Answer
Verified
375.9k+ views
Hint: In this problem, we have to find the multiplication and division of the given mixed fractions. We should first know that an improper fraction is a fraction, where the numerator is greater than or equal to the denominator. Here we can convert the mixed fraction into its improper fraction by multiplying the whole number term and the denominator and adding it to the numerator. We can then multiply and divide them to get the required solution.
Complete step-by-step solution:
1. Divide \[5\dfrac{3}{5}\div 2\dfrac{13}{15}\]
We can now convert the given mixed fractions to its improper fraction.
We can first take the whole number part of the first term, multiply the whole number part 5 and the denominator 5 and add the number 25 to the numerator 3. Write the result 28 in the numerator and the denominator remains the same there.
We can now write the mixed fraction, we get
\[\Rightarrow \dfrac{28}{5}\]
Similarly, we can convert the second term, we get
\[\Rightarrow \dfrac{43}{15}\]
We can now divide the terms, we get
\[\Rightarrow \dfrac{28}{5}\div \dfrac{43}{15}\]
Which can be written as,
\[\Rightarrow \dfrac{\dfrac{28}{5}}{\dfrac{43}{15}}=\dfrac{28}{5}\times \dfrac{15}{43}\]
We can now simplify the above step, we get
\[\Rightarrow \dfrac{28}{5}\times \dfrac{15}{43}=\dfrac{84}{43}\]
Therefore, \[5\dfrac{3}{5}\div 2\dfrac{13}{15}=\dfrac{84}{43}\]
2. Multiply \[1\dfrac{7}{8}\times \dfrac{16}{21}\times 1\dfrac{13}{15}\]
We can now convert the above mixed fraction into improper fraction, as we done in the above problem, we get
\[\Rightarrow \dfrac{15}{8}\times \dfrac{16}{21}\times \dfrac{28}{15}\]
We can now multiply the above terms, we get
\[\Rightarrow \dfrac{56}{21}\]
Therefore, \[1\dfrac{7}{8}\times \dfrac{16}{21}\times 1\dfrac{13}{15}=\dfrac{56}{21}\]
3. We can now find the smallest number between \[\dfrac{1}{20}\div \dfrac{1}{5}\] or \[\dfrac{1}{5}\div \dfrac{1}{20}\]
We can now divide the given fraction and reciprocal the fraction, by multiplying the denominator inversely to the numerator, we get
\[\Rightarrow \dfrac{\dfrac{1}{20}}{\dfrac{1}{5}}=\dfrac{1}{20}\times \dfrac{5}{1}=\dfrac{1}{4}=0.25\]……. (1)
Similarly, we can write the next terms as,
\[\Rightarrow \dfrac{\dfrac{1}{5}}{\dfrac{1}{20}}=\dfrac{1}{5}\times \dfrac{20}{1}=4\]….. (2)
Now by comparing (1) and (2), we can say that (1) is smaller.
Therefore, \[\dfrac{1}{20}\div \dfrac{1}{5}\] is smaller than \[\dfrac{1}{5}\div \dfrac{1}{20}\].
Note: Students make mistakes while converting the mixed fractions into its improper fraction, by multiplying the whole number part to the denominator and adding it to the numerator and finally writing the result in the numerator. We should concentrate while cross multiplying the numbers.
Complete step-by-step solution:
1. Divide \[5\dfrac{3}{5}\div 2\dfrac{13}{15}\]
We can now convert the given mixed fractions to its improper fraction.
We can first take the whole number part of the first term, multiply the whole number part 5 and the denominator 5 and add the number 25 to the numerator 3. Write the result 28 in the numerator and the denominator remains the same there.
We can now write the mixed fraction, we get
\[\Rightarrow \dfrac{28}{5}\]
Similarly, we can convert the second term, we get
\[\Rightarrow \dfrac{43}{15}\]
We can now divide the terms, we get
\[\Rightarrow \dfrac{28}{5}\div \dfrac{43}{15}\]
Which can be written as,
\[\Rightarrow \dfrac{\dfrac{28}{5}}{\dfrac{43}{15}}=\dfrac{28}{5}\times \dfrac{15}{43}\]
We can now simplify the above step, we get
\[\Rightarrow \dfrac{28}{5}\times \dfrac{15}{43}=\dfrac{84}{43}\]
Therefore, \[5\dfrac{3}{5}\div 2\dfrac{13}{15}=\dfrac{84}{43}\]
2. Multiply \[1\dfrac{7}{8}\times \dfrac{16}{21}\times 1\dfrac{13}{15}\]
We can now convert the above mixed fraction into improper fraction, as we done in the above problem, we get
\[\Rightarrow \dfrac{15}{8}\times \dfrac{16}{21}\times \dfrac{28}{15}\]
We can now multiply the above terms, we get
\[\Rightarrow \dfrac{56}{21}\]
Therefore, \[1\dfrac{7}{8}\times \dfrac{16}{21}\times 1\dfrac{13}{15}=\dfrac{56}{21}\]
3. We can now find the smallest number between \[\dfrac{1}{20}\div \dfrac{1}{5}\] or \[\dfrac{1}{5}\div \dfrac{1}{20}\]
We can now divide the given fraction and reciprocal the fraction, by multiplying the denominator inversely to the numerator, we get
\[\Rightarrow \dfrac{\dfrac{1}{20}}{\dfrac{1}{5}}=\dfrac{1}{20}\times \dfrac{5}{1}=\dfrac{1}{4}=0.25\]……. (1)
Similarly, we can write the next terms as,
\[\Rightarrow \dfrac{\dfrac{1}{5}}{\dfrac{1}{20}}=\dfrac{1}{5}\times \dfrac{20}{1}=4\]….. (2)
Now by comparing (1) and (2), we can say that (1) is smaller.
Therefore, \[\dfrac{1}{20}\div \dfrac{1}{5}\] is smaller than \[\dfrac{1}{5}\div \dfrac{1}{20}\].
Note: Students make mistakes while converting the mixed fractions into its improper fraction, by multiplying the whole number part to the denominator and adding it to the numerator and finally writing the result in the numerator. We should concentrate while cross multiplying the numbers.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE