Procedure: Multiply Fractions
Multiplying fractions follows a direct algorithm: multiply the numerators together and multiply the denominators together, then simplify the result. For 2/3 x 3/5 = (2x3)/(3x5) = 6/15 = 2/5. Simplifying before multiplying (cross-canceling) makes the arithmetic easier. This 6th grade procedure from enVision Mathematics Grade 6 extends from multiplying unit fractions to all fractions and mixed numbers, and is essential for scaling, probability, and any area or volume calculation involving fractional dimensions.
Key Concepts
To multiply two fractions, multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator.
Common Questions
How do you multiply fractions?
Multiply the numerators together and the denominators together. For 2/3 x 3/5: (2x3)/(3x5) = 6/15 = 2/5 after simplifying.
What is cross-canceling when multiplying fractions?
Before multiplying, simplify by dividing a numerator and a denominator from different fractions by their GCF. For 2/3 x 3/5: cancel the 3s to get 2/1 x 1/5 = 2/5 directly.
Do you need a common denominator to multiply fractions?
No. Unlike addition and subtraction, multiplying fractions does not require a common denominator. Simply multiply across: numerator x numerator over denominator x denominator.
What grade learns to multiply fractions?
Multiplying fractions is a 6th grade skill in enVision Mathematics Grade 6, building from unit fractions toward mixed number multiplication.
Why does multiplying two fractions produce a smaller result?
Multiplying by a fraction less than 1 scales down. Taking 2/3 of 3/5 means taking less than all of 3/5, so the product (2/5) is less than either factor.
How do you multiply a fraction by a whole number?
Write the whole number as a fraction over 1. For 3 x 2/5 = 3/1 x 2/5 = 6/5 = 1 and 1/5.