Change each improper fraction into a mixed number.

(a) [tex]\frac{13}{2}[/tex]

(b) [tex]\frac{19}{5}[/tex]

(c) [tex]\frac{41}{4}[/tex]



Answer :

Sure, let's convert each improper fraction into a mixed number step-by-step.

### Part (a)
[tex]\[ \frac{13}{2} \][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[ 13 \div 2 = 6 \quad \text{remainder } 1 \][/tex]
2. Express this as a mixed number:
[tex]\[ 13 = 6 \cdot 2 + 1 \implies \frac{13}{2} = 6 \frac{1}{2} \][/tex]

So, [tex]\(\frac{13}{2} = 6 \frac{1}{2}\)[/tex].

### Part (b)
[tex]\[ \frac{19}{5} \][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[ 19 \div 5 = 3 \quad \text{remainder } 4 \][/tex]
2. Express this as a mixed number:
[tex]\[ 19 = 3 \cdot 5 + 4 \implies \frac{19}{5} = 3 \frac{4}{5} \][/tex]

So, [tex]\(\frac{19}{5} = 3 \frac{4}{5}\)[/tex].

### Part (c)
[tex]\[ \frac{41}{4} \][/tex]
1. Perform the division of the numerator by the denominator:
[tex]\[ 41 \div 4 = 10 \quad \text{remainder } 1 \][/tex]
2. Express this as a mixed number:
[tex]\[ 41 = 10 \cdot 4 + 1 \implies \frac{41}{4} = 10 \frac{1}{4} \][/tex]

So, [tex]\(\frac{41}{4} = 10 \frac{1}{4}\)[/tex].

Thus, the final mixed numbers are:
- [tex]\(\frac{13}{2} = 6 \frac{1}{2}\)[/tex]
- [tex]\(\frac{19}{5} = 3 \frac{4}{5}\)[/tex]
- [tex]\(\frac{41}{4} = 10 \frac{1}{4}\)[/tex]

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