Fraction Multiplication: 2 & 1/4 × 1 & 5/7
In this article, we will discuss the multiplication of two mixed numbers: 2 & 1/4 and 1 & 5/7.
Understanding Mixed Numbers
Before we dive into the multiplication process, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 2 & 1/4 is a mixed number, where 2 is the whole number and 1/4 is the fraction.
Converting Mixed Numbers to Improper Fractions
To multiply mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 2 & 1/4 to an Improper Fraction
To convert 2 & 1/4 to an improper fraction, we need to multiply the whole number part (2) by the denominator (4) and then add the numerator (1).
2 × 4 = 8 8 + 1 = 9
So, the improper fraction of 2 & 1/4 is 9/4.
Converting 1 & 5/7 to an Improper Fraction
Similarly, to convert 1 & 5/7 to an improper fraction, we need to multiply the whole number part (1) by the denominator (7) and then add the numerator (5).
1 × 7 = 7 7 + 5 = 12
So, the improper fraction of 1 & 5/7 is 12/7.
Multiplying Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can multiply them.
Multiplying 9/4 and 12/7
To multiply two fractions, we need to multiply the numerators and multiply the denominators.
Numerators: 9 × 12 = 108 Denominators: 4 × 7 = 28
So, the result of multiplying 9/4 and 12/7 is 108/28.
Simplifying the Result
Finally, we can simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD).
GCD of 108 and 28 is 4.
108 ÷ 4 = 27 28 ÷ 4 = 7
So, the simplified result is 27/7.
Therefore, 2 & 1/4 × 1 & 5/7 = 27/7.
