Section 1 - Number Flashcards by Harriet de Sa

What’s an integer

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

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What are rational numbers

They can be written in 3 forms

Integers

Fractions

Terminating or recurring decimals

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What are irrational

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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What does bodmas stand for

Brackets
Other
Division
Multiplication
Addition
Subtraction

Tells you the order which operations should be done

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What’s the reciprocal

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

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What are the multiples of a number

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

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What are factors

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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What’s a prime number

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

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How do you find the prime factors of a number

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

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How do you make a prime factor tree

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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What’s the LCM

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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What’s the HCF

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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How do you cancel down

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

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What’s a mixed number

With an integer and a fraction part .

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What’s an improper fraction

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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How do you multiply fractions

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

How do you divide fractions

Flip the second fraction and multiply

Dividing fractions easy as pi, flip the second and multiply

What’s a common denominator

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

Tell me how to add and subtract fractions

Rewrite the mixer numbers as fractions

Find a common denominator

Combine the top lines and subtract numerators or add them

How do you work out fractions of something

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

How do you express numbers as fractions

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

How is proportion represented

Expressed in fractions, decimals and percentages

How do you convert fractions, decimals and percentages

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

How do you turn recurring decimals into fractions

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

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

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

How do you put fractions into recurring decimals

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

How do you round numbers to decimal places

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

How do you round numbers to significant figures

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

What is estimating

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

How do you estimate calculations

Round numbers to easier one usually 1 or 2 sf and do calculation Use special swirly equals signs

How do you estimate square roots

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

What's a bound

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

What's truncated

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

How do you calculate the maximum and minimum values for calculations

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

What's standard form for

Useful for writing very big or very small numbers

What are the 3 rules of standard rules

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

How do you multiply powers

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

How do you add or subtract powers

Make sure the powers of 10 are the same and add or subtract the front numbers Convert the answer to standard form is necessary