Simple fractions

Multiply numerators together and denominators together. You can cancel common factors between numerators and denominators before multiplying. For example, 2/3 × 3/5 = 2/5.

Replace division by a fraction with multiplication by its reciprocal: invert the second fraction. Then multiply numerators and denominators and simplify. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6.

Use a common denominator. Add the numerators with their signs, then simplify.

The least common multiple is the smallest positive number divisible by both given numbers. List their multiples and find the first shared one. You can also use LCM(a, b) = a × b ÷ GCD(a, b). For example, LCM(4, 6) = 12.

First calculate the sum in parentheses. Subtracting a negative number means adding its positive opposite.

Perform fraction multiplication or division before addition. To multiply, multiply numerators and denominators; to divide, multiply by the reciprocal of the second fraction. For addition, use a common denominator, add the numerators and simplify.

To find a/b of a number, divide the number by denominator b and multiply by numerator a. For example, 3/4 of 20 is 20 ÷ 4 × 3 = 15.

Negative numbers are less than zero and positive numbers. Of negative numbers, the one farther from zero is smaller.

Both fractions refer to the same original whole. Add them, then use the combined fraction and its mass to find the whole mass.

Divide numerator and denominator by the same common factor. Using their greatest common divisor simplifies the fraction in one step. It is fully simplified when no common factor greater than 1 remains.