Multiplying Mixed Numbers: 1 3/4 Cups x 2
Let's explore how to multiply a mixed number, like 1 3/4 cups, by 2.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. In our case, 1 3/4 cups represents one whole cup plus three-quarters of a cup.
Converting to an Improper Fraction
To multiply easily, it's best to convert the mixed number into an improper fraction:
- Multiply the denominator of the fraction by the whole number: 4 x 1 = 4
- Add the numerator of the fraction: 4 + 3 = 7
- Keep the same denominator: 7/4
Now, 1 3/4 cups is equivalent to 7/4 cups.
Multiplying Fractions
To multiply fractions, we multiply the numerators and the denominators:
- (7/4) x 2 = (7 x 2) / (4 x 1) = 14/4
Simplifying the Result
The fraction 14/4 can be simplified. 14 and 4 both share the common factor of 2. Dividing both the numerator and denominator by 2, we get:
- 14/4 = (14 ÷ 2) / (4 ÷ 2) = 7/2
Converting Back to a Mixed Number
The improper fraction 7/2 can be converted back to a mixed number:
- Divide the numerator (7) by the denominator (2): 7 ÷ 2 = 3 with a remainder of 1.
- The quotient (3) becomes the whole number part: 3
- The remainder (1) becomes the numerator of the fraction: 1
- Keep the same denominator (2): 3 1/2
Answer
Therefore, 1 3/4 cups multiplied by 2 equals 3 1/2 cups.