Multiply Fractions
Multiplying fractions is one of the basic skills anyone who deals with fractions should know. To multiply fractions, you just have to multiply their numerators and the denominators, and then simplify your answer if you can. With a little practice, anyone can multiply fractions like a professional mathematician.
Contents
Steps
Multiply Before Simplifying
- Write out the problem. The two fractions should be written down so that their numerators are aligned with their denominators.
- Ex: 2/4 * 2/4
- Multiply the numerators of the two fractions. Since the numerators are both 2, you can multiply 2 * 2 to get 4.
- Multiply the denominators of the two fractions. Since the denominators are both 4, just multiply 4 * 4 to get 16.
- Your answer is a fraction comprised of the new numerator and the new denominator. Your answer is 4/16.
- Simplify. To simplify a fraction, you have to divide its numerator and denominator by the largest number that can go into both numbers evenly. In the case of 4/16, 4 is the largest number that goes into both numbers evenly, so you should divide both the numerator and denominator by 4. Here's how you do it:
- 4/4 = 1
- 16/4 = 4
- Your new fraction and final answer is 1/4.
Simplify Before Multiplying
- Write out the problem. The numerators and denominators of the two fractions should be aligned.
- Ex: 2/4 * 2/4
- Simplify the first fraction. To simplify the first fraction, 2/4, simply divide its numerator and denominator by the largest number that can go into each number. Since the largest number that goes into both 2 and 4 is 2, you should divide both 2 and 4 by 2. Here's how to do it:
- 2/2 = 1
- 4/2 = 2
- Your new fraction is 1/2. It is an equivalent fraction of 2/4, which means it has the same value.
- You can also find the largest number that is divides into both the numerator and denominator by finding the greatest common factor (GCF) of both numbers. To do this, simply list all the factors of those numbers, and choose the largest one that both share. Here's how:
- 2: 1, 2.
- 4: 1, 2, 4.
- 2 is the largest number that divides into both 2 and 4.
- Simplify the second fraction. To finish the process, you need to simplify the second fraction as well as the first. Since the second fraction, 2/4, is the same as the first, your answer will be the same.
- 2/4 = 1/2
- Multiply the numerators of both fractions. Multiply the numerators of the fractions 1/2 and 1/2, which are 1 and 1.
- 1 * 1 = 1.
- Multiply the denominators of both fractions. Multiply the denominators of the fractions 1/2 and 1/2, which are 2 and 2.
- 2 * 2 = 4.
- Place the new numerator over the new denominator. Since you already simplified at the beginning of the problem, you've found your final answer.
- 1/2 * 1/2 = 1/4.
Tips
- To multiply a whole number with a fraction, write it as a fraction over one (e.g., if you wanted to multiply 36, write it as 36/1) and multiply as above.
- Though traditionally fractions are multiplied by multiplying the numerators and then the denominators, you can multiply the denominators first and will get the same answer.
- Multiplying a number by a number less than one will actually make the product smaller than either number.
