ANY QUESTIONS?

 
How can we divide $200
in the ratio 3:2?
3 + 2 = 5
$200 ÷ 5 = $40
3 × $40 = $120
2 × $40 = $80
$120 : $80
 
What is 596305003 rounded to the nearest ten million?
If we write 596305003 using commas giving 596,305,003
we can more clearly see that we have 596 million
the 6 indicates that we should increase the tens of millions by one - from 9 to 10
but this will cause the hundreds of millions to increase by one - from 5 to 6
so we get 600 million
600,000,000
 
What is the Midpoint Theorem?
If you have a line on a graph
with the end points each having
x and y coordinates
Then the x coordinate of the midpoint
can be found by adding together
the x coordinates of the end points
and dividing by 2
Also the y coordinate of the midpoint
can be found by adding together
the y coordinates of the end points
and dividing by 2
 
What is maths?
Maths is a subject
and an approach.
 
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QUESTIONS AND ANSWERS



The most recent q&a are at the top of this column.

 

Thank you very much
to the maths.com user who asked this question.
This is a very good question to receive
since it shows thinking on the part of the asker
and enables some elaboration to take place.

Can a multiplication make a number smaller?

The short answer is ....
YES

The medium answer is ....
YES
If we multiply by a number less than 1
then the result will be less than we started with.

The long answer is ....
YES
If we start with the number 100
and multiply 100 by a number less than 1
then the result will be less than 100.
EXAMPLES
100 × half = half × 100 = half of 100 = half(100) = 50
100 × 0.75 = 0.75 × 100 = 0.75 of 100 = 0.75(100) = 75

If there are further points about this topic
then please ask - they will be very welcome.

What is a cube root of a 289?
The square root of 289 is 17
since 17 × 17 = 289
Let CR be the cube root
then CR × CR × CR = 289
CR = 6.61 (1dp)
The cube root of 289 is 6.61
correct to 1 decimal place
 
What is a straight angle?
A straight angle is an angle of 180°
Just less than 180°
the angle is called obtuse
Just more then 180°
the angle is called reflex
 
What is the value of 3
in the number 94361?
1 is 1 unit = 1
6 is 6 tens = 60
3 is 3 hundreds = 300
 
What is quadrilateral?
A flat shape
with 4 straight sides
 
What is the solution of
z - 1.7 = 9.8?
the inverse of subtract 1.7 is add 1.7
add 1.7 to both sides
z - 1.7 + 1.7 = 9.8 + 1.7
consolidate on both sides
z = 11.5
 
What is a prime number?
A prime number is a number
that only divides by 1 and itself.
The first 5 prime numbers
are 2, 3, 5, 7 and 11
more >>>>
 
How do you change a
mixed number into a decimal?
A mixed number is
a whole number and a fraction.
The whole number goes
to the left of the decimal point.
Divide the top of the fraction
by the bottom
and you will get
the decimal point and what goes
to the right of the decimal point.
 
How do we solve x + 3 < 2 - x?
x + 3 is less than 2 - x
x + 3 < 2 - x is an inequality
the inverse of add 3 is subtract 3
subtract 3 from each side
x + 3 - 3 < 2 - x - 3
consolidate on each side
x < - 1 - x
the inverse of subtract x is add x
add x to each side
x + x < - 1 - x + x
consolidate on each side
2x < - 1
the inverse of multiply by 2 is divide by 2
divide each side by 2
x < - 0.5
x is less than negative 0.5
 
How many cm3 in 1L?
How many cubic centimetres in 1 litre
How many cubic centimeters in 1 liter
The answer is 1000
If you have a cube
10cm by 10cm by 10cm
then you have 1000cm3
and this cube
would hold exactly 1L
 
How do we explain
the y=mx+b equation ?
y=mx+b is also used as y=mx+c
and is
the equation of a straight line.
m is the gradient of the line
also called the slope of the line
and tells us
how the y-coordinate changes
if we
increase the x-coordinate by one
b or c is the point on the y-axis where the line crosses that axis
 
