Math and Arithmetic

tank good ness

aswome joke got from friends

ttyl

There are plenty of websites but not all of them are children friendly or virus proof but the one that is fine is bitesize or revise wise and then you just add your keystage( ks1, ks2 or ks3)

The rules for exponents are

Multiplication;

a^(n) X a^(m) = a^(n+m)

Notice the coefficient 'a' MUST be the same for addition of exponents.

For something like

a^(n) X b^(m) you CANNOT add the exponents, because the coefficients are different. 'a' & 'b'

Division

a^(n) / a^(m) = a^(n-m) Subtract the exponents)

Nesting

(a^(n))^(m) = a^(nm) (Multiply the exponents).

However, in all Cases the coefficient MUST be the same .e.g. 'a'.

e.g.

3^(2) X 3^(5) = 3^(7)

5^(3) divide 5^(2) = 5^(1) = 5

(7^(3))^4) = 7^(12)

However,

3^(2) X 5^(3) = NOT allowed. because 9 x 125 = 1125 Not equal to the sqyare root or cube root of either number.

N

'24' is a multiple of '4' ( 4 x 6 = 24)

However, '4' is a factor of '24'.

sqrt(16) = +/- 3

Both +4 & -4 are rational.

NB The square roots of prime numbers are irrational

e.g. sqrt(2) = 1.413213562....

sqrt(3) = 1.732050808....

sqrt(5) = 2.236067978....

et seq.,

84

This is subtraction of fractions.

Hence

9/16 - 9/20 =>

[9(20) - 9(16)] / (16 x 20)

[180 - 144] / 320

[36] /320

Cancel down by '4'

9/80 The answer ; this will not reduce any further.

1450 X 12

Long multiplication.

1340

X 12

13400 ( 1340 x 10)

• 2680 (1340 x 2) NB 10 + 2 = 12

16080

===== The answer!!!!!

1400

1350 ? Look at the 'tens' number, '5' in this case. If '5' or greaterm then add '1' to the 'hundreds' number.

1349 is nearer 1300

but

1350 is nearer 1400

NB THis applies to any numbers. Given a million, you inspect the 'hundred thousand' number. or 'tens' inspect the 'units' number.

The number 256000 in Scientific Notation is: 2.56 × 105

NONE!!!!

Feet is LINEAR ( a length)

150 square yards is AREA ( a region).

YES!!!

3/6 = 1/2

NB THree '3' is a common factor of both '3' and '6' , so you cancel down*reduce) by dividing both numbers by '3'

NB You can do this proceedure with any fractions

e.g. 9 /27 = 1/3

16/20 = 4/5

et seq/.

2

No such thing as a 'hepagon'. I think you mean 'HEPTAGON'. Note the spelling.

A heptagon is a seven(7) sided 2-dimensional figure.

From their Latin roots, the names of polygons are : -

3 ' Trigon (Triangle).

4 ' Tetragon ( Quadrilateral)

5 ' Pentagon

6 ' Hexagon

7' Heptagon ( as given)

8 ' Octagon

9 ' Nonagon

10 ' Decagon

100 ' Centagon

1000 ' Millagon.

'--gon' is also Latin , for '2 dimensional figure.

So learn some Latin. Science and Maths use a lot of words from these ancient languages.

An angle has no length at all. The angle is just the amount of opening between

the two lines where they meet. The length of the angle's sides is completely

irrelevant, and has no effect at all on the measure of the angle. They can be

any length from almost zero to infinite, and they don't even have to both be

the same length. It just doesn't matter. None of that changes the measure of

the angle.

Let the numbers be 'm' & 'n'

m + n = 34

4m + 4 = n (4 times smaller is 4 less than the larger).

Algebraically rearrange

m + n = 34

4m - n = -4

Add

5m = 30

m = 6

Hence n = 28 (4 x 6 + 4 = 28).

So the two numbers are 6 & 28 .

180

We note that there are a difference of '9' between terms . Hence '9n'

Next find the constant 'c'

1st term ; 9(1) + c = 20 => c = 11

2 nd term ; 9(2) + c = 29 => c = 11

nth term is 9n + 11

e.g.

7th term is 9(7) + 11 = 63 + 11 = 74

8 X x = 24

Divide both sides by '8'

x = 24/8 = 3

'3' is the answer!!!!!

YES!!!

6 billion is 6,000,000,000 = 6.0 x 10^(9)

6000 million is 6,000,000,000 = 6.0 x 10^(9)

To compare decimals, bring the decimals to the same number of decimal places, by inserting suffix 'zeroes'. Three decimal places in this case.

0.011 ^ 0.01

Hence

0.011 & 0.010

Drop the decimal point

0011 & 0010

Drop the prefix zeroes

11 & 10

I think you will agree that 11 is greater than 10 ( 11 > 10)

Hence it follows that

0.011 > 0,01

NB THis method is good for comparing all decimals to 'n' number of places.

8

You spell ' equaiateral;, correct;y as 'equilateral'.

A SCALENE triangle cannot be EQUILATERAL, because for all scalene triangles , the length of the three sides are all different and the angles are all different values.

An EQUILATERAL triangles has its three sides of equal length , and its three angles all at 60 degrees.

There are four 2-digit prime numbers that have 4 as one of their digits: 41, 43, 47, and 49. However, 49 is not a prime number because it is divisible by 7. So, the correct answer is three 2-digit prime numbers with 4 as one of their digits.