What is the result of 3 copies of 1/3?
The Correct Answer and Explanation is:
The result of 3 copies of ( \frac{1}{3} ) is:
[
3 \times \frac{1}{3} = 1
]
Explanation:
To understand why this is true, let’s start by analyzing what it means to have “3 copies of ( \frac{1}{3} ).” In mathematical terms, “3 copies of ( \frac{1}{3} )” is equivalent to multiplying 3 by ( \frac{1}{3} ), or simply:
[
3 \times \frac{1}{3}
]
When you multiply a whole number by a fraction, you’re essentially adding the fraction that many times. So, ( 3 \times \frac{1}{3} ) means adding ( \frac{1}{3} ) three times:
[
\frac{1}{3} + \frac{1}{3} + \frac{1}{3}
]
When we add fractions, we add the numerators (top numbers) while keeping the denominator (bottom number) the same, as long as the fractions share the same denominator. Here, the sum is:
[
\frac{1 + 1 + 1}{3} = \frac{3}{3}
]
Now, ( \frac{3}{3} ) simplifies to 1, because dividing a number by itself gives 1:
[
\frac{3}{3} = 1
]
Why This Works:
This multiplication problem follows a key rule of fractions and whole numbers: when you multiply a whole number by a fraction, you’re effectively scaling or resizing the fraction. In this case, we have 3 parts of ( \frac{1}{3} ), which completes a whole. Since three parts of one-third add up to one whole, ( 3 \times \frac{1}{3} = 1 ).
This concept is fundamental in understanding fractions and multiplication. By recognizing that groups of a fraction can total a whole, we see how fractions and whole numbers interact, which is essential in various real-world applications, like measuring ingredients in cooking or dividing objects into equal parts.