To put two natural fractions, it is necessary to find their common denominator. These denominators an infinite set, but as much as possible it is possible to simplify calculations, having found a least common multiple of numbers which are denominators of natural fractions. It will also be the smallest common denominator.
It is required to you
- - concept about prime numbers;
- - to know actions with fractions;
- - ability to display number on simple multipliers.
Instruction
1. After fractions are written down, put an equal-sign and draw common feature of fraction. Then calculate the smallest common denominator. For this purpose each of numbers which is a fraction denominator present in the form of set of simple multipliers (the simple multiplier represents number which totally is divided only into number 1 and into itself). As such multipliers can repeat, group them, having specified the number of repetitions of such multipliers in a type of degree.
2. If there is no simple multiplier in decomposition of this number, and in decomposition of another is, we consider that this number exists, just its degree 0. For each of simple multipliers which met in decomposition of numbers, choose the greatest degree of each multiplier and multiply these values. The least common multiple of denominators which is a common denominator of fraction which will turn out as a result of addition will be result.
3. For example, if it is necessary to put fractions 5/18, 3/16 and 7/20, make the following sequence of actions: 1. Spread out all numbers which are denominators of fractions on simple multipliers: 18=2·3 · 316=2·2 · 2·227=2 · 2 · 52. Write down degrees of all simple multipliers: 18=2^1•3^2•5^016=2^4•3^0•5^020=2^2•3^0•5^1 3. Choose multipliers with the biggest degree from each decomposition and find their work: 2^4•3^2•5^1=720.
4. Number 720 is a least common multiple for numbers 18, 16 and 20. At the same time same number is the smallest common denominator for fraction which will turn out as a result of addition of fractions 5/18, 3/16 and 7/20. To find additional multipliers, divide a least common multiple into each of denominators 720/18=40, 720/16=45, 720/20=36. Also multiply the corresponding numerators before their summation by these numbers. At the same time leave a common denominator invariable, it will be equal in the reviewed example to 720.