Class 6 math formulas

HCF and LCM of two numbers

HCF(a, b) × LCM(a, b) = a × b

Holds for two positive integers. It does not always hold for three or more numbers.

Even and odd

even = 2n, odd = 2n + 1 (n = 0, 1, 2, …)

A number divides another exactly

a = bq + r, 0 ≤ r < b

q is the quotient and r the remainder. If r = 0, b divides a exactly.

Add or subtract like fractions

a/c + b/c = (a + b)/c

Unlike fractions

a/b + c/d = (ad + bc) / (bd)

First make a common denominator (LCM), then add or subtract the numerators.

Multiply fractions

(a/b) × (c/d) = (a × c) / (b × d)

Divide fractions

(a/b) ÷ (c/d) = (a/b) × (d/c)

Mixed number to improper fraction

a b/c = (a × c + b) / c

Decimal place value

0.abc = a/10 + b/100 + c/1000

Ratio

a : b = a/b

Units must match. Write the ratio in lowest terms.

Proportion

a : b = c : d ⇒ ad = bc

Percentage

percentage = (part / whole) × 100

Percentage of a quantity

p% of x = (p / 100) × x

Percentage increase or decrease

change % = (difference / original) × 100

Add like terms

ax + bx = (a + b)x

Linear equation in one variable

ax + b = c ⇒ x = (c − b) / a

a ≠ 0. Adding, subtracting, multiplying or dividing both sides by the same non-zero number keeps the equality.

Angles on a straight line

∠AOB + ∠BOC = 180°

Angles around a point

sum of angles around a point = 360°

Complementary angles

α + β = 90°

Supplementary angles

α + β = 180°

Vertically opposite angles

α = β

When two lines cross, vertically opposite angles are equal.

Angle sum of a triangle

∠A + ∠B + ∠C = 180°

Exterior angle of a triangle

exterior angle = sum of two opposite interior angles

Perimeter of a rectangle

P = 2(l + b)

Area of a rectangle

A = l × b

Perimeter of a square

P = 4a

Area of a square

A = a²

Area of a triangle

A = (1/2) × base × height

Area of a parallelogram

A = base × height

Arithmetic mean

mean = (sum of the numbers) / (how many numbers)