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Maths, maths, and more maths!
Transcript of Maths, maths, and more maths!
There will be pictures, words and videos to explain everything so everything hopefully won't be too difficult! hope you enjoy it! for example 3 (three to the power of two) means the base number is 3 and the index number is 2.
to find the value of 3 we multiply.
We do this to all numbers-
3 =3x3x3=27 4 =4x4x4=64 2 =2x2x2=8 Find 3 x 3 So 3 =3x3=27 and 3 =3x1=3
That means really it's 3 This gives us our first rule.
That X x X = x but this rule only works if the base number (x) is the same Learning intention It's
Clear It's Easy It's well presented example-
x x = x Rule with Brackets! Zero Index! This is a simple rule, but is very important! Rule- 3 =1 any number to the power of zero = 1 example- evaluate 3 x3 3 = 3 x3 3 =(3 3 =3 =3 )= 1 Standard Form We convert numbers into
standard form so that we can
represent large numbers both
in writing and on the calculator. examples Standard form - Basics 10=10 100=10 1000=10 etc. We write the number
like a power. when there is a number like 385, we go to the first number that is over 0 but less than 10 ( in this case 3). it works out like this - 3.85 x 10 (We put ___ multiplied by 10 to the power of___) Fractions in Indices Example- Simplify ( ) To change a power minus to plus or plus to minus, we turn the fraction upside down. then we change the power to a positive Significant Figures To give an amount to a certain number of significant figures is another way of rounding Significant Figures examples in the number 578
5 is the first significant figure
7 is the second
8 is the third The 1st significant figure is the 1st non-zero digit. An digit including zero to the right after it will be significant. Writing a number to a certain amount of figures Examples How could you write 308 to 2 significant figures? Well, we always look at the next significant figure after the one required. In this case, as we are asked for the 2nd SF (significant figure) we look at the 3rd one. 308 look at the 3rd SF. If it is 5 or over you round up the 2nd SF (0) So the answer to this question would be... 310 REMEMBER!
once you round up the 3rd SF, you have to replace it with a zero Significant figures and deciamals 0.08463 1st Sf 2nd Sf 3rd Sf 4th Sf This is the same as before, except when your done, you do not replace the rest of the numbers to the right, you just keep them the same. So the answer would be... 0.0846 Multiplying fractions the textbook way of multiplying fractions is much more difficult than the theory Mrs Murphy has came up with. It works every time and is quicker too! Examples It makes the problem easier if we simplify the fractions BEFORE we multiply Mrs Murphys theory is to SWAP the two denominators (the bottom lines) over. so it all simplifies down to.. Multiply! We can do this as 49x18 is the same as 18x49 Success Criteria That we now understand... What Indices are
How to multiply, divide and use brackets in Indices
What zero index is and how to use it
What Significant Figures are
What Standard Form is
How to multiply fractions with the easier theory
How to change mixed numbers into improper fractions and use it in a sum
How to divide fractions
How to create 2 way tables
How to expand brackets
More about algebra Changing a mixed number into an improper fraction When we want to change a mixed number into a improper fraction, we do this- Eg- Change 1 1/2 into an improper fraction. 1 1 / 2 Times Add so it would be 1X2=2+1=3.
That would be your numerator
(top of the fraction) Now to get your denominator
(bottom of the fraction)
All you have to do is take the denominator from the first fraction.
in this sum, what would be the denominator? If you answered 2, you would be right! Now you try! Change 3 3/5 into an improper fraction? If you answered 18/5, you are correct! to do this, you would... 3 3 / 5 times add so it would become
numerator and the original 5
for your denominator So that equals...
18/5 Multiplying Fractions with Mixed Numbers example- 4 1/2 X 4/21 so, start the same with the mixed numbers - multiply then add. you end up with 17/4 now you have an easier sum to work with 17/4 X 4/21 then, you use Mrs Murphy's theory to complete the sum! 17/21 X 4/4 17/21 x 1 = simplifies to 17/21 Dividing Fractions find - 18/4 19/16 All you have to do is turn the fraction on the right upside down and turn the divide sign to a multiply sign. 18/4 X 16/19 so now you have an easy multiplying fractions sum! 18/19 X 16/4 simplify that- 2/1 X 4/1= 8 Ratio Ratio is to simply make sharing things out in maths when they are not in fractions easier. Ratio Example 1 - Share 8500 between the ratio of 10:9:6 Step 1: Add 10+9+6=25 Step 2: Divide 8500 by 25= 340 Haven't got a calculator?
divide by 50 then 5! Step 3 (and answer):
340 X 10 = 3400
340 X 9 = 3060
340X 6 = 2040 Example 2 - Share 30 in the ratio 3:1:2 So what do you do? the answer is...
2=10 You would add 3+2+1=6. 30 divided by 6 = 5 5 X 3 = 15
5 X 2 = 10
5 X 1 = 5 How did you do it? Probability - 2 way tables Examples - 1 bag contains 2 red, 1 yellow and 1 blue counter. Another bag contains 2 yellow, 1 red and 1 blue. Red Yellow Yellow Blue Red Red Yellow Blue R R Y R Y R B R R R
B R R Y
B Y R B
B B This is how we turn the statement above into a table, so it is easier for us to answer the questions Questions and Answers 1) What is the probability that you pick two blues? 1/16 This is because the total of counters is sixteen on the table, and only 1 of the 16 pairs have both blues, making the answer 1/16
This is because again the total of pairs is 16, and this time two of them have both yellow 2) What is the probability that you pick two yellow? 2/16 Expanding Brackets Example - Expand 3 (x + 2) Multiply the number outside the bracket with the term inside the bracket So your answer is... 3 (x + 2) Multiply 3 X + 6 More Algebra! Example - 4x = 36 Bring the number in front of X across. Because the number was a multiply on the left, when we bring it over the equals sign to the right, it becomes divide. x = 36/4 x = 9 Sometimes, thought, it can be a bit more complicated, as there is more than one number on the right. Eg - 2x = 12 - 3 It is quite simple - do the maths on the right then the same as last time. 12 - 3 = 9
2x = 9
x = 9/2 Nine divided by two is 4 remainder one, so it's written 4 1/2 as 2 was the number underneath last time. x = 4 1/2 Even more Algebra! Example - x/3 = 9 We want to find x, so we bring over the 3 and put it with the nine, making it a multiply because it was a divide before you brought it over. x = 9 x 3
x = 27 Polygons A polygon is a plane (flat) figure held together by straight lines eg - 3 sided polygon = triangle 4 sided polygon = Quadrilateral 5 sided polygon = Pentagon 6 sided polygon = hexagon 8 sided polygon = Octagon There are two types of ploygon -
Regular and Irregular.
Regular polygons (like the ones on the left) have equal sides.
Irregular polygons (like the hexagon below) do not have equal sides. Irregular Hexagon Tessellation Tessellation is a pattern made with identical shapes with no gaps in between the shapes and no shapes overlapping Hexagons Some shapes that tessellate Squares Some shapes that don't tessellate