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Estimations, equations and variables

Educator section


14. (a) 100

(b) 12

(c) 124

(d) 8

15. (a) 10 99 75 5


______ 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

Leaner section


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 = _______________________


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


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.



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

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Missy Reply
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Lale Reply
no can't
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Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
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Jyoti Reply
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Crow Reply
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RAW Reply
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yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
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The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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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