Understanding fractions and how to manipulate them is a fundamental aspect of mathematics. One common operation involving fractions is multiplication. When you're asked to calculate 3/4 times 2, you're essentially being asked to multiply the fraction 3/4 by the whole number 2. To approach this, it's helpful to think of the whole number 2 as the fraction 2/1, because any whole number can be represented as a fraction over 1.
Multiplying Fractions
To multiply fractions, you simply multiply the numerators (the numbers on top) together to get the new numerator, and multiply the denominators (the numbers on the bottom) together to get the new denominator. So, when multiplying 3⁄4 by 2 (or 2⁄1), the calculation looks like this: (3⁄4) * (2⁄1) = (3*2)/(4*1).
Performing the Calculation
Now, let’s perform the multiplication: 3*2 = 6 (this will be the new numerator), and 4*1 = 4 (this will be the new denominator). Therefore, (3⁄4) * (2⁄1) = 6⁄4. This result, 6⁄4, can be simplified further because both the numerator and the denominator share a common factor of 2.
| Step | Calculation |
|---|---|
| 1. Multiply numerators and denominators | (3*2)/(4*1) = 6/4 |
| 2. Simplify the fraction | 6/4 = 3/2 |
This simplification process involves dividing both the numerator and the denominator by their greatest common divisor, which is 2 in this case, resulting in 3/2. This fraction, 3/2, is also known as one and a half when converted to a mixed number.
Key Points
- To multiply a fraction by a whole number, convert the whole number to a fraction over 1.
- Multiply the numerators together and the denominators together.
- Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor.
- The result of multiplying 3/4 by 2 is 6/4, which simplifies to 3/2 or one and a half.
- Understanding how to multiply fractions is crucial for more complex mathematical operations and real-world applications.
Real-World Applications
Being able to multiply fractions is not just a mathematical exercise; it has numerous real-world applications. For example, in cooking, recipes often require doubling or tripling, which involves multiplying fractions of ingredients. In construction, understanding fraction multiplication is essential for calculating materials needed for a project. The ability to perform these operations confidently can make a significant difference in the accuracy and efficiency of various tasks.
Conclusion and Further Learning
In conclusion, multiplying 3⁄4 by 2 to get 3⁄2 is a straightforward process that involves converting the whole number to a fraction, multiplying the numerators and denominators, and simplifying the result. This foundational skill in mathematics opens the door to more complex calculations and has practical applications across various fields. For those looking to deepen their understanding of fractions and their operations, exploring additional resources on simplifying fractions, comparing fractions, and applying fractions in real-world scenarios can be highly beneficial.
What is the first step in multiplying a fraction by a whole number?
+The first step is to convert the whole number into a fraction, with 1 as the denominator. For example, the whole number 2 is converted to 2⁄1.
How do you simplify a fraction like 6⁄4?
+To simplify a fraction, you find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this GCD. For 6⁄4, the GCD is 2, so dividing both the numerator and the denominator by 2 gives 3⁄2.
What are some real-world applications of fraction multiplication?
+Fraction multiplication is used in cooking for scaling recipes, in construction for calculating materials, and in any scenario where quantities need to be adjusted proportionally.
