Answer
Verified
479.7k+ views
Hint:
At first convert the mixed fraction into improper fraction. Then check if you can cancel out any common factors from the numerator and the denominator.
Complete step-by-step answer:
We have to multiply following the fractions:
$\dfrac{3}{2}\times 5\dfrac{1}{3}$
Now, look at the fractions very carefully. The first one, $\dfrac{3}{2}$ is an improper fraction.
Improper fraction: where the numerator is greater than the denominator. Here the numerator is 3 and the denominator is 2. 3 is bigger than 2. So $\dfrac{3}{2}$ is an improper fraction.
The second one $5\dfrac{1}{3}$ is a mixed fraction.
Mixed fraction consists of a whole number and a proper fraction. Here 5 is whole number. The proper fraction is $\dfrac{1}{3}$ .
Proper fraction: where the numerator is less than the denominator. Here the numerator is 1 and the denominator is 3. 1 is smaller than 3. So $\dfrac{1}{3}$ is a proper fraction.
Now, before multiplying we have to convert the mixed fraction into an improper faction.
The formula for converting a mixed fraction into an improper fraction is:
$a\dfrac{c}{d}=\dfrac{\left( a\times d \right)+c}{d}$
For this problem: $a=5,c=1,d=3$
Now, by substituting the values of a, c and d we will get:
$\begin{align}
& 5\dfrac{1}{3}=\dfrac{\left( 5\times 3 \right)+1}{3}=\dfrac{15+1}{3}=\dfrac{16}{3} \\
& \\
\end{align}$
Now our multiplication looks like:
$\dfrac{3}{2}\times \dfrac{16}{3}$
Now in the numerator of the first fraction we have one 3 and in the denominator of the second fraction we also have a 3. So we can cancel them out.
$\dfrac{3}{2}\times \dfrac{16}{3}$
$=\dfrac{1}{2}\times \dfrac{16}{1}$
$\begin{align}
& =\dfrac{16}{2} \\
& =\dfrac{2\times 8}{2} \\
\end{align}$
Now, cancel out the 2 from the numerator and the denominator.
$\begin{align}
& =\dfrac{1\times 8}{1} \\
& =8 \\
\end{align}$
Hence the result of the multiplication is 8.
Note: When we multiply a mixed fraction with a proper fraction or an improper fraction, always convert the mixed fraction into an improper fraction first. Do not multiply the proper fraction part of the mixed fraction with any other fraction before converting the mixed fraction into an improper fraction.
Always cancel out the common factors from the numerator and the denominator.
At first convert the mixed fraction into improper fraction. Then check if you can cancel out any common factors from the numerator and the denominator.
Complete step-by-step answer:
We have to multiply following the fractions:
$\dfrac{3}{2}\times 5\dfrac{1}{3}$
Now, look at the fractions very carefully. The first one, $\dfrac{3}{2}$ is an improper fraction.
Improper fraction: where the numerator is greater than the denominator. Here the numerator is 3 and the denominator is 2. 3 is bigger than 2. So $\dfrac{3}{2}$ is an improper fraction.
The second one $5\dfrac{1}{3}$ is a mixed fraction.
Mixed fraction consists of a whole number and a proper fraction. Here 5 is whole number. The proper fraction is $\dfrac{1}{3}$ .
Proper fraction: where the numerator is less than the denominator. Here the numerator is 1 and the denominator is 3. 1 is smaller than 3. So $\dfrac{1}{3}$ is a proper fraction.
Now, before multiplying we have to convert the mixed fraction into an improper faction.
The formula for converting a mixed fraction into an improper fraction is:
$a\dfrac{c}{d}=\dfrac{\left( a\times d \right)+c}{d}$
For this problem: $a=5,c=1,d=3$
Now, by substituting the values of a, c and d we will get:
$\begin{align}
& 5\dfrac{1}{3}=\dfrac{\left( 5\times 3 \right)+1}{3}=\dfrac{15+1}{3}=\dfrac{16}{3} \\
& \\
\end{align}$
Now our multiplication looks like:
$\dfrac{3}{2}\times \dfrac{16}{3}$
Now in the numerator of the first fraction we have one 3 and in the denominator of the second fraction we also have a 3. So we can cancel them out.
$\dfrac{3}{2}\times \dfrac{16}{3}$
$=\dfrac{1}{2}\times \dfrac{16}{1}$
$\begin{align}
& =\dfrac{16}{2} \\
& =\dfrac{2\times 8}{2} \\
\end{align}$
Now, cancel out the 2 from the numerator and the denominator.
$\begin{align}
& =\dfrac{1\times 8}{1} \\
& =8 \\
\end{align}$
Hence the result of the multiplication is 8.
Note: When we multiply a mixed fraction with a proper fraction or an improper fraction, always convert the mixed fraction into an improper fraction first. Do not multiply the proper fraction part of the mixed fraction with any other fraction before converting the mixed fraction into an improper fraction.
Always cancel out the common factors from the numerator and the denominator.
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
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
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
Why is there a time difference of about 5 hours between class 10 social science CBSE