Work out Fractions
For many people, fractions are the first big stumbling block in math. The concept of fractions is a difficult one, and it doesn't help that you must learn special terms to describe them. Because they also have special rules for adding, subtracting, multiplying and dividing, fractions make any equation more intimidating. However, with practice, anyone can learn to work out fractions and solve equations that include them.
Contents
Steps
Understanding Fractions
- Know that a fraction is a way of indicating parts of a whole. The top number, called the numerator, represents the number of parts you're working with. The bottom number, called the denominator, represents how many parts there are in total.
- Keep in mind that you can write fractions on the same line using a slash; the left number is the numerator and the right number is the denominator. If you are working with fractions that are on the same line, it's helpful to rewrite them so the numerator is on top of the denominator.
- For example, if you have 1 piece of a pizza that was cut into 4 pieces, you have 1/4 of a pizza. If you have 7/3 pizzas, you have two whole pizzas plus 1 piece of a pizza that was cut into three pieces.
Compound Fractions versus Simple Fractions
- Understand that a compound fraction has a whole number and a fraction, such as 2 1/3 or 45 1/2. Usually, you must convert a compound fraction to a simple fraction before you can add, subtract, multiply or divide it.
- Convert compound fractions by multiplying the whole number by the denominator of the fraction and then adding the numerator. Write a new fraction with the total as the numerator and the same number as the denominator.
- For example, 2 1/3 becomes 7/3: 2 times 3, plus 1.
- Change a simple fraction to a compound fraction by dividing the numerator by the denominator. Write down the whole number you get by dividing and make the remainder the numerator of the fraction. The denominator is the same.
- For example, for the fraction 7/3, divide 7 by 3 to get 2 with the remainder of one; the compound fraction is 2 1/3. You can only do this if the numerator is larger than the denominator.
Adding and Subtracting Fractions
- Find the common denominator of the fractions you are adding or subtracting. To do this, you can multiply the denominators together, then multiply each numerator by the number you used to find its denominator. Sometimes you can find a common denominator that is a smaller number than you would get if you simply multiplied denominators together.
- For example, to add the fractions 1/2 and 1/3, you first make the denominators the same by multiplying them together to get 6. Multiply 1 by 3 to get 3 as the new numerator for the first fraction. Multiply 1 by 2 to get 2 as the new numerator for the second fraction. Your new fractions are 3/6 and 2/6.
- If you study the fractions, you'll see that 3 is half of 6, which is the same as saying 1/2, and 2 is one-third of 6, which is the same as saying 1/3. The fractions 1/3 and 1/6 would have a common denominator of 6, because 3 goes into 6 2 times. Therefore, 1/3 becomes 2/6.
- Add the numerators together and keep the same denominator.
- For example, 3/6 and 2/6 becomes 5/6; 2/6 and 1/6 becomes 3/6.
- Use the same technique to subtract fractions as you did to add fractions by finding the common denominator first, but instead of adding, subtract the numerator of the second fraction from the numerator of the first.
- For example, to subtract 1/3 from 1/2, first rewrite the fractions as 3/6 and 2/6, then subtract 2 from 3 to get 1. The result is 1/6.
- Reduce the fraction if you can by dividing the numerator and denominator by the same number.
- For example, a fraction such as 5/6 can't be reduced, but 3/6 can be reduced to 1/2 by dividing both halves by 3.
- Convert the fraction to a compound fraction if the numerator is larger than the denominator.
Multiplying and Dividing Fractions
- Multiply the numerators and denominators separately to get the result.
- For example, when you multiply 1/2 and 1/3, you will get 1/6 (1 times 1 over 2 times 3). It's not necessary to find a common denominator when multiplying. Reduce or convert the result if you can.
- To divide fractions, turn the second fraction upside down, the multiply them together.
- For example, if you want to divide 1/2 by 1/3, first rewrite the equation so the second fraction is 3/1. Multiply 1/2 by 3/1. The result will be 3/2. Reduce the fraction or convert it to a compound fraction if you can.
Working with More Complicated Fractions
- Work out all fractions in the same way, no matter how complicated they look.
- To add and subtract more than two fractions, you can find a common denominator for all of them or you can work with them in pairs from left to right.
- For example, to add 1/2, 1/3 and 1/4, you can change them 6/12, 4/12, and 3/12 to get 13/12 or you can add 3/6 and 2/6 to get 5/6, then add 5/6 to 1/4 (10/12 plus 3/12) to get 13/12. Convert this to 1 1/12.
Tips
- Try to remember that you already know a lot more math than you think. It's like a language that you already know how to speak, but are trying to learn to read and write as well.
