Multiplying Fractions: 1 2/3 x 4/5
Let's break down how to multiply the mixed number 1 2/3 by the fraction 4/5.
Step 1: Convert the mixed number to an improper fraction.
- Multiply the whole number (1) by the denominator of the fraction (3): 1 x 3 = 3
- Add the numerator of the fraction (2): 3 + 2 = 5
- Keep the same denominator (3).
- This gives us the improper fraction 5/3.
Step 2: Multiply the fractions.
- Multiply the numerators: 5 x 4 = 20
- Multiply the denominators: 3 x 5 = 15
- This gives us 20/15.
Step 3: Simplify the answer (optional).
- Find the greatest common factor (GCD) of the numerator and denominator: The GCD of 20 and 15 is 5.
- Divide both the numerator and denominator by the GCD: 20 ÷ 5 = 4 and 15 ÷ 5 = 3.
- This simplifies our answer to 4/3.
Step 4: Convert back to a mixed number (optional).
- Divide the numerator (4) by the denominator (3): 4 ÷ 3 = 1 with a remainder of 1.
- The whole number of our mixed number is 1.
- The numerator of our fraction is the remainder (1).
- The denominator stays the same (3).
- This gives us the mixed number 1 1/3.
Conclusion
Therefore, 1 2/3 x 4/5 is equal to 20/15 or 4/3, which can also be expressed as the mixed number 1 1/3.