Section 1 - Number Flashcards

1
Q

What’s an integer

A

It’s another name for a whole number - either s positive or negative number or 0

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2
Q

What are rational numbers

A

They can be written in 3 forms

Integers

Fractions

Terminating or recurring decimals

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3
Q

What are irrational

A

They can’t be written as fractions - they are never ending, non repeating decimals. Square roots of positive integers are either integers or irrational eg square root of 3 is irrational but square root of 4 is 2 and so is rational

Pi is irrational

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4
Q

What does bodmas stand for

A
Brackets
Other
Division
Multiplication
Addition
Subtraction

Tells you the order which operations should be done

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5
Q

What’s the reciprocal

A

The reciprocal of a number is just 1 divided by the number eg 1/8

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6
Q

What are the multiples of a number

A

Just it’s time table we some multiples of 8 are 16,32

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7
Q

What are factors

A

Factors of a number are all the numbers that divide into it

Eg factors of 12 are 1, 12, 6, 3, 4

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8
Q

What’s a prime number

A

A number that’s only factors are itself and 1 - only exception is one which is not a prime number

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9
Q

How do you find the prime factors of a number

A

Can be broken down into a string of prime factors all multiplied together - called prime factor decomposition or prime factorisation

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10
Q

How do you make a prime factor tree

A

Start with the number at the top and split the number into factors

Every time you get a prime number ring it

Just keep factorising the numbers, then write out the primers in numerical order and if there’s more than one the same - put it as a power

Eg prime numbers are 2 X 2 X 3 X 5

Do 2^2 X 3 X 5

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11
Q

What’s the LCM

A

Least common multiple

The smallest number that will divide by all the numbers in the question

so LCM of 12 and 15 is 60

Lowest common MULTIPLE

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12
Q

What’s the HCF

A

The biggest number that will divide into all the numbers in the question

Eg the HCF of 36 and 54 is 18

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13
Q

How do you cancel down

A

To cancel down or simplify a fraction, divide top and bottom by the same number until you can’t

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14
Q

What’s a mixed number

A

With an integer and a fraction part .

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15
Q

What’s an improper fraction

A

Where the top number is larger than the bottom number - need to be able to convert mixed numbers to improper fractions and other way around

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16
Q

How do you multiply fractions

A

You can cross cancel then just multiply the numerators by the denomenators

17
Q

How do you divide fractions

A

Flip the second fraction and multiply

Dividing fractions easy as pi, flip the second and multiply

18
Q

What’s a common denominator

A

A denominator that can fit into all the fractions in a question

Easiest way to find it is to find the LCM bad there it, then multiply up to that denominator so all fractions have the same denominator

19
Q

Tell me how to add and subtract fractions

A

Rewrite the mixer numbers as fractions

Find a common denominator

Combine the top lines and subtract numerators or add them

20
Q

How do you work out fractions of something

A

Eg 9/20 of £360

Of means multiply the something by the top of the fraction and divide it by the bottom

Eg 360 divided by 20 X 9 = £162

21
Q

How do you express numbers as fractions

A

Eg write 180 as a fraction of 80 so then just write 180/80 and cancel down

22
Q

How is proportion represented

A

Expressed in fractions, decimals and percentages

23
Q

How do you convert fractions, decimals and percentages

A

Fraction -> divide -> decimal -> X 100 -> percentage

Percentages -> divide by 100 -> decimal

To convert decimals to fractions it’s awkward

For terminating decimals, the digits after the decimal point go on top and a power of 10 on bottom - same number of 0s as there were decimal places

For recurring decimals to fractions see next questions

24
Q

How do you turn recurring decimals into fractions

A

So name the decimal - eg r

R= 0.234 recurring
The multiply until the recurring part is in interfere and fully repeated so

1000r = 234.234 recurring

Now subtract to get rid of decimal part

1000r = 234.234 - R=0.234 =
999r = 234 

So r = 234/999 = 26/111

25
Q

Tell me how to turn recurring decimals into fractions - the difficult way

A

Eg write 0.16 recurring as a decimal

Name decimal r = 0.16 recurring

Multiply to move non recurring part of decimal past decimal point

So 10r = 1.6 recurring

Now multiply again to move full repeated Lump past decimal point

100r = 16.6 recurring

Subtract to get rid of decimal part

100r = 16.6 - 10r = 1.6

= 90r = 15

r = 15/90 = 1/6

26
Q

How do you put fractions into recurring decimals

A

8/33 as a recurring decimal

2 methods

Find an equivalent fraction with all nines on bottom and number on top is the recurring part so 24/99 = 0.24 recurring

Or divide if you have a calculator 8 divided by 33

27
Q

How do you round numbers to decimal places

A

Identify the position of the last digit from the number of decimal places - look at next digit to the right and round - must be no more digits after the last digit you want

Eg to round 7.4748 to 2 decimal places

7 is last digit and the 4 on the right is the decider so it’s 7.47

28
Q

How do you round numbers to significant figures

A

The 1st significant figure of any number is the first digit not a 0

2nd, 3rd etc significant figures follow on immediately after the 1st regardless of being 0s or not 0s

29
Q

What is estimating

A

Taking a look at numbers and making them easier to do calculations- won’t need to be as accurate as the real thing

30
Q

How do you estimate calculations

A

Round numbers to easier one usually 1 or 2 sf and do calculation

Use special swirly equals signs

31
Q

How do you estimate square roots

A

Find 2 square numbers, one either side of number given

Decide which is closest to and make a sensible estimate of the digit after the decimal point

32
Q

What’s a bound

A

When a measurement is rounded to a given unit, the actual measurement Can be up to half a unit bigger or smaller

The lower bond is the smallest a measurement can be and the upper bound is the largest

You can work out intervals
- difference between them

Eg is greater than or equal to the lower bound but less than the upper bound

33
Q

What’s truncated

A

When a measurement is truncated to a given unit, the actual measurement can be up to a whole unit bigger but no smaller

34
Q

How do you calculate the maximum and minimum values for calculations

A

You need to calculate the lower and upper bounds for measurements and use them

35
Q

What’s standard form for

A

Useful for writing very big or very small numbers

36
Q

What are the 3 rules of standard rules

A

The front number must always be between 1 and 10

The power of 10, n, is how far the decimal point moves

N is positive for big number and negative for small numbers

37
Q

How do you multiply powers

A

Rearrange front numbers and powers of 10 together

Multiply or divide front numbers and multiply or divide powers of ten (add or subtract powers)

Make sure answer is still in standard form

38
Q

How do you add or subtract powers

A

Make sure the powers of 10 are the same and add or subtract the front numbers

Convert the answer to standard form is necessary