To convert each mixed number into an improper fraction, we use the formula for converting a mixed number [tex]\( a \frac{b}{c} \)[/tex] where 'a' is the whole number part, 'b' is the numerator of the fractional part, and 'c' is the denominator of the fractional part. The improper fraction is given by:
[tex]\[
\frac{a \times c + b}{c}
\][/tex]
Let's apply this formula step by step for each mixed number.
### (a) [tex]\( 4 \frac{3}{5} \)[/tex]
1. Identify the whole number part: [tex]\( a = 4 \)[/tex]
2. Identify the numerator of the fractional part: [tex]\( b = 3 \)[/tex]
3. Identify the denominator of the fractional part: [tex]\( c = 5 \)[/tex]
Using the formula:
[tex]\[
\frac{a \times c + b}{c} = \frac{4 \times 5 + 3}{5}
\][/tex]
Calculate the numerator:
[tex]\[
4 \times 5 + 3 = 20 + 3 = 23
\][/tex]
So, the improper fraction is:
[tex]\[
\frac{23}{5}
\][/tex]
### (b) [tex]\( 3 \frac{4}{9} \)[/tex]
1. Identify the whole number part: [tex]\( a = 3 \)[/tex]
2. Identify the numerator of the fractional part: [tex]\( b = 4 \)[/tex]
3. Identify the denominator of the fractional part: [tex]\( c = 9 \)[/tex]
Using the formula:
[tex]\[
\frac{a \times c + b}{c} = \frac{3 \times 9 + 4}{9}
\][/tex]
Calculate the numerator:
[tex]\[
3 \times 9 + 4 = 27 + 4 = 31
\][/tex]
So, the improper fraction is:
[tex]\[
\frac{31}{9}
\][/tex]
### (c) [tex]\( 6 \frac{2}{7} \)[/tex]
1. Identify the whole number part: [tex]\( a = 6 \)[/tex]
2. Identify the numerator of the fractional part: [tex]\( b = 2 \)[/tex]
3. Identify the denominator of the fractional part: [tex]\( c = 7 \)[/tex]
Using the formula:
[tex]\[
\frac{a \times c + b}{c} = \frac{6 \times 7 + 2}{7}
\][/tex]
Calculate the numerator:
[tex]\[
6 \times 7 + 2 = 42 + 2 = 44
\][/tex]
So, the improper fraction is:
[tex]\[
\frac{44}{7}
\][/tex]
Thus, the improper fractions corresponding to the given mixed numbers are:
(a) [tex]\( \frac{23}{5} \)[/tex]
(b) [tex]\( \frac{31}{9} \)[/tex]
(c) [tex]\( \frac{44}{7} \)[/tex]
