1 sometimes it is helpful to rewrite mixed numbers in a form that includes a fraction greater than 1. use the number line to write the missing numbers. a. $1\frac{3}{6}=\frac{\square}{6}$ b. $2\frac{5}{6}=1\frac{\square}{6}$ c. $2\frac{2}{6}=1\frac{\square}{\square}$ d. $3\frac{1}{6}=\square\frac{\square}{\square}$ 4 what is $3\frac{1}{3}-1\frac{1}{2}$? show your work.

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Accepted Answer

### Part 1: Rewriting Mixed Numbers (a - d)
#### a. $1\frac{3}{6}=\frac{\square}{6}$
# Explanation:
## Step 1: Convert mixed number to improper fraction.
A mixed number $a\frac{b}{c}=\frac{a\times c + b}{c}$. For $1\frac{3}{6}$, $a = 1$, $b = 3$, $c = 6$. So $1\times6+3 = 6 + 3=9$.
# Answer:
$9$

#### b. $2\frac{5}{6}=1\frac{\square}{6}$
# Explanation:
## Step 1: Subtract 1 from the whole number part.
The whole number part of $2\frac{5}{6}$ is 2. Subtract 1: $2 - 1 = 1$. Now, add the fraction part to the remaining whole number's fraction contribution. The fraction part is $\frac{5}{6}$, and the remaining whole number (1) can be written as $\frac{6}{6}$. So $\frac{6}{6}+\frac{5}{6}=\frac{11}{6}$ for the fraction part of the new mixed number.
# Answer:
$11$

#### c. $2\frac{2}{6}=1\frac{\square}{\square}$
# Explanation:
## Step 1: Subtract 1 from the whole number part.
Whole number part: $2 - 1 = 1$.
## Step 2: Add the fraction part and the fraction from the subtracted whole number.
The fraction part of $2\frac{2}{6}$ is $\frac{2}{6}$, and 1 (the subtracted whole number) is $\frac{6}{6}$. So $\frac{6}{6}+\frac{2}{6}=\frac{8}{6}$.
# Answer:
$\frac{8}{6}$ (or simplified $\frac{4}{3}$, but keeping denominator 6 as per the pattern, it's $\frac{8}{6}$)

#### d. $3\frac{1}{6}=\square\frac{\square}{\square}$
# Explanation:
## Step 1: Subtract 1 from the whole number part (or keep as is with fraction adjustment).
We can write $3\frac{1}{6}$ as $2 + 1\frac{1}{6}$, but more accurately, using the same method as before: subtract 1 from 3 (whole number part) to get 2, and then the fraction part: 1 (the subtracted 1) is $\frac{6}{6}$, so $\frac{6}{6}+\frac{1}{6}=\frac{7}{6}$? Wait, no. Wait, $3\frac{1}{6}=2 + 1\frac{1}{6}$, but if we want to write it as $2\frac{7}{6}$ (since $1\frac{1}{6}=\frac{7}{6}$ when considering $2 + \frac{7}{6}$? Wait, no, let's do it properly. A mixed number $a\frac{b}{c}$ can be rewritten by decreasing the whole number by 1 and increasing the fraction by $\frac{c}{c}$. So for $3\frac{1}{6}$, decrease whole number by 1: $3 - 1 = 2$, increase fraction by $\frac{6}{6}$: $\frac{1}{6}+\frac{6}{6}=\frac{7}{6}$. So $3\frac{1}{6}=2\frac{7}{6}$.
# Answer:
$2\frac{7}{6}$ (or $2\frac{7}{6}$, the numerator is 7, denominator is 6, whole number is 2)

### Part 2: $3\frac{1}{3}-1\frac{1}{2}$
# Explanation:
## Step 1: Convert mixed numbers to improper fractions.
For $3\frac{1}{3}$: $3\times3 + 1=9 + 1 = 10$, so $3\frac{1}{3}=\frac{10}{3}$. For $1\frac{1}{2}$: $1\times2+1 = 2 + 1 = 3$, so $1\frac{1}{2}=\frac{3}{2}$.
## Step 2: Find a common denominator.
The least common denominator of 3 and 2 is 6. Convert $\frac{10}{3}$ to sixths: $\frac{10}{3}=\frac{10\times2}{3\times2}=\frac{20}{6}$. Convert $\frac{3}{2}$ to sixths: $\frac{3}{2}=\frac{3\times3}{2\times3}=\frac{9}{6}$.
## Step 3: Subtract the fractions.
$\frac{20}{6}-\frac{9}{6}=\frac{20 - 9}{6}=\frac{11}{6}$.
## Step 4: Convert back to a mixed number (optional, but common).
$\frac{11}{6}=1\frac{5}{6}$ (since $6\times1 + 5 = 11$).
# Answer:
$1\frac{5}{6}$ (or $\frac{11}{6}$)

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Question

Explanation:

Part 1: Rewriting Mixed Numbers (a - d)

a. \(1\frac{3}{6}=\frac{\square}{6}\)

Step 1: Convert mixed number to improper fraction.

Step 1: Subtract 1 from the whole number part.

Step 1: Subtract 1 from the whole number part.

Step 2: Add the fraction part and the fraction from the subtracted whole number.

Answer:

b. \(2\frac{5}{6}=1\frac{\square}{6}\)