Fraction Calculation: 3 1/2 x 3/4
In this article, we will explore the calculation of multiplying two mixed numbers: 3 1/2 and 3/4.
Understanding the Fractions
Before we dive into the calculation, let's break down the two fractions:
- 3 1/2: This is a mixed number, consisting of a whole number part (3) and a fractional part (1/2).
- 3/4: This is a fraction, where 3 is the numerator and 4 is the denominator.
Converting to Improper Fractions
To multiply these two numbers, we need to convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
- 3 1/2 = 7/2: To convert the mixed number to an improper fraction, we multiply the whole number part (3) by the denominator (2), then add the numerator (1). This gives us 7/2.
Now we can rewrite the problem as:
Multiplying the Fractions
To multiply two fractions, we multiply the numerators and denominators separately.
- Numerators: 7 × 3 = 21
- Denominators: 2 × 4 = 8
So, the product of the two fractions is:
21/8
Simplifying the Fraction
We can simplify the fraction 21/8 by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 21 and 8 is 1, so the fraction is already in its simplest form.
Therefore, the result of multiplying 3 1/2 and 3/4 is 21/8.
