Questions: Quilters Newsletter Magazine gave instructions on making a quilt. The quilt required 1 1/4 yards of white-on-white print, 3 yards blue check, 1/4 yard blue-and-white stripe, 6 1/4 yards blue scraps, 1/4 yard yellow scraps, and 5 3/8 yards lining. How many total yards are needed? Total yards needed are

Solution Steps

To find the total yards needed, we need to sum up all the given yard measurements. Each measurement is either a whole number, a mixed number, or a fraction. We will convert all mixed numbers to improper fractions, sum all the fractions, and then convert the result back to a mixed number if necessary.

First, we convert all mixed numbers to improper fractions:

• \(1 \frac{1}{4} = \frac{5}{4}\)
• \(6 \frac{1}{4} = \frac{25}{4}\)
• \(5 \frac{3}{8} = \frac{43}{8}\)

Next, we sum all the fractions: \[ \frac{5}{4} + 3 + \frac{1}{4} + \frac{25}{4} + \frac{1}{4} + \frac{43}{8} \]

To add these fractions, we need a common denominator. The least common multiple of 4 and 8 is 8. Converting all fractions to have a denominator of 8: \[ \frac{5}{4} = \frac{10}{8}, \quad 3 = \frac{24}{8}, \quad \frac{1}{4} = \frac{2}{8}, \quad \frac{25}{4} = \frac{50}{8}, \quad \frac{1}{4} = \frac{2}{8}, \quad \frac{43}{8} = \frac{43}{8} \]

Now, we add the fractions: \[ \frac{10}{8} + \frac{24}{8} + \frac{2}{8} + \frac{50}{8} + \frac{2}{8} + \frac{43}{8} = \frac{131}{8} \]

Finally, we convert \(\frac{131}{8}\) to a mixed number: \[ \frac{131}{8} = 16 \frac{3}{8} \]

Final Answer