Multiply and reduce to lowest form and convert into a mixed fraction.
$
\left( i \right){\text{ 7}} \times \dfrac{3}{5}{\text{ }}\left( {ii} \right){\text{ 4}} \times \dfrac{1}{3}{\text{ }} \\
\left( {iii} \right){\text{ 2}} \times \dfrac{6}{7}{\text{ }}\left( {iv} \right){\text{ 5}} \times \dfrac{2}{9}{\text{ }} \\
\left( v \right){\text{ }}\dfrac{5}{2} \times 6{\text{ }}\left( {vi} \right){\text{ }}11 \times \dfrac{4}{7}{\text{ }} \\
\left( {vii} \right){\text{ 20}} \times \dfrac{4}{5}{\text{ }}\left( {viii} \right){\text{ }}\dfrac{2}{3} \times 4{\text{ }} \\
$
Answer
381.9k+ views
Hint- Use the concept that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1.
Whenever the numerator is greater than the denominator, the fraction is called an improper fraction. For example $\dfrac{5}{4}$
As we know that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1.
Now as we know mixed fraction$ = $quotient \[\dfrac{{{\text{remainder}}}}{{{\text{divisor}}}}\]
So, using this property of fraction we have,
$\left( i \right) = 7 \times \dfrac{3}{5} = \dfrac{{21}}{5}$ So, this is in lowest form as $\dfrac{{21}}{5}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{21}}{5} = 4\dfrac{1}{5}\], because \[\left( {\left( {\left( {5 \times 4} \right) + 1} \right) = 21} \right)\]
(Where 5 is divisor, 4 is quotient and 1 is remainder)
$\left( {ii} \right) = 4 \times \dfrac{1}{3} = \dfrac{4}{3}$ So, this is in lowest form as $\dfrac{4}{3}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{4}{3} = 1\dfrac{1}{3}\], because \[\left( {\left( {\left( {1 \times 3} \right) + 1} \right) = 4} \right)\]
(Where 3 is divisor, 1 is quotient and 1 is remainder)
$\left( {iii} \right) = 2 \times \dfrac{6}{7} = \dfrac{{12}}{7}$ So, this is in lowest form as $\dfrac{{12}}{7}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{12}}{7} = 1\dfrac{5}{7}\], because \[\left( {\left( {\left( {1 \times 7} \right) + 5} \right) = 12} \right)\]
(Where 7 is divisor, 1 is quotient and 5 is remainder)
$\left( {iv} \right) = 5 \times \dfrac{2}{9} = \dfrac{{10}}{9}$ So, this is in lowest form as $\dfrac{{10}}{9}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{10}}{9} = 1\dfrac{1}{9}\], because \[\left( {\left( {\left( {1 \times 9} \right) + 1} \right) = 10} \right)\]
(Where 9 is divisor, 1 is quotient and 1 is remainder)
$\left( v \right) = \dfrac{5}{2} \times 6 = 15$
Now, we have to convert 15 into fraction so multiply by any number in numerator and denominator but we have to write the lowest form of fraction so we multiply 1 in numerator and denominator.
$ \Rightarrow 15 = \dfrac{{15 \times 1}}{1} = \dfrac{{15}}{1}$ So, this is written in lowest form and has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{15}}{1} = 15\dfrac{0}{1}\], because \[\left( {\left( {\left( {15 \times 1} \right) + 0} \right) = 15} \right)\]
(Where 1 is divisor, 15 is quotient and 0 is remainder)
$\left( {vi} \right) = 11 \times \dfrac{4}{7} = \dfrac{{44}}{7}$ So, this is in lowest form as $\dfrac{{44}}{7}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{44}}{7} = 6\dfrac{2}{7}\], because \[\left( {\left( {\left( {7 \times 6} \right) + 2} \right) = 44} \right)\]
(Where 7 is divisor, 6 is quotient and 2 is remainder)
$\left( {vii} \right) = 20 \times \dfrac{4}{5} = \dfrac{{80}}{5} = 16$
Now, we have to convert 16 into fraction so multiply by any number in numerator and denominator but we have to write the lowest form of fraction so we multiply 1 in numerator and denominator.
$ \Rightarrow 16 = \dfrac{{16 \times 1}}{1} = \dfrac{{16}}{1}$ So, this is written in lowest form and has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{16}}{1} = 16\dfrac{0}{1}\], because \[\left( {\left( {\left( {16 \times 1} \right) + 0} \right) = 16} \right)\]
(Where 1 is divisor, 16 is quotient and 0 is remainder)
$\left( {viii} \right) = \dfrac{2}{3} \times 4 = \dfrac{8}{3}$ So, this is in lowest form as $\dfrac{8}{3}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{8}{3} = 2\dfrac{2}{3}\], because \[\left( {\left( {\left( {2 \times 3} \right) + 2} \right) = 8} \right)\]
(Where 3 is divisor, 2 is quotient and 2 is remainder)
So, these are the required answers.
