denominator is same as mixed number, so 15, the numerator is (denominator x whole number)+numerator so 16
Improper Fractions to Mixed Numbers 140/42
See how many 42s go into 140. This the whole number, 3, and then the denominator stays the same, 42, and the numerator is the remainder, 16. so the answer is 3, 16/42
BIDMAS
Brackets, Indices , Division, Multiplication, Addition, Subtraction
3 SF of 2997924
30000000 because the fourth digit is 7 which is larger than 5 so the whole number rounds up
1d.p of 211.32723
211.3
Add 73ab and 933ab
1006ab because they are like terms
Add 4a+ 5b
cannot add since they are not like terms
Multiply 4r x 5t
20rt , you can multiply any algebra even if they are not like terms
Multiply 5a x 7c^3
35ac^3
Expand method
FOIL
Factorise 35x-7
7(5x-1) take a common factor
Solve x 8(x+5)= 10(x+3)
expand the brackets 8x+40= 10x+30collect like terms 40=2x+30 10=2xx=0.2
Sum of 3 consecutive numbers is 219, what are the numbers?
x + (x+1) + (x+2)= 219 3x+3= 2193x=216x=72 72,73,74
Sum of 3 consecutive even numbers is y, what are the numbers?
x + (x+2) + (x+4)= y
Gradient
rise/run
Gradient from two coordinates
y-y/x-x
Gradient=m, what does c=?
y intercept
Angles on a straight line
Add up to 180
Opposite angles are
equal
Alternate angles in parallel lines
Z
Corresponding angles in parallel lines
F
Interior angles in parallel lines
add to 180, C
Exterior angles of any quadrilateral adds to
360*
Interior Angles of a Triangle
180*
Interior angles method
(n-2)180 where n is number of sides the shape has
Bearings rules
3 digits, from north, clockwise
How to draw triangle with given sides 7,3 and 5
1) Draw longest side as the base (7cm)2) Open compass to 5cm 3) Put needle to one end of the line you just drew and draw an arc4) Repeat 2 and 3 for 3cm5) Join the intersection to the two sides
Construct a perpendicular bisector for a line of 9cm
1) Draw the line 9cm2) Extend compass to be greater than half the line3) Put needle on one end and draw an arc above and below the line4) Repeat for the other side5) Draw vertical line through intersection
Construct an angle bisector for the angle of 80*
1) Draw the angle of 80* using a protractor2) Place the needle at the vertex (corner of angle) and draw an arc crossing both the lines 3) Keep compass same length, move needle to one point where the arc crossed the line and make another arc4) Repeat 3 for the other side5) Join the intersection of those two arcs to the vertex
Working out scale factor in similar triangles
Take same sides of both and divide them. ie if the base of a triangle on one is 2cm and the base of another is 8cm then you do 8/2= 4 so SF=4
Exterior angle of a triangle equals
The sum of the 2 non-adjacent interior angles
10^2 x 10^3=
10^ 2+3
10^2 / 10^3=
10^ 2-3
(10^3)^2
10^2x3
3x 10 ^3
3000
3.69 x 10^4
36900 because it takes after 4 moves of the decimal place, this was the number
7.24 x10^-3
0.00724 because after 3 moves of the decimal place to the left, this was the answer
calculate (2x10^4)(4.2x10^5)
either do 2x4.2= 8.4 and 10^4 x 10^5= 10^9 so 8.4 x 10^9= 8400000000or 20000 x 420000 = 8400000000