MULTIPLY

Write out the fractions with a multiply sign between them.

See if the product can be simplified by looking for common factors in the numerators and denominators. For example, if there is an even number in the denominators and another even number in the denominators, 2 is a common factor, and the even numerator and denominator can by divided by 2. Similarly, look for other common factors and divide by them until no more division is possible.

Finally, multiply all the numerators together on top and multiply all the denominators together on the bottom, and that is the resultant product as a fraction. Sometimes you will end up with 1 in the denominator, so the product is a whole number and the denominator is discarded.

DIVISION

You convert this into a multiplication by turning the divisor fraction upside down so that numerator and denominator change places. Now you can follow the rules of multiplication.

ADDITION (SUBTRACTION)

When adding or subtracting fractions the first thing to do is to find a number which all the denominators divide into. The lowest common denominator (LCD) is the preferred one because it makes the ensuing arithmetic easier. To find the LCD the easiest way is to break down each denominator into its prime number components. For example, 12 is 2×2×3 and 15 is 3×5. From this we see that 3 is a common factor for both 12 and 15. It’s easy to see that the LCD must contain 3 as a factor, so we build the LCD by writing down 3 and multiplying by all the other factors from both denominators: 3×2×2×5=60. So now we need to express each fraction as a multiple of a 60th. To do this we divide each denominator into 60 and multiply the result by the numerator. So, for example, 7/12 becomes 35/60, because 12 goes into 60 5 times, and 5×7=35. All the fractions in our sum are similarly expressed so we just carry out the add or subtract operations on the numerators. When we get the result we just place it over the LCD, and reduce it to its lowest form by looking for common factors in the numerator and denominator (for example, even numbers so that both can by divided by 2).