Basic Steps of Multiplying Fractions

Congratulations for getting this far. We are expecting you to know the basics of adding fractions and subtracting fractions before you begin here. Guess what? Multiplying fractions is so much easier. It's really just two multiplication problems and a little simplifying. Multiply the tops and then multiply the bottoms and you're good. You'll have no problems here. Ha.

Multiplying Simple Fractions

We'll start off with some simple fractions with small numbers. You know your multiplication tables up to ten. We'll work with single digits. You'll see that we aren't worried about common denominators anymore. As we said, multiply the tops and then multiply the bottoms.

2/5 * 2/3 = ?
• Multiply the numerators to get the numerator of the product: 2 * 2 = 4
• Multiply the denominators to get the denominator of the product: 5 * 3 = 15
• Place the new numerator and denominator together: 4/15
• Simplify: No simplifying for this fraction.
Answer: 2/5 * 2/3 = 4/15


Can you do three fractions this way? Sure.

1/2 * 3/4 * 2/5 = ?
• Multiply the numerators to get the numerator of the product: 1*3*2 = 6
• Multiply the denominators to get the denominator of the product: 2*4*5 = 40
• Place the new numerator and denominator together: 6/40
• Simplify: 6 and 40 have the common factor of 2. Divide the top and bottom by two and get the simplified fraction 3/20.
Answer: 1/2 * 3/4 * 2/5 = 3/20

Multiplying Complex Fractions

Sometimes you're going to get stuck with fractions that are more difficult. If you ever start to measure objects, you might have to work with thirty-seconds. Let's try an example with multiplication that is a bit harder.

5/12 * 5/6 = ?
• Multiply the numerators to get the numerator of the answer: 5 * 5 = 25
• Multiply the denominators to get the denominator of the answer: 12 * 6 = 72
• Place the new numerator and denominator together: 25/72
• Simplify: No simplifying for this fraction.
Answer: 5/12 * 5/6 = 25/72


See? You will use the same process even if you have big numbers to multiply.

Multiplying Mixed Numbers

Remember when we were subtracting mixed numbers? We made improper fractions before we started to do the problem. Our first example is going to use that process.

5 1/3 * 2 4/9 = ?
Convert each factor into an improper fraction:
5 1/3 = 5 + 1/3 = 15/3 + 1/3 = 16/3
2 4/9 = 2 + 4/9 = 18/9 + 4/9 = 22/9
Multiply the numerators: 16 * 22 = 352
Multiply the denominators: 3 * 9 = 27
• Write the raw product with the new numerator and denominator: 352/27
Convert the improper fraction to a whole number:
352/27 = 352 √∑ 27 = 13r1 = 13 1/27
Simplify the fraction: No need for this one.
Answer: 5 1/3 * 2 4/9 = 13 1/27


Remember that the denominators don't matter when you multiply fractions. There are just three steps...

1. Multiply the numerators to get the numerator for your answer.
2. Multiply the denominators to get the denominator for your answer.
3. Simply the answer if you need to.

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