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Mathematics WRP, Root Numbers - Coggle Diagram
Mathematics WRP
Number System
Rational numbers
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square: the product of a number multiplied by itself, e.g. 1, 4, 9, 16.
Natural: the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
Irrational Numbers
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a number that can be expressed as an infinite decimal with no set of consecutive digits repeating itself indefinitely and that cannot be expressed as the quotient of two integers.
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Factors:
Prime Numbers
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Prime factorization is the process of finding the prime numbers, which are multiplied together to get the original number. For example, the prime factors of 16 are 2 × 2 × 2 × 2.
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HCF: highest common factor. noun. the largest number or quantity that is a factor of each member of a group of numbers or quantities.
LCM stands for Least Common Multiple. A multiple is a number you get when you multiply a number by a whole number (greater than 0)
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APPROXIMATION:
An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations .
WHAT IS APPROXIMATION IN SIMPLE TERMS
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UPPER BOUND AND LOWER BOUND:
The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value. For example, a mass of 70 kg, rounded to the nearest 10 kg, has a lower bound of 65 kg, because 65 kg is the smallest mass that rounds to 70 kg.
ESTIMATION OF MATHEMATICAL OPERATION:
The general rule for estimating is to look at the digit to the right of the digit you want to estimate. Estimating or rounding to the nearest whole number means looking at the digit to the right of the decimal. If you see a digit greater than 5, round up, and if it's less than 5, round down.
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UPPER AND LOWER BOUND EQUATION
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integers, fractions, decimals, and percentages
fractions is a single unit that can be broken into equal parts are called fractions if for example the unit is broken into 10 equal parts and three equal parts are then taken the fraction is written as 3 / 10. that is three parts out of 10 parts.
WORKED EXAMPLES
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percentage
a fraction whose denominator is 100 can be expressed as a percentage; 29 / 100 can be written as 29%. by using equivalent fractions to change the denominator 200 other fractions can be written as percentages
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mixed operations
when a calculation involves a mixture of compressions the order of the operation is important therefore multiplications and divisions are done first since while additions and subtractions are done afterwards. to override this brackets are to be used
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and improper fraction has its numerator more than its denominator another name for an improper fraction is a vulgar fraction
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ration and proportion
direct proportion
unitary method
3g OF COPPER MIXES WITH 8g OF TIN, 1g OF COPPER MIXES WITH 8/3g OF TIN, SO 36g OF COPPER MIXES WITH 36X8/3g OF TIN
THEREFORE 36gOF COPPER MIXES WITH 96g OF TIN
ratio method
TIN AND COPPER ARE MIXED IN THE RATIO 8:3. HOW MUCH TIN IS NEEDED TO MIX WITH 36g OF COPPER?
THE RATIO METHOD:
LET x GRAMS BE THE MASS OF TIN NEEDED,
x/36=8/3
THEREFORE, x=8X36/3
96
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Compound measures:
A compound measure is one made up of two or more other measures. The most common ones, which we will consider here, are speed, density and population density.
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Root Numbers
Root of a number. The root of a number x is another number, which when multiplied by itself a given number of times, equals x. For example the second root of 9 is 3, because 3x3 = 9. The second root is usually called the square root.
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