Question

1. alicia measured $\frac{1}{4}$ yard of the blue diamonds fabric and $\frac{5}{6}$ yard of the yellow bonnets fabric to make a quilt. rename each length of fabric. use the number of inches in a yard as a common denominator. hint: 1 yard = 3 feet; 1 foot = 12 inches

Explanation:

Step1: Find inches in a yard

1 yard = 3 feet, 1 foot = 12 inches, so 1 yard = \(3\times12 = 36\) inches.

Step2: Rename \(\frac{1}{4}\) yard

To convert \(\frac{1}{4}\) yard to inches with denominator 36, we know that to get denominator 36, we multiply numerator and denominator of \(\frac{1}{4}\) by 9 (since \(4\times9 = 36\)). So \(\frac{1}{4}=\frac{1\times9}{4\times9}=\frac{9}{36}\) yard (in terms of 36 - inch denominator, but actually we can also calculate inches: \(\frac{1}{4}\times36 = 9\) inches, and as a fraction of 36 inches, it's \(\frac{9}{36}\)).

Step3: Rename \(\frac{5}{6}\) yard

To convert \(\frac{5}{6}\) yard to a fraction with denominator 36, we multiply numerator and denominator by 6 (since \(6\times6 = 36\)). So \(\frac{5}{6}=\frac{5\times6}{6\times6}=\frac{30}{36}\) yard (also, \(\frac{5}{6}\times36 = 30\) inches, and as a fraction of 36 inches, it's \(\frac{30}{36}\)).

Answer:

\(\frac{1}{4}\) yard is \(\frac{9}{36}\) (or 9 inches) and \(\frac{5}{6}\) yard is \(\frac{30}{36}\) (or 30 inches) when using 36 (inches in a yard) as the common denominator.