Claire had \( 4 \frac{1}{6} \) feet of string. She used some string to hang party decorations. Now she has \( 1 \frac{5}{6} \) feet of string left. How much string did Claire use? Draw a model and solve.

To find out how much string Claire used, we can subtract the amount of string she has left from the amount she started with. First, let’s convert the mixed numbers to improper fractions. Claire starts with \( 4 \frac{1}{6} \) feet of string, which can be converted as follows: \[ 4 \times 6 + 1 = 24 + 1 = 25 \quad \text{(so, } 4 \frac{1}{6} = \frac{25}{6} \text{)} \] Next, we convert \( 1 \frac{5}{6} \) feet of string left: \[ 1 \times 6 + 5 = 6 + 5 = 11 \quad \text{(so, } 1 \frac{5}{6} = \frac{11}{6} \text{)} \] Now we subtract the two: \[ \frac{25}{6} - \frac{11}{6} = \frac{25 - 11}{6} = \frac{14}{6} = \frac{7}{3} \] So, Claire used \( \frac{7}{3} \) feet of string, which is equivalent to \( 2 \frac{1}{3} \) feet. Now, let's visualize it! Picture a long piece of string (the starting amount) with a section cut out (the used string) and a remainder on the side (the leftover portion). It’s like cutting a slice out of a cake; you see the yummy part you’ve eaten minus what’s left on your plate! In total, Claire used \( 2 \frac{1}{3} \) feet to hang those fabulous party decorations!