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This becomes easier with experience and having the ability to recognise that certain numbers are factors of both the numerator and denominator.
Until this experience is gained simply try dividing the numerator and denominator by prime numbers of increasing value. (2, 3, 5, 7, 11, 13, 17 etc)
Obviously if this division is successful then the fraction can be simplified but this does not necessarily mean further simplification is not possible.
Simplification ceases when either the numerator or the denominator becomes a Prime number or has the value 1. This last condition usually applies to just the numerator.
All non-prime numbers can be factored into prime numbers so it is only necessary, at this stage, to divide using prime numbers.
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A half belongs to what family of real numbers?
A half belongs to the positive fractions family, which comes under fractions, which comes under the large family of rational numbers.
Why would you need to find the GCF and LCM of a set of numbers?
They GCF and LCM are useful in working with fractions: In simplifying a fraction dividing the numerator (top) and denominator (bottom) by the same number reduces the fraction. By dividing through by the GCF of the numerator and denominator the fraction cannot be simplified any further (except converting improper (top heavy) fractions to mixed numbers). For large numbers, it may not be obvious what are the common factors of the numerator and denominator so using a general algorithm to find their GCF makes this easier. When adding or subtracting fractions a common denominator is needed. One number which is guaranteed to work is to multiply all the denominators together. However, this can lead to extremely large numbers which can be difficult with which to work and lead to a fraction that will require simplifying. By using the LCM as the new denominator (hence its alternative name of LCD - Lowest Common Denominator) it ensures the numbers shouldn't get too big and should be easier with which to work.
Are smaller fractions larger?
the numbers are larger, but could mean less or more: 1/20000000 is small and 20000000/1 is large
Why is it important to write the answer in simplest form?
Because most people find it easier to work with fractions involving small numbers rather than equivalent fractions involving large numbers. They would rather use 1/6 than try to work with 261/1566.
How do you divide small numbers by large ones for example 7divided by 11?
0.6364
A half belongs to what family of real numbers?
A half belongs to the positive fractions family, which comes under fractions, which comes under the large family of rational numbers.
How is the GCF related to fractions?
To simplify fractions, you need to divide the numerator and denominator by their GCF. Otherwise you'll end up with fractions with unnecessarily large numbers.
Why would you need to find the GCF and LCM of a set of numbers?
They GCF and LCM are useful in working with fractions: In simplifying a fraction dividing the numerator (top) and denominator (bottom) by the same number reduces the fraction. By dividing through by the GCF of the numerator and denominator the fraction cannot be simplified any further (except converting improper (top heavy) fractions to mixed numbers). For large numbers, it may not be obvious what are the common factors of the numerator and denominator so using a general algorithm to find their GCF makes this easier. When adding or subtracting fractions a common denominator is needed. One number which is guaranteed to work is to multiply all the denominators together. However, this can lead to extremely large numbers which can be difficult with which to work and lead to a fraction that will require simplifying. By using the LCM as the new denominator (hence its alternative name of LCD - Lowest Common Denominator) it ensures the numbers shouldn't get too big and should be easier with which to work.
Where is factorization practically applied?
Factorization is practically applied when reducing fractions. This is because it is easier to work with small numbers than with large numbers.
What can you use the GCF of?
You can use the GCF for simplifying large equations.
Are smaller fractions larger?
the numbers are larger, but could mean less or more: 1/20000000 is small and 20000000/1 is large
Why is it important to write the answer in simplest form?
Because most people find it easier to work with fractions involving small numbers rather than equivalent fractions involving large numbers. They would rather use 1/6 than try to work with 261/1566.
How do you divide small numbers by large ones for example 7divided by 11?
0.6364
What is Prime Factorization used for?
It allows you to find all the factors of a number. Prime factorisation is necessary for calculating the greatest common factor and least common multiple of sets of numbers. That information is essential for working with rational numbers.
How many numbers are cannot be written in roman numeral numbers?
None, except for fractions other than 1/12ths. However, large numbers soon become extremely difficult to notate, even with shorthand: CↂƆCCↂƆƆↂCↂƆↀↂCↀXCIX is 999,999 while CCↂƆƆ is 1 million.
Why do you switch a fraction into a percent?
In the real world the most common reason is because comparing the sizes of fractions which may have different denominators is not easy to do, especially if numerators and denominators are both large numbers. Ordering numbers is very easy when they are expressed as percentages.
What are names of large numbers?
Obviously "large numbers"
