Question

To create a table for a report, you need two columns, each \(1 \frac{1}{2}\) inches wide, and five columns, each \(\frac{3}{4}\) inch wide. Will your table fit on a piece of paper \(8 \frac{1}{2}\) inches wide?

Short answer

Answer: Yes, the table will fit on the paper.

Step-by-step solution

Calculate the total width of the two columns

We have two columns, each \(1 \frac{1}{2}\) inches wide. To find the total width of these columns, we multiply the width of one column by the number of columns: Total width of two columns = \(1 \frac{1}{2} inches \times 2\) We can rewrite the mixed fraction \(1 \frac{1}{2}\) as an improper fraction: \(1 \frac{1}{2} = \frac{3}{2}\) So now our expression becomes: Total width of two columns = \(\frac{3}{2} \times 2\)

Perform the multiplication

Multiply the fractions: Total width of two columns = \(\frac{3}{2} \times 2 = \frac{3 \times 2}{2} = \frac{6}{2}\) Since \(\frac{6}{2}\) can be simplified to \(3\): Total width of two columns = \(3 inches\)

Calculate the total width of the five columns

We have five columns, each \(\frac{3}{4}\) inch wide. To find the total width of these columns, we multiply the width of one column by the number of columns: Total width of five columns = \(\frac{3}{4} inches \times 5\)

Perform the multiplication

Multiply the fraction by the whole number: Total width of five columns = \(\frac{3}{4} \times 5 = \frac{3 \times 5}{4} = \frac{15}{4}\) Since \(\frac{15}{4}\) cannot be simplified further, we can convert it into a mixed fraction: Total width of five columns = \(3 \frac{3}{4} inches\)

Calculate the total width of all columns

Add the total width of the two columns and the total width of the five columns: Total width of all columns = \(3 inches + 3 \frac{3}{4} inches\) Since we can't directly add a whole number to a mixed fraction, we should first convert \(3\) into an improper fraction with the same denominator as in \(3 \frac{3}{4}\): \(3 = \frac{12}{4}\) Now our expression becomes: Total width of all columns = \(\frac{12}{4} + 3 \frac{3}{4}\)

Perform the addition

Add the fractions: Total width of all columns = \(\frac{12}{4} + 3 \frac{3}{4} = \frac{15+3}{4}= \frac{18}{4}\) Since \(\frac{18}{4}\) can be simplified to \(4 \frac{1}{2}\): Total width of all columns = \(4 \frac{1}{2} inches\)

Compare the total width of all columns with the paper width

The total width of all columns is \(4 \frac{1}{2}\) inches, and the width of the paper is \(8 \frac{1}{2}\) inches. We need to compare the two widths to determine whether the table will fit on the paper: \(4 \frac{1}{2} inches \le 8 \frac{1}{2} inches\) Since \(4 \frac{1}{2} inches\) is less than or equal to \(8 \frac{1}{2}\) inches, the table will fit on the paper.