Nina’s garden is 4(1)/(5) meters long and (3)/(10) meter wide. What is the area of Nina’s garden? 4(3)/(50) square meter 1(3)/(50) square meter 4(13)/(50) square meter 1(13)/(50) square meter
The correct answer and explanation is:
Correct Answer: 4(13)/(50) square meters
Explanation :
To determine the area of Nina’s garden, we use the formula for the area of a rectangle: Area=Length×Width\text{Area} = \text{Length} \times \text{Width}
The given length is 4154\frac{1}{5} meters, and the width is 310\frac{3}{10} meter. First, convert the mixed number 4154\frac{1}{5} into an improper fraction: 415=5×4+15=215.4\frac{1}{5} = \frac{5 \times 4 + 1}{5} = \frac{21}{5}.
Now, calculate the area by multiplying the two fractions: Area=215×310.\text{Area} = \frac{21}{5} \times \frac{3}{10}.
To multiply fractions, multiply the numerators and denominators: Area=21×35×10=6350.\text{Area} = \frac{21 \times 3}{5 \times 10} = \frac{63}{50}.
Convert the improper fraction 6350\frac{63}{50} into a mixed number. Divide 63 by 50: 63÷50=1 remainder 13.63 \div 50 = 1 \text{ remainder } 13.
Thus, 6350=11350\frac{63}{50} = 1\frac{13}{50}.
The area of Nina’s garden is therefore: 41350 square meters.\boxed{4\frac{13}{50} \text{ square meters}}.
Why This is the Correct Answer
- Conversion of Mixed Numbers: The first step ensures the length is expressed in a fraction compatible with multiplication.
- Multiplication of Fractions: The second step accurately calculates the area using the standard method for multiplying fractions.
- Simplification: The improper fraction is converted into a mixed number for clarity, as is standard in many contexts.
By following these steps, we arrive at 413504\frac{13}{50}, making it the correct answer among the options provided.