Rewrite 2/3 x 15 as a single fraction

Rewrite 2/3 x 15 as a single fraction

The Correct Answer and Explanation is:

To rewrite the expression (\frac{2}{3} \times 15) as a single fraction, follow these steps:

Step 1: Express 15 as a fraction

Any whole number can be expressed as a fraction by placing it over 1. So, rewrite 15 as:

[
15 = \frac{15}{1}
]

Step 2: Multiply the two fractions

Now, we multiply the two fractions (\frac{2}{3}) and (\frac{15}{1}). When multiplying fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers) separately:

[
\frac{2}{3} \times \frac{15}{1} = \frac{2 \times 15}{3 \times 1}
]

Step 3: Perform the multiplication

Now, multiply the numerators and the denominators:

[
\frac{2 \times 15}{3 \times 1} = \frac{30}{3}
]

Step 4: Simplify the fraction

Next, simplify (\frac{30}{3}). To simplify, divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

[
\frac{30}{3} = 10
]

Final Answer:

So, (\frac{2}{3} \times 15 = 10).

Explanation:

This process illustrates how to multiply fractions and simplify the result. The key steps in fraction multiplication are:

1. Convert any whole numbers into fractions (in this case, 15 becomes (\frac{15}{1})).
2. Multiply the numerators and denominators.
3. Simplify the resulting fraction if possible.

Multiplying fractions is straightforward: you just multiply the numerators together and the denominators together. When the result is a fraction like (\frac{30}{3}), you can simplify it by dividing both the numerator and the denominator by their GCD (in this case, 3). In this example, (\frac{30}{3}) simplifies to 10, which is the final result.

This process helps ensure that the multiplication and simplification steps are both clear and correct, turning a multiplication of fractions into a simple whole number.