Note- In such types of questions the key concept is that while converting the fraction into lowest form fraction i.e. in $\dfrac{p}{q}$ form where $q \ne 0$, then p and q must have no common factors except 1. So, if a fraction has some common factors simply cancel out, it will be converted into the lowest form fraction, then apply a mixed fraction formula to convert the fraction into mixed fraction, we will get the required answer.
Whenever the numerator is greater than the denominator, the fraction is called an improper fraction. For example $\dfrac{5}{4}$
As we know that whenever the fraction $\dfrac{p}{q}$ is in lowest form then the fraction has no common factors except 1.
Now as we know mixed fraction$ = $quotient \[\dfrac{{{\text{remainder}}}}{{{\text{divisor}}}}\]
So, using this property of fraction we have,
$\left( i \right) = 7 \times \dfrac{3}{5} = \dfrac{{21}}{5}$ So, this is in lowest form as $\dfrac{{21}}{5}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{21}}{5} = 4\dfrac{1}{5}\], because \[\left( {\left( {\left( {5 \times 4} \right) + 1} \right) = 21} \right)\]
(Where 5 is divisor, 4 is quotient and 1 is remainder)
$\left( {ii} \right) = 4 \times \dfrac{1}{3} = \dfrac{4}{3}$ So, this is in lowest form as $\dfrac{4}{3}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{4}{3} = 1\dfrac{1}{3}\], because \[\left( {\left( {\left( {1 \times 3} \right) + 1} \right) = 4} \right)\]
(Where 3 is divisor, 1 is quotient and 1 is remainder)
$\left( {iii} \right) = 2 \times \dfrac{6}{7} = \dfrac{{12}}{7}$ So, this is in lowest form as $\dfrac{{12}}{7}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{12}}{7} = 1\dfrac{5}{7}\], because \[\left( {\left( {\left( {1 \times 7} \right) + 5} \right) = 12} \right)\]
(Where 7 is divisor, 1 is quotient and 5 is remainder)
$\left( {iv} \right) = 5 \times \dfrac{2}{9} = \dfrac{{10}}{9}$ So, this is in lowest form as $\dfrac{{10}}{9}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{10}}{9} = 1\dfrac{1}{9}\], because \[\left( {\left( {\left( {1 \times 9} \right) + 1} \right) = 10} \right)\]
(Where 9 is divisor, 1 is quotient and 1 is remainder)
$\left( v \right) = \dfrac{5}{2} \times 6 = 15$
Now, we have to convert 15 into fraction so multiply by any number in numerator and denominator but we have to write the lowest form of fraction so we multiply 1 in numerator and denominator.
$ \Rightarrow 15 = \dfrac{{15 \times 1}}{1} = \dfrac{{15}}{1}$ So, this is written in lowest form and has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{15}}{1} = 15\dfrac{0}{1}\], because \[\left( {\left( {\left( {15 \times 1} \right) + 0} \right) = 15} \right)\]
(Where 1 is divisor, 15 is quotient and 0 is remainder)
$\left( {vi} \right) = 11 \times \dfrac{4}{7} = \dfrac{{44}}{7}$ So, this is in lowest form as $\dfrac{{44}}{7}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{44}}{7} = 6\dfrac{2}{7}\], because \[\left( {\left( {\left( {7 \times 6} \right) + 2} \right) = 44} \right)\]
(Where 7 is divisor, 6 is quotient and 2 is remainder)
$\left( {vii} \right) = 20 \times \dfrac{4}{5} = \dfrac{{80}}{5} = 16$
Now, we have to convert 16 into fraction so multiply by any number in numerator and denominator but we have to write the lowest form of fraction so we multiply 1 in numerator and denominator.
$ \Rightarrow 16 = \dfrac{{16 \times 1}}{1} = \dfrac{{16}}{1}$ So, this is written in lowest form and has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{{16}}{1} = 16\dfrac{0}{1}\], because \[\left( {\left( {\left( {16 \times 1} \right) + 0} \right) = 16} \right)\]
(Where 1 is divisor, 16 is quotient and 0 is remainder)
$\left( {viii} \right) = \dfrac{2}{3} \times 4 = \dfrac{8}{3}$ So, this is in lowest form as $\dfrac{8}{3}$ has no common factors except 1.
And this is an improper fraction according to the above condition.
Now, convert it into mixed fraction \[ \Rightarrow \dfrac{8}{3} = 2\dfrac{2}{3}\], because \[\left( {\left( {\left( {2 \times 3} \right) + 2} \right) = 8} \right)\]
(Where 3 is divisor, 2 is quotient and 2 is remainder)
So, these are the required answers.
Note- In such types of questions the key concept is that while converting the fraction into lowest form fraction i.e. in $\dfrac{p}{q}$ form where $q \ne 0$, then p and q must have no common factors except 1. So, if a fraction has some common factors simply cancel out, it will be converted into the lowest form fraction, then apply a mixed fraction formula to convert the fraction into mixed fraction, we will get the required answer.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
State Gay Lusaaccs law of gaseous volume class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

Which is the tallest animal on the earth A Giraffes class 9 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
