A rectangle measures 2 1/2 ft by 1 3/4 ft. What is the area
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The area of a rectangle is calculated by multiplying its length and width. This fundamental formula, Area equals length times width, applies to all rectangles regardless of their size.
Mixed numbers combine a whole number with a fraction. In our problem, we have two mixed numbers: 2 and a half, which means 2 plus one-half, and 1 and three-quarters, which means 1 plus three-quarters. Understanding these representations is key to solving our area problem.
To multiply mixed numbers, we first convert them to improper fractions. For 2 and a half, we multiply the whole number 2 by the denominator 2, getting 4. Then we add the numerator 1, getting 5. The improper fraction is 5 halves. For 1 and three-quarters, we multiply 1 by 4 to get 4, add 3 to get 7. The improper fraction is 7 quarters.
Now we can set up our area calculation. The area of our rectangle is length times width, which is 2 and a half feet times 1 and three-quarter feet. Substituting our improper fractions, this becomes 5 halves times 7 quarters.
To multiply fractions, we multiply the numerators together and the denominators together. So 5 halves times 7 quarters equals 5 times 7 over 2 times 4. This gives us 35 over 8.
Our result is 35 eighths, which is an improper fraction. To express this as a mixed number, we divide 35 by 8. This gives us 4 with a remainder of 3. So our mixed number is 4 and 3 eighths. The quotient 4 becomes the whole number, the remainder 3 becomes the new numerator, and the denominator 8 stays the same.
Let's verify our answer and summarize our solution. Our rectangle with dimensions 2 and a half feet by 1 and three-quarter feet has an area of 4 and 3 eighths square feet. To check, we can convert to decimals: 2.5 times 1.75 equals 4.375, which is exactly 4 and 3 eighths. The key steps were: converting mixed numbers to improper fractions, multiplying numerators and denominators separately, and converting the result back to a mixed number.