What expression is equivalent to 2/3 X 5
The correct Answer and Explanation is:
To find an expression equivalent to ( \frac{2}{3} \times 5 ), we can start by rewriting the multiplication in a way that makes it easier to understand.
Step 1: Rewrite the Multiplication
The expression ( \frac{2}{3} \times 5 ) involves a fraction multiplied by a whole number. To compute this, we can express the whole number ( 5 ) as a fraction. Thus, we can rewrite ( 5 ) as ( \frac{5}{1} ). The expression now looks like this:
[
\frac{2}{3} \times \frac{5}{1}
]
Step 2: Multiply the Fractions
When multiplying two fractions, we multiply the numerators together and the denominators together. Therefore, we have:
[
\frac{2 \times 5}{3 \times 1} = \frac{10}{3}
]
Step 3: Interpret the Result
The result ( \frac{10}{3} ) can be left as an improper fraction, or it can be converted into a mixed number. To convert ( \frac{10}{3} ) into a mixed number, we divide ( 10 ) by ( 3 ):
- ( 3 ) goes into ( 10 ) three times, which equals ( 9 ).
- The remainder is ( 10 – 9 = 1 ).
Thus, we can express ( \frac{10}{3} ) as:
[
3 \frac{1}{3}
]
Conclusion
Therefore, the expression ( \frac{2}{3} \times 5 ) is equivalent to ( \frac{10}{3} ) or ( 3 \frac{1}{3} ).
This demonstrates how to work with fractions and whole numbers in multiplication. It emphasizes the concept of expressing whole numbers as fractions for consistency in mathematical operations. Understanding these foundational skills is critical in mathematics, as they lay the groundwork for more complex concepts in algebra and beyond.