Question

Simplify{(220 - 140) + (10 x 9 + (-2 x 5)]}
The LCM and HCF of two numbers are 432 and 72 respectively. If one of the
numbers is 216. what is the other?
-8
3
52
13​

Answer 1

Given: a)${(220 - 140) + (10 \times9 + (-2 \times 5))$

b)The LCM and HCF of the two numbers are $432$and $72$respectively and one of  the  numbers is 216.

We have to find the other number.

a)${(220 - 140) + (10 \times9 + (-2 \times 5))$

We are solving in the following way:

By using the Bodmas rule, we are solving the above equation.

As we know that the Bodmas rule is used to remember the order of operations to be followed while solving expressions in mathematics.

Where,

$\begin{array}{l}\mathrm{B}=\text{brackets}\\\mathrm{O}=\text { order of powers or rules } \\\mathrm{D}=\text { division } \\\mathrm{M}=\text { multiplication } \\\mathrm{A}=\text { addition } \\\mathrm{S}=\text { subtraction }\end{array}$

We have,

${(220 - 140) + (10 \times9 + (-2 \times 5))$

$\begin{array}{l}=(220-140)+\left(10{\times} 9+\left(-2{\times} 5\right)\right) \\=(80)+\left(10^{\times} 9+\left(-2{\times} 5\right)\right) \\=80+\left(10{\times} 9+\left(-2{\times} 5\right)\right) \\=80+\left(10{\times} 9+(-10)\right) \\=80+\left(10{\times} 9+-10\right) \\=80+\left(10{\times} 9-10\right) \\=80+(90-10) \\=80+(80) \\=80+80 \\=160\end{array}$

Hence, the solution of the above equation is$160$.

b) The LCM and HCF of the two numbers are $432$and $72$respectively and one of  the  numbers is 216.

We have to find the other number.

We are solving in the following way:

Let assume the other number be x.

As we know that the product of LCM and HCF of the two numbers is equal to the product of these numbers.

So, from the above statement:

$=432\times72=216\timesx\\\\=\frac{432\times72}{216} =x\\\\=>x=144$

Hence, the other number will be$144$.

a) The solution of the above equation is$160$.

b) The other number will be$144$.

Answer 2

(220 - 140) + (10 x 9 + (-2 x 5)) = 160

The LCM and HCF of two numbers are 432 and 72 respectively one of the

numbers is 216 , then other is 144

Solution:

Use BODMAS  

B - Bracket  

O - of  

D - Division

M - Multiplication

A  - Addition  

S - Subtraction

Step 1 :

Solve Parenthesis

(220 - 140) + (10 x 9 + (-2 x 5))

Subtract the numbers

= (80) + (10 x 9 + (-2 x 5))

Multiply the numbers

= 80 + (10 x 9 + (-10))

Step 2 :

Use + (-a) = - a

= 80 + (10 x 9 - 10 )

Step 3 :

Multiply the numbers

= 80 + (90 - 10 )

Step 4 :

Subtract the numbers

= 80 + (80 )

Step 5 :

Remove the parenthesis and add the number

= 80 + 80

= 160

(220 - 140) + (10 x 9 + (-2 x 5)) = 160

Product of Two numbers (a , b)  = LCM (a , b) x HCF (a , b)

LCM (a , b) = 432

HCF (a , b) = 72

a = 216

b = ?

Substitute the values

216b = 432 x 72

=> b = 2 x 72

=> b = 144

Hence other number is 144