiply by 1000; L → m³ divide by 1000.

Small amounts use mL: a juice box is about 250 mL.

Because 100 × 100 × 100 = 1,000,000.

Changing between units — mind the direction.

A capacity example: home water tanks are about 1–2 m³.

Flat space a circle covers: A = πr².

About 3.14; used in both area and circumference.

Centre-to-edge distance; the area formula needs it.

r × r: for r = 3, r² = 9.

Area units cm²; circumference is plain cm.

Circle area ÷ 2.

Halve the diameter first: d = 10 → r = 5.

Circumference 2πr is a length; area πr² multiplies r twice.

Distance covered per unit time, e.g. 50 km per hour.

How far something travels, e.g. 100 km.

How long it takes, e.g. 2 hours.

Kilometres per hour; the usual speed unit.

Metres per second; used for running and in physics.

Speed = distance ÷ time.

The "per" idea: per hour, per second — match units when comparing.

Bigger is faster: 80 km/h beats 70 km/h.

A part of a circle: two radii and an arc, like a pizza slice.

The angle between the sector's radii, e.g. 90°.

Angle ÷ 360: 90° is a quarter of the circle.

A 90° sector.

A 180° sector.

The curved edge of the sector.

Circle area × central angle ÷ 360.

From a sector's area you can find the whole circle's area.

Overall rate of a whole journey: total distance ÷ total time.

All legs added: outward + return.

All time added, including stops.

The journey out.

The journey back.

Two speeds cannot simply be (a+b)÷2 — the times differ.

Only equal times allow direct averaging.

Look only at the two grand totals: distance and time.

The big capacity unit: a large soft drink is about 1.5 L.

The small unit: a juice box holds about 250 mL.

The fixed conversion rate.

L → mL multiply by 1000: 2.5 L = 2500 mL.

mL → L divide by 1000: 3500 mL = 3.5 L.

×1000 shifts right 3 places; ÷1000 shifts left 3.

Convert everything to one unit before adding.

A jug marked in mL for measuring.

The big weight unit: a bag of rice is 5 kg.

The small unit: an apple weighs about 200 g.

The fixed rate — same pattern as capacity.

kg → g multiply by 1000: 1.2 kg = 1200 g.

g → kg divide by 1000: 4500 g = 4.5 kg.

The measuring tool, marked in g and kg.

Convert to one unit before comparing.

1 t = 1000 kg, for very heavy things (lorries).

A chart joining data points with lines, used to show trends over time.

The bottom line, usually time, e.g. 8am, 9am, 10am.

The side line showing the quantity, e.g. temperature (°C).

One plotted value, e.g. the point at 9am is 25°C.

The overall direction: rising, falling or flat.

The change between neighbouring points, e.g. 22 → 25 rises by 3.

How much each grid square stands for, e.g. 2°C per square.

The spacing on the time axis, e.g. one square per hour.

The "levelled-out" value of a data set: total ÷ count.

The result of adding all values.

How many values there are, e.g. 3 scores.

Divide the total equally, e.g. 12 sweets shared by 3 gives 4 each.

Bigger than the mean, e.g. with mean 4, a score of 5 is above average.

Smaller than the mean.

The unknown value found from the mean and the rest.

Mean × count = total, used to verify.

A circle divided into sectors showing each part's share of the whole.

One "slice" of the pie, bounded by two radii and an arc.

The full circle = 100%, e.g. the whole class.

Each part's share; all shares add to 100%.

The angle of a sector; a full circle is 360°.

A 25% sector = a 90° slice.

The key telling you what each colour means.

Percentage × 360°, e.g. 25% × 360° = 90°.

The top number: how many parts are taken.

The bottom number: how many equal parts the whole is divided into.

Every part must be the same size.

A fraction with numerator 1, like 14.

The horizontal line in a fraction, e.g. the middle of 38.

The complete object being divided; a whole pizza counts as 1.

A fraction with numerator smaller than denominator, like 38; always less than 1.

Read the denominator first: 38 is read "three eighths".

The result of adding.

The line between numerator and denominator.

The part that remains.

Each number being added, e.g. 15 and 25 in 15 + 25.

The bottom number; unchanged in same-denominator addition.

The top number; directly added in same-denominator addition.

Reduce the answer to simplest form, e.g. 48 = 12.

The complete amount, written as 55 or 88 where numerator equals denominator.

A number that divides another exactly, e.g. 1, 2, 4, 8 are factors of 8.

A factor shared by numerator and denominator.

The fraction that cannot be simplified further, like 34.

Fractions with the same value but different forms, like 68 and 34.

The largest common factor, e.g. GCF of 12 and 16 is 4.

Divide numerator and denominator by the same number; the value stays the same.

A number divisible by 2; if both parts are even you can at least halve, e.g. 812 → 46.

The act of simplifying, e.g. 1015 reduces to 23.

A shared denominator for both fractions.

Multiply numerator and denominator by the same number.

The smallest common multiple, e.g. LCM of 3 and 4 is 12.

Reduce the answer to simplest form.

The result of multiplying by 1, 2, 3…, e.g. multiples of 4 are 4, 8, 12, 16.

Changing fractions so their denominators match.

Check equivalence by cross multiplying: 13 = 412 because 1×12 = 3×4.

Rough check with decimals, e.g. 13 + 14 ≈ 0.33 + 0.25 ≈ 0.58.

The result of subtracting.

The number being subtracted from.

The number that is subtracted.

The part that remains.

The top number; directly subtracted in same-denominator subtraction.

The bottom number; unchanged in subtraction.

Reduce after subtracting, e.g. 48 = 12.

The fraction left over, e.g. eat 28 and 68 remains.