What are the solutions of
x2 + 5x + 10 = 24?
x2 + 5x + 10 = 24
Subtract 24 from each side
x2 + 5x + 10 - 24 = 24 - 24
Simplify each side
x2 + 5x - 14 = 0
Factorise
(x - 2)(x + 7) = 0
(x - 2) = 0 => x = 2
OR
(x + 7) = 0 => x = - 7
Both x = - 7 AND x = 2
are solutions of the equation.
9x(8x6)+3=?
9x(8x6)+3
= 9x(64)+3
=9x64+3
=576+3
=579
What are integers?
See here
What are rational numbers?
See here

 


 

 

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Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.
What is the mode of
6, 9, 5, 6, 8, 7, 5 and 6?
5, 5, 6, 6, 6, 7, 8, 9
6 is the MODE
the MOST OFTEN is 6
Video showing another example
 
Why are 6 and 28 special?
The factors of 6 below 6
are 1, 2 and 3
1 + 2 + 3 = 6
The factors of 28 below 28
are 1, 2, 4, 7 and 14
1 + 2 + 4 + 7 + 14 = 28
The name given to such numbers is
PERFECT NUMBERS
 
What is a negative number?
A number less than zero.
 
What is the square root of 48.8?
6.985699679 because
6.985699679 × 6.985699679 = 48.8
You can go to this Calculator
input 48.8 and click on 'sqrt'
One method to do a check mentally
is to round 48.8 up to 49
7 × 7 = 49 so the square root of 49 is 7
the square root of 48.8 will be just less than 7
 
What is the area of a trapezoid?
Some people use the word trapezoid
whilst others use the word trapesium
Video showing example
 
If 5 hats cost £28
how much will 7 hats cost?
5 hats cost £28
1 hat costs £28 ÷ 5 = £5.60
7 hats cost 7 × £5.60 = £39.20
 
Is a square a rectangle?
A square is a rectangle because it is a quadrilateral with 4 right angles.
 
What is a quadrilateral?
A flat shape with 4 straight sides.
 
How many mm in a metre?
1000mm = 1metre
1000mm = 1meter
1000millemetre = 1metre
1000millemeter = 1meter
In some countries the 're' ending is used
whilst in others the 'er' ending
 
What is the lowest
common multiple of 6 and 5?
6 12 18 24 30
5 10 15 20 25 30
LCM = 30
In some countries the expression
Least Common Multiple is used
Video showing other examples
 
What is 624
as a percentage of 5383?
(624 ÷ 5383) × 100
= 0.11592049 × 100
= 11.592049
= 11.6 correct to 1 decimal place
 
How can I solve x2 = 4x?
x2 = 4x
subtract 4x from both sides
x2 - 4x = 4x - 4x
consolidate on both sides
x2 - 4x = 0
x2 and 4x have a common factor x
x(x - 4) = 0
if two things multiply together to give 0
then one of them must be 0
so x = 0 OR (x - 4) = 0 so x = 4
The solutions are x = 0 and x = 4
CHECK
x2 = 4x
x = (0)
(0)2 = 4(0) giving 0 = 0 so x = 0 works
x = (4)
(4)2 = 4(4) giving 16 = 16 so x = 4 works
 
What do you get
when you differentiate 3x2?
3x2 = 3x(2)
Differentiating with respect to x
we get 3(2)x(2) - 1
which simplifies to 6x1
which is 6x
 
What is the volume of a cube?
All sides (edges) of a cube
are of equal length
Volume = Side × Side × Side
Please remember the units
if the lengths are measured in cm
then the volume is in cm3
centimetre cubed
or cubic centimetres
 
What is 5% of 2700?
100% = 2700
1% = 2700 ÷ 100 = 27
5% = 5 × 27 = 135
 
What is 12.5% of 1000?
100% = 1000
1% = 1000 ÷ 100 = 10
12.5% = 12.5 × 10 = 125