# 2.3 Estimations, equations and variables (algebraic equations)

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## Memorandum

14. (a) 100

(b) 12

(c) 124

(d) 8

15. (a) 10 99 75 5

(c)

 ______ 8 ______ 21 39 ______ 74 ______

16.2 (a) 5 х + 7 = 22

(b) 8 х - 10 = 46

(c) 5 + 9 х = 59

(d) х - 13 = 6

16.3 (a) 21

(b) 17

(c) 34

18 (a) 72 (j) 30

(b) 12 (k) 5

(c) 7 (l) 57

(d) 141 000 (m) 9

1. 900 (n) 9 987
2. 47 (o) 125

(g) 135

(h) 336

(i) 7

20. (a) х >10

(b) y <2 000

(c) ( c +8)>6

(d) y <50

(e) k – ( k ÷ 2)<20

## Activity: estimations, equations and variables (algebraic equations) [lo 1.7.2, lo 1.9.1, lo 1.10, lo 2.5]

14. Now replace the letters with the correct numbers in the following flow diagram:

15. Puzzles!

a) Can you solve the following?

I am thinking of a particular number. When I multiply this number by 7, then subtract 6 and divide the answer by 8, the quotient is 8. What is the number that I have in mind?________________________________________________________

I am starting with 9. When I multiply this by 12, than add 2 and subtract 11, the answer is_____________________________________________________________

What answer will I get if I start with 7? ____________________________________

And if I start with 5?____________________________________________________

b) We can compile a table that will help us with problems like these.

 Number 9 7 5 Number × 12 + 2 – 11 99 75 51

c) We could replace the word "number" with any letter of the alphabet. Can you fill in the missing numbers in the following table?

 k 6 ________ 13 _________ (k × 5) + 9 49 114

d) Tell your partner how you obtained the answers.

16.1 Did you know?

The statement (k x 5) + 9 = 49 is referred to as an algebraic equation. “Algebra” is the “study of number sentences”.

16.2 Write the algebraic equation for the following:

a) A particular number x 5 + 7 = 22

____________________________________________________________________

b) 8 x a number – 10 = 46 ______________________________________

c) 5 + (9 x a number) = 59 _______________________________________

d) When 13 is subtracted from a bigger number the difference is 6.

_____________________________________________________________________

16.3 Solve the following equations: (You may use your pocket calculator).

a) 49 x a – 29 = 1 000

_____________________________________________________________________

b) (b + 15) x 6 = 192

_____________________________________________________________________

c) 16 x c – 15 = 529

_____________________________________________________________________

17. Did you know?

The letters that are used in place of numbers are called variables.

18. Let's first see how you do in your next mental arithmetic test.

a) 9 x 8 = ___________________________

b) ___________________________ x 4 = 48

c) 4 x ___________________________ = 28

d) 6 x 235 x 100 = ______________________

e) 25 x 9 x 4 = _________________________

f) 16 + 17 + 14 = ______________________

g) 104 + 15 + 16 = _____________________

h) Triple: 112: = _________________________

i) 42 ÷ 6 = ___________________________

j) ___________________________ ÷ 6 = 5

k) 35 ÷ ___________________________ = 7

l) (7 x 3) + (4 x 9) =_______________________

m) 4 x 9 + ___________________________ = 45

n) 10 000 – 13 = ___________________________

o) 5 to the power of 3 = _______________________

15

19. Did you know?

When we use>and<-signs in numbers sentences, e.g. when we

want to say that a number divided by 4 is smaller than 5, we write

it like this:

y ÷ 4<5

If we, for example, wished to say that a number multiplied by 5 is greater than 16, we would write it like this:

b x 5>16

Number sentences like these, which do not have the = sign, are called

inequalities.

20. Write the following word sentences as inequalities:

a) The number of sweets that I have is more than 10.

_____________________________________________________________________

b) The number of learners in our school is greater than 2 000.

_____________________________________________________________________

c) A number increased by 8, is greater than 6.

_____________________________________________________________________

d) There are less than 50 learners in our class.

_____________________________________________________________________

e) If I give away half of my marbles, I shall have fewer than 20.

_____________________________________________________________________

## Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.2: multiple operations with integers;

1.7.7: exponents;

1.10: uses a range of strategies to check solutions and judges the reasonableness of solutions.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.1: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).

Assessment Standard 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns;

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:

2.3.2: flow diagrams;

2.3.3: tables;

Assessment Standard 2.5: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).

#### Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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