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How to Calculate the Area of a Fractional-Side Square Dog Play Space
Mathematics
Grade 5 (Primary School)
Question Content
Mr. Morales designs a square park with a side length of 1 mile. His design includes another square with 5/10-mile sides for a dog play space. How many square miles of the park does he use for the dog play space?
Correct Answer
1/4 square miles or 0.25 square miles
Detailed Solution Steps
1
Step 1: Recall the formula for the area of a square: Area = side length × side length
2
Step 2: Identify the side length of the dog play space square, which is 5/10 mile. Simplify 5/10 to 1/2 mile for easier calculation.
3
Step 3: Substitute the side length into the area formula: Area = (1/2) × (1/2)
4
Step 4: Multiply the fractions: Multiply the numerators (1×1=1) and multiply the denominators (2×2=4), so the area is 1/4 square miles, or 0.25 in decimal form.
Knowledge Points Involved
1
Area of a Square
The area of a square is calculated by multiplying the length of one side by itself, expressed as the formula A = s×s where s is the side length. This formula applies to all squares and is used to find the amount of space enclosed by the square's sides.
2
Simplifying Fractions
Simplifying fractions means reducing a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor. For 5/10, the greatest common divisor of 5 and 10 is 5, so dividing both by 5 gives the simplified fraction 1/2. This makes fraction multiplication calculations easier.
3
Multiplying Proper Fractions
To multiply two proper fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. For example, (a/b) × (c/d) = (a×c)/(b×d). This method is used to find the product of fractional values, such as when calculating area with fractional side lengths.
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