Gabriel's father has a garden in the back yard. The dimensions of the garden are shown here.
A green rectangle is shown. The width is labeled as 2 and two-thirds feet. The length is labeled as 7 and three-fourths feet.
Part A
Calculate the area of the garden. Show at least one step before you show your solution. PLEASE HELPP!!
Area = (2 2/3)(7 3/4) ft^2
= (8/3)(31/4) ft^2
= 248/12) ft^2
= 62/3 ft^2
To calculate the area of the garden, we need to multiply the width by the length.
Given that the width is 2 and two-thirds feet, we can convert it to an improper fraction: 2 and two-thirds is equivalent to (2 * 3) + 2 = 6 + 2 = 8 thirds or 8/3 feet.
Similarly, the length is 7 and three-fourths feet, which can be converted to an improper fraction: 7 and three-fourths is equivalent to (7 * 4) + 3 = 28 + 3 = 31 fourths or 31/4 feet.
Now, we multiply the width (8/3 feet) by the length (31/4 feet):
(8/3 feet) * (31/4 feet) = (8 * 31) / (3 * 4) = 248/12 = 62/3 square feet.
Therefore, the area of the garden is 62/3 square feet, or approximately 20 and two-thirds square feet.
To calculate the area of the garden, we need to multiply the length by the width.
Step 1: Convert 2 and two-thirds feet to an improper fraction.
2 and two-thirds can be written as 2 + 2/3.
To convert the mixed number to an improper fraction, we multiply the whole number (2) by the denominator (3) and add the numerator (2). This gives us 6/3 + 2/3 = 8/3.
So, the width is 8/3 feet.
Step 2: Convert 7 and three-fourths feet to an improper fraction.
7 and three-fourths can be written as 7 + 3/4.
To convert the mixed number to an improper fraction, we multiply the whole number (7) by the denominator (4) and add the numerator (3). This gives us 28/4 + 3/4 = 31/4.
So, the length is 31/4 feet.
Step 3: Multiply the length (31/4 feet) by the width (8/3 feet) to find the area of the garden.
Area = length × width = 31/4 × 8/3
To multiply fractions, multiply the numerators (top numbers) and multiply the denominators (bottom numbers). This gives us (31 × 8) / (4 × 3) = 248/12.
Step 4: Simplify the fraction if possible.
The fraction 248/12 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. (248 ÷ 4) / (12 ÷ 4) = 62/3.
So, the area of the garden is 62/3 square feet.