Sure, let's work through each part of the question systematically:
### (a) [tex]\( 2 \frac{4}{5} \times 11 \)[/tex]
1. Convert the mixed fraction to an improper fraction:
[tex]\[ 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \][/tex]
2. Now, multiply the improper fraction by 11:
[tex]\[ \frac{14}{5} \times 11 = \frac{14 \times 11}{5} = \frac{154}{5} \][/tex]
3. Convert the improper fraction back to a mixed fraction:
[tex]\[ \frac{154}{5} = 30 \frac{4}{5} \][/tex]
So the product is: [tex]\( 30 \frac{4}{5} \)[/tex].
### (6) [tex]\( 7 \frac{2}{8} \times \frac{4}{5} \)[/tex]
1. Simplify the mixed fraction:
[tex]\[ 7 \frac{2}{8} = 7 \frac{1}{4} \][/tex]
2. Convert to an improper fraction:
[tex]\[ 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4} \][/tex]
3. Multiply by [tex]\( \frac{4}{5} \)[/tex]:
[tex]\[ \frac{29}{4} \times \frac{4}{5} = \frac{29 \times 4}{4 \times 5} = \frac{116}{20} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{116}{20} = \frac{29}{5} = 5 \frac{4}{5} \][/tex]
So the product is: [tex]\( 5 \frac{4}{5} \)[/tex].
### (d) [tex]\( 7 \times \frac{2}{9} \)[/tex]
1. Multiply the whole number by the fraction:
[tex]\[ 7 \times \frac{2}{9} = \frac{7 \times 2}{9} = \frac{14}{9} \][/tex]
2. Convert to a mixed fraction:
[tex]\[ \frac{14}{9} = 1 \frac{5}{9} \][/tex]
So the product is: [tex]\( 1 \frac{5}{9} \)[/tex].
### (e) [tex]\( 24 \times \frac{3}{15} \)[/tex]
1. Simplify the fraction [tex]\( \frac{3}{15} \)[/tex]:
[tex]\[ \frac{3}{15} = \frac{1}{5} \][/tex]
2. Multiply the whole number by the simplified fraction:
[tex]\[ 24 \times \frac{1}{5} = \frac{24}{5} \][/tex]
3. Convert to a mixed fraction:
[tex]\[ \frac{24}{5} = 4 \frac{4}{5} \][/tex]
So the product is: [tex]\( 4 \frac{4}{5} \)[/tex].
### (c) [tex]\( 3 \frac{1}{7} \times \)[/tex] (missing factor)
Since the factor to multiply is missing, I'll address the reciprocal section and skip this part.
### (क) [tex]\( \frac{8}{9} \times \frac{2}{} \)[/tex] (missing denominator)
The denominator is not provided. Instead, let's quickly discuss reciprocals as requested.
### Reciprocal of a Fraction
Given a fraction [tex]\( \frac{a}{b} \)[/tex], its reciprocal is [tex]\( \frac{b}{a} \)[/tex].
For example:
- Reciprocal of [tex]\( \frac{3}{4} \)[/tex] is [tex]\( \frac{4}{3} \)[/tex].
- Reciprocal of [tex]\( \frac{7}{5} \)[/tex] is [tex]\( \frac{5}{7} \)[/tex].
Remember, to find the reciprocal, simply switch the numerator and the denominator, ensuring the fraction is non-zero.
