Question

1. charlie, dan, and ellie each made a paper chain. charlie’s was 9 ½ feet long, dan’s was 6 ⅓ feet long, and ellie’s was 8 ⅓ feet long. when put together, how long were the three chains?
2. holden and bryson started to hike a portion of the appalachian trail that is 12 ⅔ miles long. due to snow, they had to stop after hiking 7 ½ miles. how much of the trail did they miss hiking?
3. the whole class of 26 students made friendship bracelets. each bracelet took ⅔ of a yard of yarn to make. how many yards of yarn were used in all?
4. christina’s hair measured 16 ⅗ inches before her haircut. after the cut, it measured 9 ⅖ inches. how much did she let the hairdresser cut?

Explanation:

Problem 5

Step1: Convert mixed numbers to improper fractions

$9\frac{1}{2} = \frac{19}{2}$, $6\frac{1}{3} = \frac{19}{3}$, $8\frac{1}{3} = \frac{25}{3}$

Step2: Add the fractions with same denominator

$\frac{19}{3} + \frac{25}{3} = \frac{44}{3}$

Step3: Add the remaining fraction, find common denominator

$\frac{19}{2} + \frac{44}{3} = \frac{57}{6} + \frac{88}{6} = \frac{145}{6}$

Step4: Convert back to mixed number

$\frac{145}{6} = 24\frac{1}{6}$

Problem 6

Step1: Convert mixed numbers to improper fractions

$12\frac{3}{5} = \frac{63}{5}$, $7\frac{1}{2} = \frac{15}{2}$

Step2: Find common denominator and subtract

$\frac{63}{5} - \frac{15}{2} = \frac{126}{10} - \frac{75}{10} = \frac{51}{10}$

Step3: Convert back to mixed number

$\frac{51}{10} = 5\frac{1}{10}$

Problem 7

Step1: Set up multiplication for total yarn

$26 \times \frac{2}{3}$

Step2: Calculate the product

$\frac{26 \times 2}{3} = \frac{52}{3}$

Step3: Convert back to mixed number

$\frac{52}{3} = 17\frac{1}{3}$

Problem 8

Step1: Convert mixed numbers to improper fractions

$16\frac{3}{5} = \frac{83}{5}$, $9\frac{2}{3} = \frac{29}{3}$

Step2: Find common denominator and subtract

$\frac{83}{5} - \frac{29}{3} = \frac{249}{15} - \frac{145}{15} = \frac{104}{15}$

Step3: Convert back to mixed number

$\frac{104}{15} = 6\frac{14}{15}$

Answer:

1. The total length of the three chains is $24\frac{1}{6}$ feet.
2. They missed hiking $5\frac{1}{10}$ miles of the trail.
3. A total of $17\frac{1}{3}$ yards of yarn were used.
4. The hairdresser cut $6\frac{14}{15}$ inches of Christina's hair.