Multiplying Fractions: 1 3/4 x 2
This article will guide you through the steps of multiplying a mixed number by a whole number, specifically 1 3/4 x 2.
Understanding Mixed Numbers
First, let's understand what a mixed number is. A mixed number consists of a whole number and a fraction. In this case, 1 3/4 represents one whole unit plus three-quarters of another unit.
Converting Mixed Numbers to Fractions
To make multiplication easier, we need to convert the mixed number into an improper fraction. Here's how:
- Multiply the whole number by the denominator: 1 x 4 = 4
- Add the numerator: 4 + 3 = 7
- Keep the original denominator: 7/4
Therefore, 1 3/4 is equivalent to 7/4.
Multiplying Fractions
Now we can multiply the fractions:
(7/4) x (2/1)
To multiply fractions, we multiply the numerators and the denominators.
(7 x 2) / (4 x 1)
= 14/4
Simplifying the Answer
The fraction 14/4 can be simplified. Both the numerator and denominator are divisible by 2:
(14/2) / (4/2)
= 7/2
Converting Back to a Mixed Number
Finally, we can convert the improper fraction 7/2 back to a mixed number:
- Divide the numerator by the denominator: 7 ÷ 2 = 3 with a remainder of 1
- The quotient becomes the whole number: 3
- The remainder becomes the numerator: 1
- Keep the original denominator: 2
Therefore, 7/2 is equivalent to 3 1/2.
Conclusion
In conclusion, 1 3/4 x 2 = 3 1/2. By following these steps, you can confidently multiply mixed numbers and fractions.