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Multiply mixed numbers and fractions with step-by-step solutions. Learn how to multiply fractions by converting to improper fractions first.
• 2 1/2 × 1 1/3 = 3 1/3
• 3 1/4 × 2 = 6 1/2
• 1 1/2 × 2 2/3 = 4
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Step 1: Convert: 2 1/2 = 5/2 and 1 1/3 = 4/3
Step 2: Multiply numerators: 5 × 4 = 20
Step 3: Multiply denominators: 2 × 3 = 6
Step 4: Result: 20/6 = 10/3 (simplified)
Step 5: Convert: 10/3 = 3 1/3
Before multiplying, look for common factors between any numerator and any denominator. Cancel these factors first to keep numbers smaller and simplify your work:
Example: 6/8 × 4/9
• 6 and 9 share factor 3: 6÷3=2, 9÷3=3
• 4 and 8 share factor 4: 4÷4=1, 8÷4=2
• Result: 2/2 × 1/3 = 2/6 = 1/3
Multiplication only works directly with fractions in the form numerator/denominator. Mixed numbers like 2 1/2 aren't in this form - they're a sum (2 + 1/2). Converting to 5/2 gives you a single fraction you can multiply. Trying to multiply mixed numbers directly without converting leads to incorrect results.
Yes! After converting to improper fractions but before multiplying, look for common factors between any numerator and any denominator. Cancel these first. For example, with 6/8 × 4/9, you can cancel 6 and 9 (divide by 3), and cancel 4 and 8 (divide by 4), making the math much easier.
Convert the whole number to a fraction by putting it over 1. For example, 5 becomes 5/1. Then multiply as usual: 2 1/2 × 5 becomes 5/2 × 5/1 = 25/2 = 12 1/2. This works because any number divided by 1 equals itself.
No! Unlike addition and subtraction, multiplication doesn't require a common denominator. Simply multiply the numerators together and the denominators together. This is what makes multiplication easier than addition or subtraction of fractions.
In most cases, final answers should be expressed as mixed numbers (like 3 1/4 instead of 13/4) unless the problem specifically asks for an improper fraction. Mixed numbers are easier to visualize and understand in real-world contexts. Check your teacher's or textbook's preferences.
That's perfectly normal! Many multiplication problems result in mixed numbers. Convert the improper fraction by dividing: the quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator. For example, 17/4 = 4 R1 = 4 1/4.