Answer to Question #197336 in Algebra for Accordance

Question

Activity 2.3 Application of mathematical concepts and procedures in algebra

Mathematical idea (concept or procedure) Example of application in algebra

    1. Learnersmustbeabletoswitchcomfortablybetween all operations involving whole numbers and apply these operations.

Two ideas come together here:

• command of number and number sense

• comfortably operating numbers

In the Intermediate Phase these numbers are positive; in the Senior Phase learners start operating on integers (including positive and negative whole numbers).

What is the rule that you can abstract from what you found above?

Explain why this is the case.

Generalise your findings to predict what you will observe in the sum of

(a) fiveconsecutivemultiples of 10 like (30 + 40 + 50 + 60 + 70)

(b) three consecutive numbers like

(7 + 8 + 9)

(c) seven consecutive numbers like

(2 + 3 + 4 + 5 + 6 + 7 + 8)

Answer 1

(a)

$30 + 40 + 50 + 60 + 70=250$

we divide the sum of the numbers by tally of the numbers

$\frac{250}{5}=50\implies 5^{th}multiple \space of \space 50=50\times 5=250$

Fifth multiple of the median number is equal to the sum of the numbers.

(b)

$7 + 8 + 9=24$

we divide the sum of the numbers by tally of the numbers

$\frac{24}{3}=8\implies 3^{rd}multiple \space of \space 8=8\times 3=24$

Third multiple of the median number is equal to the sum of the numbers.

(c)

$2 + 3 + 4 + 5 + 6 + 7 + 8=35$

we divide the sum of the numbers by tally of the numbers

$\frac{35}{7}=5\implies 7^{th}multiple \space of \space 5=5\times 7=35$

Seventh multiple of the median number is equal to the sum of the numbers.

We can conclude that median number multiplied by the total numbers is equal to the sum of the numbers .This is the case because when we calculate the fifth, third and seventh from multiple from “a” ’b””c” consecutively, It is always equal to sum of the numbers.