Using the expression 10 x 2/5 as an example, describe how to multiply a whole number by a fraction that is less than one.
The Correct Answer and Explanation is :
The correct answer is: 4
To multiply a whole number by a fraction that is less than one, we can use the expression (10 \times \frac{2}{5}) as an example. Here’s a step-by-step explanation of how to perform this operation.
Step 1: Understand the Components
In our example, we have the whole number (10) and the fraction (\frac{2}{5}). The fraction represents a part of a whole, specifically, two parts out of five equal parts. When you multiply a whole number by a fraction, you are essentially finding a part of that whole number.
Step 2: Rewrite the Whole Number as a Fraction
To make the multiplication easier, we can rewrite the whole number as a fraction. The whole number (10) can be expressed as (\frac{10}{1}). This helps us visualize the multiplication of two fractions.
Step 3: Multiply the Numerators
Now that both numbers are in fraction form, we can multiply them. The rule for multiplying fractions states that you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
For our example:
[
\frac{10}{1} \times \frac{2}{5} = \frac{10 \times 2}{1 \times 5}
]
Step 4: Perform the Multiplication
Calculating the multiplication:
- Numerator: (10 \times 2 = 20)
- Denominator: (1 \times 5 = 5)
Putting it together, we get:
[
\frac{20}{5}
]
Step 5: Simplify the Fraction
Now, we simplify (\frac{20}{5}):
[
\frac{20}{5} = 4
]
Conclusion
Thus, the product of (10) and (\frac{2}{5}) is (4). In summary, multiplying a whole number by a fraction less than one involves converting the whole number into a fraction, multiplying the numerators and denominators, and then simplifying the result. This method clearly demonstrates how a whole number can be effectively scaled down by a fraction, providing a straightforward process to understand the relationship between whole numbers and parts of a whole.