Answer to Question #205839 in Algebra for accordance

Question

1.5 You want to put up a poster in your mathematics classroom, where learners can see the

seven (7) properties of operations on real numbers. List those properties, with one very

clear example next to each one of the properties, so that learners can immediately see

what these properties mean in the mathematics they do. Do NOT use the examples of

the Study Guide, but your own

2.1 The number 100 can be written as the sum of five consecutive whole numbers like this:

100 = 18 + 19 + 20 + 21 + 22. Showing all your working, find

2.1.1 four consecutive odd numbers whose sum is 120. (5)

2.1.2 five consecutive whole numbers which add up to 1000. (5)

2.1.3 a rule for the sum of any four consecutive even numbers. (5)

2.2 A moringa tree, when planted, was 90cm tall. It then grew an equal number of centimetres

each month. At the end of the seventh month, it was 132cm tall. How tall was the tree at

the end of the twelfth month? Show all your calculations.

Answer 1

(1.5) Real numbers are rational and irrational numbers that present a quantity along a continuous number line.

(a, b and c are real numbers, variables or algebraic expressions

• Distributive Property [a • (b + c) = a • b + a • c]

example:5• (2 + 1) = 5 • 2+ 5 • 1

[multiplication distributes across addition]

• Commutative Property of Addition [a + b = b + a]

example:2 + 4 = 4 + 2

[switch places]

• Commutative Property of Multiplication [a • b = b • a]

example:2 • 4 = 4 • 2

[switch places]

• Additive Identity Property [a + 0 = a]

example:6+ 0 = 6

[ value returns the input unchanged]

• Multiplicative Identity Property [a • 1 = a]

example:8 • 1 = 8

[ value returns the input unchanged]

• Additive Inverse Property [a + (-a) = 0]

example:7 + (-7) = 0

[ value brings you back to the identity element under addition]

• Zero Property of Multiplication [a • 0 = 0]

example:2• 0 = 0

[ zero times any value is 0]

(2.1)

2.1.1 lets take the first odd number to be x

$x+(x+2)+(x+4)+(x+6)=120\\4x+12=120\\4x=108\\x=27\\27 +29+31+33=120$

2.1.2 lets take the first odd number to be x

$x+(x+1)+(x+2)+(x+3)(x+4)=1000\\5x+10=1000\\5x=990\\x=198\\198 +199+200+201+202=1000$

2.1.3

At least the position and value of one number of the four even onsecutive numbers should be known.

Assume the first/smallest number is t1, then the second is t1+2, the third is t1+4, and the fourth is t1+6. Their sum is then:

t1+(t1+2)+(t1+4)+(t1+6)

= 4*t1 + 12.

Given any of the four terms, determine the smallest number, t1 and use the above formula for the sum.

(2.2) lets take x to be centimeters the tree grew in each month

$90\times (x\times 7)=132\\90+7x=132\\7x=132-90\\7x=42\\x=6cm$

so at

the end of the twelfth month the tree will be

$90+(6\times 20)=210cm$