A rectangle measures 3 1/2 ft by 2 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 formula, Area equals length times width, gives us the amount of space inside the rectangle. We can visualize this by dividing the rectangle into unit squares.
Mixed numbers combine a whole number with a fraction. In our problem, we have two mixed numbers: 3 and a half, and 2 and three quarters. We can visualize these on a number line or as fraction bars showing the whole parts and fractional parts separately.
To multiply mixed numbers, we first convert them to improper fractions. For 3 and a half, we multiply the whole number 3 by the denominator 2, then add the numerator 1, keeping the same denominator. This gives us 7 halves. Similarly, for 2 and three quarters, we multiply 2 by 4, add 3, and keep denominator 4, giving us 11 quarters.
Now we apply the area formula using our converted fractions. The area of our rectangle is length times width, which is 3 and a half times 2 and three quarters. Substituting our improper fractions, this becomes 7 halves times 11 quarters.
To multiply fractions, we multiply the numerators together and the denominators together. So 7 halves times 11 quarters equals 7 times 11 over 2 times 4. Calculating the numerator: 7 times 11 equals 77. Calculating the denominator: 2 times 4 equals 8. Therefore, our result is 77 eighths.
Now let's convert our improper fraction result back to a mixed number. We divide 77 by 8. 8 goes into 77 nine times with a remainder of 5, since 8 times 9 is 72 and 77 minus 72 is 5. Therefore, 77 eighths equals 9 and 5 eighths. The area of our rectangle is 9 and 5 eighths square feet.
Let's verify our answer and summarize the key steps. Converting to decimals, 3.5 times 2.75 equals 9.625. Converting our mixed number answer, 9 and 5 eighths also equals 9.625. The answers match! To summarize: First, we used the area formula. Second, we converted mixed numbers to improper fractions. Third, we multiplied fractions by multiplying numerators and denominators. Fourth, we converted the result back to a mixed number. The area of our rectangle is 9 and 5 eighths square feet.