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Number Theory/Percentages

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Question
Hello:

I have seen in textbooks the following regarding how to change a
number to a percentage: "Multiply the number by 1, expressed as
100/100, to change the number to a fraction with the denominator
100."
I have seen this explanation in at least two textbooks.

Why is the number "1" used in this method? I know that any
fraction, in which the numerator and denominator are the same,
equals 1, but what is the logical reason for multiplying by 1? I also know that when a number is multiplied by 1, it does not change its value. It would be more reasonable to multiply by just 100/100 and not mention anything regarding the number "1", but I suppose there is some logical reason.

I thank you for your reply.

Answer
Hi Kenneth
I think that most students would realise that multiplying by the number 1 does not change the value of the fraction, but might not realise that multiplying by 100/100 did the same, unless they were reminded that 1 could be expressed as 100/100.

Best wishes for your researches.

Vijilant

Number Theory

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Vijilant

Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

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