Content

• To step
• Method 1 of 4: Multiplying fractions
• Method 2 of 4: Dividing fractions
• Method 3 of 4: Converting mixed fractions to improper fractions
• Method 4 of 4: Addition and subtraction of fractions
• Tips
• Warnings

Fractions sometimes seem a bit tricky to solve, but with a little practice and some extra knowledge, this will become much easier. Once you have understood the basics, you will notice that solving fractions is actually a piece of cake.

To step

Method 1 of 4: Multiplying fractions

1. Make sure you are dealing with two fractions. These instructions only work with two fractions. If you are dealing with a mixed fraction, first convert it to an improper fraction ...
2. Multiply numerator 1 by numerator 2, and multiply denominator 1 by denominator 2.
   • So, let's say we have 1/2 x 3/4, then we multiply like this: 1 x 3 and 2 x 4. The answer is 3/8.

Method 2 of 4: Dividing fractions

1. Make sure you are dealing with two fractions. Again, this process ONLY works if you have converted any mixed fractions into improper fractions.
2. Reverse the second fraction. It doesn't matter which fraction, as long as you don't reverse both fractions.
3. Change the division sign to a multiplication.
   • If the problem was 8/15 ÷ 3/4, this will now be 8/15 x 4/3.
4. Multiply both numerators and both denominators.
   • 8 x 4 = 32 and 15 x 3 = 45, so the answer is 32/45.

Method 3 of 4: Converting mixed fractions to improper fractions

1. Convert mixed fractions to improper fractions. Improper fractions are those fractions whose numerator is greater than the denominator. (For example, 5/17.) If you are multiplication and division, you must convert mixed fractions to improper fractions before continuing with the problem.
   • Suppose you have the mixed fraction 3 2/5.
2. Take the whole number (the number before the fraction) and multiply it by the denominator.
   • In our example this would be: 3 x 5 = 15.
3. Add that answer to the counter.
   • In our example: 15 + 2 = 17
4. Place this number as a new numerator above the fraction line and you have an improper fraction.
   • In our case this will be: 17/5.

Method 4 of 4: Addition and subtraction of fractions

1. Find the least common multiple of the denominators (the bottom number). For both addition and subtraction of fractions, you start with the same thing. Find the smallest number that fits both denominators.
   • For example, if you take the fractions 1/4 and 1/6, the least common multiple is 12. (4x3 = 12, 6x2 = 12)
2. Multiply the fractions depending on the least common multiple. Remember not to change the fraction, just how it is expressed. Think of a pizza - 1/2 or 2/4 of a pizza is the same amount of pizza, just expressed differently.
   • Determine how many times the current denominator goes into the least common multiple. For 1/4, 4 x 3 = 12. For 1/6, 6 x 2 = 12.
   • Multiply the numerator and denominator of the fraction by that number. For ¼, you multiply both 1 and 4 by 3, which works out to 3/12. 1/6 x 2 = 2/12. Now this statement looks like this: 3/12 + 2/12 or 3/12 - 2/12.
3. Add or subtract the two numerators (top number), but NOT the denominators. This is not allowed because you want to calculate how much of this fraction you have in total. If you also include the denominators, the fractions will change.
   • So for 3/12 + 2/12 the answer is 5/12. For 3/12 - 2/12, it's 1/12

Tips

• Make sure you have mastered the basics of math skills (addition, subtraction, multiplication and division) so that the calculations do not take unnecessarily long and are difficult.
• The reverse of an integer is to put that number as the denominator in a fraction, with a 1 as the numerator. For example, 5 becomes 1/5.
• You can multiply and divide mixed fractions without converting them to improper fractions first. But then you need different math skills, and the calculation becomes a lot more complex. So it is generally better to follow the route of improper fractions.
• Remember: Dividing is the same as multiplying by the reverse.
• When you take the reverse of a negative number, the minus sign remains in the numerator.

Warnings

• Ask your teacher if you should convert improper fractions to mixed fractions.
  • For example, 3 1/4 instead of 13/4.
• Convert mixed fractions to improper fractions before you begin.
• Ask your teacher whether or not you should simplify the answers.
  • For example, 2/5 cannot be simplified further, but 16/40 can.