Answer
384.6k+ views
Hint: First consider the unknown number to be some variable and then express the given algebraic phrase in algebraic expression. After writing the phrase in the equation check all the constants should be at right side and variables at left side of the equation if not then send them with help of algebraic operations. And finally divide both sides with the coefficient of the variable to get the required number.
Complete step by step solution:
In order to find the number in the phrase “Two-thirds of a number is five-sixths”, we will first consider that number to be a variable.
Let us consider the required number be $x$
Two-thirds can also be written as two parts of a whole divided in three parts and expressed algebraically as $\dfrac{2}{3}$
Similarly, five-sixth can also be written as five parts of a whole divided in six parts and expressed algebraically as $\dfrac{5}{6}$
Now we can express the given phrase “Two-thirds of a number is five-sixths” in algebraic expression as follows
$ \Rightarrow \dfrac{2}{3} \times x = \dfrac{5}{6}$
Dividing both sides with coefficient of $x$, we will get
$
\Rightarrow \dfrac{2}{3} \div \dfrac{2}{3} \times x = \dfrac{5}{6} \div \dfrac{2}{3} \\
\Rightarrow x = \dfrac{5}{6} \div \dfrac{2}{3} \\
$
It can also be written as
$
\Rightarrow x = \dfrac{5}{6} \times \dfrac{3}{2} \\
\Rightarrow x = \dfrac{5}{4} \\
$
Therefore the required number is equals to $\dfrac{5}{4}$
Note: Division sign between the two factors is converted into multiplication sign along with the multiplicative inverse of the second term, because as we know that division and multiplication are the inverse operation for each other. Also when solving this type of word problems where an unknown number is present, then your first step should be to consider that number to be a variable and the second step is to express the problem algebraically.
Complete step by step solution:
In order to find the number in the phrase “Two-thirds of a number is five-sixths”, we will first consider that number to be a variable.
Let us consider the required number be $x$
Two-thirds can also be written as two parts of a whole divided in three parts and expressed algebraically as $\dfrac{2}{3}$
Similarly, five-sixth can also be written as five parts of a whole divided in six parts and expressed algebraically as $\dfrac{5}{6}$
Now we can express the given phrase “Two-thirds of a number is five-sixths” in algebraic expression as follows
$ \Rightarrow \dfrac{2}{3} \times x = \dfrac{5}{6}$
Dividing both sides with coefficient of $x$, we will get
$
\Rightarrow \dfrac{2}{3} \div \dfrac{2}{3} \times x = \dfrac{5}{6} \div \dfrac{2}{3} \\
\Rightarrow x = \dfrac{5}{6} \div \dfrac{2}{3} \\
$
It can also be written as
$
\Rightarrow x = \dfrac{5}{6} \times \dfrac{3}{2} \\
\Rightarrow x = \dfrac{5}{4} \\
$
Therefore the required number is equals to $\dfrac{5}{4}$
Note: Division sign between the two factors is converted into multiplication sign along with the multiplicative inverse of the second term, because as we know that division and multiplication are the inverse operation for each other. Also when solving this type of word problems where an unknown number is present, then your first step should be to consider that number to be a variable and the second step is to express the problem algebraically.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)