Converting Mixed Numbers to Fractions: 1 1/2 x 2 3/4
When working with mixed numbers, it's essential to understand how to convert them to fractions. This can be particularly useful when performing arithmetic operations, such as multiplication. In this article, we'll explore how to convert the mixed numbers 1 1/2 and 2 3/4 to fractions and then multiply them together.
Converting 1 1/2 to a Fraction
To convert the mixed number 1 1/2 to a fraction, we need to follow a few simple steps:
- The whole number part (1) becomes the numerator.
- The denominator is the same as the denominator of the fraction part (2).
- The numerator of the fraction part (1) is added to the product of the whole number and the denominator.
Let's apply these steps:
- Numerator: 1 × 2 + 1 = 3
- Denominator: 2
So, 1 1/2 as a fraction is 3/2.
Converting 2 3/4 to a Fraction
Now, let's convert the mixed number 2 3/4 to a fraction:
- Numerator: 2 × 4 + 3 = 11
- Denominator: 4
Therefore, 2 3/4 as a fraction is 11/4.
Multiplying the Fractions
Now that we have both mixed numbers converted to fractions, we can multiply them together:
3/2 × 11/4
To multiply fractions, we need to multiply the numerators (3 and 11) and multiply the denominators (2 and 4), as shown below:
Numerator: 3 × 11 = 33 Denominator: 2 × 4 = 8
So, the result of multiplying 1 1/2 and 2 3/4 is 33/8.
In conclusion, we've successfully converted the mixed numbers 1 1/2 and 2 3/4 to fractions and multiplied them together. The result is a new fraction, 33/8.
