mastering+fractions

//**Note:** If there is a 1 or any whole number that has to operated with another fraction, always put the whole number as a fraction over 1. For example, 2 will become 2/1.//

If the fractions have different denominators, change both fractions to the same denominator by finding the least common multiple. For example, (2/3 + 4/5). Least common multiple of 3 and 5 is 15. The numerators would be multiplied by the opposite fraction's denominator. So 2 is multiplied by 5 and 4 is multiplied by 3. This becomes, (10/15 +12/15). Follow the first rule by just adding the numerators. The final answer is (22/15). This is in improper fraction. Always simplify the fraction to lowest terms. To change it to mixed fraction form, divide 22 by 15. This gives you a whole of 1 and a remainder of 7. The answer is 1 7/15. If the fractions are in mixed form, change it to improper form and also make sure they have the same denominator before adding.
 * Addition:** When the fractions have the same denominator, only add the numerators. For example, (4/7 + 2/7 = 6/7).

If the fractions have different denominators, change both fractions to the same denominator by finding the least common multiple. For example, (4/5 - 2/3). Least common multiple of 5 and 3 is 15. The numerators would be multiplied by the opposite fraction's denominator. So 4 is multiplied by 3 and 2 is multiplied by 5. This becomes, (12/15 - 10/15). Follow the first rule by just subtracting the numerators. The final answer is (2/15). Always simplify the fraction to lowest terms. If the fractions are in mixed form, change it to improper form and also make sure they have the same denominator before subtracting.
 * Subtraction:** When the fractions have the same denominator, only subtract the numerators. For example, (4/7- 2/7 = 2/7).

It doesn't matter if they have different denominators. For example, (4/7 x 6/9 =24/63). 24 and 63 have a common factor of 3 so you can simplify it to 8/21. Always simplify the fraction to lowest terms. If the fractions are in mixed form, change it to improper form before multiplying.
 * Multiplication:** For multiplication, multiply the numerators together and the denominators together.

There is a rule of multiplying the first fraction with the reciprocal of the second fraction. The reciprocal is when the numerator and the denominator switch places. For example, 2/3 becomes 3/2. If it is a whole number like 5, it becomes 1/5. Here is an example of a division question: (4/7) / (2/3) The second fraction's reciprocal is 3/2. Now multiply the first fraction with the reciprocal. (4/7 x 3/2). Follow the rules of multiplication. Numerators multiplied together and denominators multiplied together. The answer is 12/14 but in simplest form, it is 6/7. Always simplify the fraction to lowest terms. If the fractions are in mixed form, change it to improper form before dividing.
 * Division:** For division, again it does not matter if they have different denominators.

//If any questions, please send kbalachandran a message.//