How do you simplify 4(0.2m – 0.3n) – 6(0.7m – 0.5n)?

Hint:
We will first of all use the distributive property to find out the values of 4(0.2m – 0.3n) and – 6(0.7m – 0.5n) separately, then we will add them and combine all the like terms.

Complete step by step solution:
We are given that we are required to simplify 4(0.2m – 0.3n) – 6(0.7m – 0.5n).
We can assume that x = 4 (0.2m – 0.3n) and y = - 6 (0.7m – 0.5n).
Therefore, we have the following expression with us:-
$ \Rightarrow $ 4(0.2m – 0.3n) – 6(0.7m – 0.5n) = x + y ………………(1)
Now, we will just find the values of x and y individually and then add them up.
Now, using the distributive property on x, we will then obtain the following expression with us:-
$ \Rightarrow $ x = 4(0.2m – 0.3n) = (0.2)(4)m – (0.3)(4)n
Simplifying the calculations in the right hand side of the above expression, we will then obtain the following expression:-
$ \Rightarrow $ x = 0.8m – 1.2n ……………(2)
Now, using the distributive property on y, we will then obtain the following expression with us:-
$ \Rightarrow $ y = - 6 (0.7m – 0.5n) = - (0.7)(6)m + (0.5)(6)n
Simplifying the calculations in the right hand side of the above expression, we will then obtain the following expression:-
$ \Rightarrow $ x = - 4.2m – 3n ……………(3)
Now, we will just put in the equations number (2) and (3) in equation number 1 and we will then obtain the following expression with us:-
$ \Rightarrow $ 4(0.2m – 0.3n) – 6(0.7m – 0.5n) = (0.8m – 1.2n) + (- 4.2m – 3n)
Simplifying the right hand side of the above expression, we will then obtain the following expression:-
$ \Rightarrow $ 4(0.2m – 0.3n) – 6(0.7m – 0.5n) = 0.8m – 1.2n - 4.2m – 3n
Now, combining the like terms by taking m and m common, we will then obtain the following expression:-
$ \Rightarrow $ 4(0.2m – 0.3n) – 6(0.7m – 0.5n) = (0.8 – 4.2)m – (1.2 + 3)n
Simplifying the right hand side of the above expression, we will then obtain the following expression:-
$ \Rightarrow $ 4(0.2m – 0.3n) – 6(0.7m – 0.5n) = -3.4m – 4.2n

Hence, the answer is – 3.4 m – 4.2 n.

Note:
The students must note that we have used the distributive property in the above solution, as we mentioned but the definition of distribution function was not mentioned there, so here it is.
Distributive Property: If we have any 3 numbers a, b and c, then we have:
a (b + c) = ab + ac
Here, we just replaced a, b and c by the required numbers and thus obtained the expressions as we did in the solution above.
The students must note that they may also use the same property without taking two different variables x and y and just solving everything in the same line.