A rectangle measures 4 1/2 ft by 3 3/4 ft. What is the area
视频信息
答案文本
视频字幕
The area of a rectangle is calculated by multiplying its length by its width. This fundamental formula, Area equals length times width, applies to all rectangles regardless of their dimensions.
Mixed numbers combine a whole number with a fraction. For example, 4 and 1/2 means 4 wholes plus an additional half. Similarly, 3 and 3/4 means 3 wholes plus 3 quarters. Understanding mixed numbers is essential for our area calculation.
To multiply mixed numbers, we first convert them to improper fractions. For 4 and 1/2, we multiply the whole number 4 by the denominator 2, then add the numerator 1, giving us 9/2. For 3 and 3/4, we multiply 3 by 4 and add 3, resulting in 15/4.
Now we apply our knowledge to calculate the area of the rectangle. The area is the product of its dimensions: 4 and 1/2 feet times 3 and 3/4 feet. After converting to improper fractions, this becomes 9/2 times 15/4.
To multiply fractions, we multiply the numerators together and the denominators together. So 9/2 times 15/4 equals 9 times 15 over 2 times 4. This gives us 135 over 8.
We simplify 135/24 by finding the greatest common divisor, which is 3. Dividing both numerator and denominator by 3 gives us 45/8. Converting this improper fraction to a mixed number, we divide 45 by 8 to get 5 with a remainder of 5, resulting in 5 and 5/8. Therefore, the area is 5 and 5/8 square feet.
Let's verify our answer by converting to decimals. 4 and 1/2 equals 4.5, and 3 and 3/4 equals 3.75. Multiplying these decimals gives 16.875. Converting our fraction answer, 5 and 5/8 equals 5.625. Both methods confirm our solution is correct. The area of the rectangle is 5 and 5/8 square feet.