Converting Mixed Numbers to Improper Fractions: 3 1/3 × 2 1/2
Mixed numbers are a combination of a whole number and a fraction. To perform arithmetic operations on mixed numbers, it's often necessary to convert them to improper fractions. In this article, we'll explore how to convert the mixed numbers 3 1/3 and 2 1/2 to improper fractions and then multiply them together.
Converting 3 1/3 to an Improper Fraction
To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator.
3 1/3 = ?
- Whole number part: 3
- Numerator: 1
- Denominator: 3
Multiply the whole number part by the denominator: 3 × 3 = 9 Add the numerator: 9 + 1 = 10
So, 3 1/3 = 10/3
Converting 2 1/2 to an Improper Fraction
Let's apply the same process to convert 2 1/2 to an improper fraction.
2 1/2 = ?
- Whole number part: 2
- Numerator: 1
- Denominator: 2
Multiply the whole number part by the denominator: 2 × 2 = 4 Add the numerator: 4 + 1 = 5
So, 2 1/2 = 5/2
Multiplying the Improper Fractions
Now that we have the improper fractions, we can multiply them together.
10/3 × 5/2 = ?
To multiply fractions, we multiply the numerators and multiply the denominators.
- Numerator: 10 × 5 = 50
- Denominator: 3 × 2 = 6
So, 10/3 × 5/2 = 50/6
Simplifying the Result
We can simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 50 and 6 is 2. Divide both numbers by 2:
- Numerator: 50 ÷ 2 = 25
- Denominator: 6 ÷ 2 = 3
So, 50/6 = 25/3
Therefore, 3 1/3 × 2 1/2 = 25/3.
