Convert the following to mixed number: a) 5/4 b) 21/5 c) 32/10

Here are the conversions of the improper fractions to mixed numbers:

a) Convert $\frac{5}{4}$ to a mixed number.

Step 1: Divide the numerator (5) by the denominator (4). $5 \div 4 = 1 \text{ with a remainder of } 1$

Step 2: Write the mixed number using the whole number, remainder, and original denominator. $\frac{5}{4} = 1\frac{1}{4}$ The mixed number is $\boxed{\mathbf{1\frac{1}{4}}}$.

b) Convert $\frac{21}{5}$ to a mixed number.

Step 1: Divide the numerator (21) by the denominator (5). $21 \div 5 = 4 \text{ with a remainder of } 1$

Step 2: Write the mixed number using the whole number, remainder, and original denominator. $\frac{21}{5} = 4\frac{1}{5}$ The mixed number is $\boxed{\mathbf{4\frac{1}{5}}}$.

c) Convert $\frac{32}{10}$ to a mixed number.

Step 1: Divide the numerator (32) by the denominator (10). $32 \div 10 = 3 \text{ with a remainder of } 2$

Step 2: Write the mixed number using the whole number, remainder, and original denominator. $\frac{32}{10} = 3\frac{2}{10}$

Step 3: Simplify the fractional part of the mixed number. Both 2 and 10 are divisible by 2. $3\frac{2}{10} = 3\frac{2 \div 2}{10 \div 2} = 3\frac{1}{5}$ The mixed number is $\boxed{\mathbf{3\frac{1}{5}}}$.