The concept of "two thirds times three" is a mathematical expression that involves both multiplication and fraction operations. To understand this, let's break it down step by step. First, we have the fraction two thirds, which is written as 2/3. When we say "times three," we're referring to the multiplication operation. Therefore, the expression "two thirds times three" translates to (2/3) * 3 in mathematical terms.
Mathematical Operation
To solve this, we follow the order of operations, which in this case is straightforward since we’re only dealing with multiplication. The multiplication of a fraction by a whole number involves multiplying the numerator of the fraction by that number. So, (2⁄3) * 3 = (2*3)/3 = 6⁄3. Simplifying 6⁄3 gives us 2, because 6 divided by 3 equals 2.
Simplification and Result
The simplification process here illustrates a basic principle of fraction multiplication and simplification. When multiplying fractions by whole numbers, we multiply the numerator, and then simplify the resulting fraction if possible. In the case of “two thirds times three,” the result is a whole number, 2, because the multiplication and subsequent division yield a whole number quotient.
| Operation | Expression | Result |
|---|---|---|
| Multiplication | (2/3) * 3 | 6/3 |
| Simplification | 6/3 | 2 |
Key Points
- The mathematical expression "two thirds times three" translates to (2/3) * 3.
- Multiplying a fraction by a whole number involves multiplying the numerator by that number.
- The expression simplifies to 6/3, which further simplifies to 2.
- Understanding fraction multiplication is crucial for various mathematical and practical applications.
- Simplification of fractions after multiplication is an essential step to obtain the final result in its simplest form.
By grasping these principles, one can tackle more complex mathematical operations involving fractions and whole numbers. The ability to simplify and understand the results of such operations is vital for problem-solving in numerous fields. Furthermore, this understanding can lead to a deeper appreciation of how mathematical concepts underpin our daily lives and the world around us.
Real-World Applications
In real-world scenarios, understanding how to multiply fractions by whole numbers is essential. For instance, in a recipe, if a ingredient is required in a fraction of a unit (e.g., 2⁄3 cup of flour) and the recipe needs to be tripled, knowing that “two thirds times three” equals 2 cups is crucial for accurate measurement. Similarly, in construction or manufacturing, precise calculations involving fractions are critical for ensuring the quality and safety of the final product.
Conclusion and Further Learning
In conclusion, “two thirds times three” equals 2, which is a simple yet fundamental mathematical operation. This operation and its understanding have far-reaching implications in both theoretical mathematics and practical, real-world applications. For those interested in furthering their mathematical knowledge, exploring more complex operations involving fractions, such as addition, subtraction, and division, as well as understanding how these operations apply to different areas of study, can provide a deeper and more nuanced understanding of mathematics and its role in our world.
What is the result of multiplying two thirds by three?
+The result of multiplying two thirds by three is 2, because (2⁄3) * 3 = 6⁄3, which simplifies to 2.
How do you multiply a fraction by a whole number?
+To multiply a fraction by a whole number, you multiply the numerator of the fraction by that number and then simplify the resulting fraction if possible.
What are some real-world applications of understanding fraction multiplication?
+Understanding fraction multiplication has applications in cooking, construction, manufacturing, finance, and science, among other areas, where precise calculations involving fractions are necessary.
