How to Multiply Fractions With Negative Numbers

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When you multiply a fraction by another fraction or a fraction by a whole number, the rules of fractions dictate the form of the answer. If at least one of the values is negative, you also use the rules for positive and negative signs to determine if the result is positive or negative.

Fractions and Whole Numbers

    Multiply the numerator, or top number of the fraction, to the whole number. For example, if the fraction is -1/4 and the whole number is -3, then multiply 1 by 3 to get a result of 3.

    Place the result over the denominator, or bottom number of the fraction. For the example in the first step, place 3 over 4 to get 3/4.

    Look at the number of minus or negative signs in the two numbers you're multiplying. An odd number of minus signs means that the answer is negative. An even number means that it is positive. For the example, multiplying -1/4 by -3, the numbers have two minus signs. That means the answer, 3/4, is positive.

Fractions and Fractions

    Multiply the numerators together. For example, to multiply 1/3 by -2/5, multiply 1 by 2 to get a result of 2.

    Multiply the denominators together. For the example in the first step, multiply 3 by 5. The result is 15.

    Place the product of the numerators over the products of the denominators. For the example, multiplying 1/3 by -2/5, place 2 over 15 to get a result of 2/15.

    Count the number of negative or minus signs in two numbers you're multiplying. The example only has one negative number. One is an odd number, so the result is a negative number, -2/15.

    Tips

    • The numerator and denominator of a fraction follow the rule of signs. If the numerator and denominator are both negative, then the value is positive since it has an even number of negative signs. For example, -1/-4 is equivalent to just writing 1/4.

References

  • "Basic Math and Pre-algebra"; Jerry Bobrow; 1995
  • "Decimals and Fractions"; Rebecca Wingard-Nelson; 2008

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

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