Examine the following fraction, 4/5. It is read as four-fifths or four over five. This is an example of a proper fraction.
Examine the fraction, 8/7, read as eight-sevenths. This is an example of an improper fraction.
Look at the fraction, 1 2/3, read as one and two-thirds. This is an example of a mixed number. It contains a whole number and a fractional unit.
Examine the following fractions: 5/6, 10/12 and 20/24. These fractions are equivalent fractions, meaning they are equal to each other. As you work with fractions, you need to remember to reduce the fraction to its simplest form. The fraction 20/24 reduces to 10/12, which then reduces to 5/6.
Add 3/4 + 2/4 and then subtract 3/4 -- 2/4. Because the denominators are the same, we can explain the steps for both properties at the same time.
Add the numerators: 3 + 2 = 5. Keep the denominator the same. The sum of 3/4 + 2/4 = 5/4. Although this is an improper fraction, it is still considered a correct answer.
Subtract the numerators: 3 -- 2 = 1. Again, keep the denominator the same. The difference of 3/4 -- 2/4 = 1/4.
Add 3/4 + 5/6 and then subtract 3/4 -- 5/6. Even though the denominators are different, we can show the first few steps together.
Find the least common multiple (LCM) of four and six. In this case, the LCM is 12, which becomes the common denominator for both fractions.
Multiply the numerator by three to find the equivalent fraction. Multiply by three because the denominator was multiplied by three to find the LCM. Remember that whatever you do to one side of the fraction, you must also do to the other. 3/4 = 9/12.
Multiply the second numerator, five, by two. Again, multiply the numerator by the same factor that the denominator was multiplied by. 5/6 = 10/12. Now the denominators are the same.
Add the equivalent fractions, 9/12 + 10/12 = 19/12. Subtract the equivalent fractions, 9/12 -- 10/12 = - 1/12. It does not matter if you write the negative sign before the fraction or on either the numerator or denominator. Just remember that you only need one negative sign for the whole fraction. Do not use two because this creates a division problem with a positive solution, which is incorrect.
Examine the fractions 5/6 x 8/9.
Multiply the numerators, 5 x 8 = 40.
Multiply the denominators, 6 x 9 = 54. Therefore, 5/6 x 8/9 = 40/54.
Reduce the fraction. Two goes into both the numerator and denominator evenly. 40/54 = 20/27.
Examine the expression 8/9 ÷ 2/3. To divide the fractions, you must flip the second fraction, also called the reciprocal, thereby turning the problem into a multiplication problem.
Flip the second fraction and change the property to multiplication. 8/9 x 3/2. Multiply straight across. 8 x 3 = 24 and 9 x 2 = 18. The product is 24/18.
Reduce the answer. Six divides into both the numerator and denominator. 24 ÷ 6 = 4 and 18 ÷ 6 = 3. The simplified answer is 4/3.
Compare 8/9 and 7/6. If asked to locate the fractions on a number line, which one is bigger? To compare fractions, use a process called cross-multiplying.
Multiply the first denominator by the second numerator, 9 x 7 = 63. Write 63 above the seven.
Multiply the second denominator by the first numerator, 6 x 8 = 48. Write 48 above the eight. This process provides an easy visual comparison, showing that 63 is bigger than 48, and therefore, 7/6 is larger than 8/9.
Convert 3/4 to a decimal. Divide the numerator by the denominator: 3 ÷ 4 = 0.75
Convert 3/4 to a percentage. Divide the numerator by the denominator: 3 ÷ 4 = 0.75. Multiply by 100, or move the decimal to the right two places: 3/4 = 75 percent.
Convert 5/4 to a mixed number. Divide the numerator by the denominator, 5 ÷ 4 = 1 with a remainder of 1. Write the remainder over the denominator for a solution of 1 and 1/4. If you are using a calculator, the decimal equivalent is 1.25.
Convert 1 and 2/3 to an improper fraction. Multiply the denominator by the whole number, 3 x 1 = 3. Add the numerator, 3 + 2 = 5. Write the sum as the numerator of the improper fraction and keep the original denominator: 5/3.