The whole number part of $53\div 8$ must be ${\color{blue}6},$ because

• $8$ can go into $53$ a total of ${\color{blue}6}$ times ($8 \times {\color{blue}6} = 48$), but

• $8$ cannot go into $53$ a total of $7$ times ($8 \times 7 = 56$).

The remainder is $53 - 48 = {\color{red}5},$ so

$$53\div 8 = {\color{blue}{6}} \,\textrm{R}\, {\color{red}{5}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($8$). Therefore,

$$53\div 8 = {\color{blue}6}\,\dfrac{\color{red}5}{8}\,.$$

The whole number part of $28\div 3$ must be ${\color{blue}9},$ because

• $3$ can go into $28$ a total of ${\color{blue}9}$ times ($3 \times {\color{blue}9} = 27$), but

• $3$ cannot go into $28$ a total of $10$ times ($3 \times 10 = 30$).

The remainder is $28 - 27 = {\color{red}1},$ so

$$28 \div 3 = {\color{blue}{9}} \,\textrm{R}\, {\color{red}{1}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($3$). Therefore,

$$28 \div 3 = {\color{blue}9}\,\dfrac{\color{red}1}{3}\,.$$

We need to work out $77\div 6.$ We start by going through the long division procedure as usual:

From the long division, we conclude that

$$77\div 6 = {\color{blue}{12}} \,\textrm{R}\, {\color{red}{5}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($6$). So, the mixed number is

$$77 \div 6 = {\color{blue}12} \, \dfrac{\color{red}5}{6}.$$

Therefore, Alice cuts the ribbon into $12 \, \dfrac{5}{6}$ inch pieces.

We need to work out $99\div 8.$ We start by going through the long division procedure as usual:

From the long division, we conclude that

$$99\div 8 = {\color{blue}{12}} \,\textrm{R}\, {\color{red}{3}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($8$). So, the mixed number is

$$99 \div 8 = {\color{blue}12} \, \dfrac{\color{red}3}{8}.$$

Therefore, each person gets $12 \, \dfrac{3}{8}$ pounds of rice.

We start by going through the long division procedure as usual:

From the long division, we conclude that

$$62\div 4 = {\color{blue}{15}} \,\textrm{R}\, {\color{red}{2}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($4$). So, the mixed number is

$$62\div 4 = {\color{blue}{15}} \, \dfrac{\color{red}2}{4}.$$

We can simplify the fractional part by dividing the numerator and denominator by $2\mathbin{:}$

$$\dfrac{2}{4} = \dfrac{2 \div 2}{4 \div 2} = \dfrac{1}{2}$$

Therefore, the simplified mixed number is $$62\div 4 = 15 \, \dfrac{1}{2}\,.$$

We start by going through the long division procedure as usual:

From the long division, we conclude that $$54\div 4 = {\color{blue}{13}} \,\textrm{R}\, {\color{red}{2}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($4$). So, the mixed number is $$54\div 4 = {\color{blue}{13}} \, \dfrac{\color{red}{2}}{4}.$$

We can simplify the fractional part by dividing the numerator and denominator by $2$:

$$\dfrac24 = \dfrac{2 \div 2}{4 \div 2} = \dfrac{1}{2}$$

Therefore, the simplified mixed number is $$54\div 4 = 13 \, \dfrac{1}{2}\,.$$

Here, we need to work out $323\div 7.$

We start by going through the long division procedure as usual:

From the long division, we conclude that

$$323\div 7 = {\color{blue}{46}} \,\textrm{R}\, {\color{red}{1}}.$$

To write the remainder as a fraction, we divide it by the original divisor ($7$). Therefore,

$$323\div 7 = {\color{blue}{46}} \,\dfrac{\color{red}{1}}{7}.$$

So, each plot will be $46 \, \dfrac{1}{7}$ acres.

We start by going through the long division procedure as usual:

From the long division, we conclude that $$495 \div 6 = {\color{blue}{82}} \,\textrm{R}\, {\color{red}{3}}.$$

To write the remainder as a fraction, we divide it by the original divisor $(6).$ So, the mixed number is $$495 \div 6 = {\color{blue}{82}} \,\dfrac{\color{red}{3}}{6}.$$

We can simplify the fractional part by dividing the numerator and denominator by $3$:

$$\dfrac{3}{6} =\dfrac{3 \div 3}{6 \div 3} = \dfrac{1}{2}$$

Therefore, the simplified mixed number is $$495 \div 6 = 82 \, \dfrac{1}{2}.$$