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How do you find out the HCF of the numerator and denominator of a fraction?
Wiki User
∙ 10y ago
Example: 30/42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Wiki User
∙ 10y ago
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How do you find the quotient in simplest form?
Find the Highest Common Factor (HCF) of the numerator and denominator of the fraction. Divide both by their HCF and you will have the fraction in its simplest form.
How do you simplify fractions?
Divide the numerator and the denominator by a common factor. For example, 16/24 = 8/12 = 4/6 = 2/3 Find the GCF of the numerator and the denominator and divide them both by it. If the GCF is 1, the fraction is already in its simplest form.
What algorithms will produce the correct result for the sum a b where a and b each represent rational numbers?
You are basically asking how to add two fractions together: Assuming your rational numbers are in the form of a fraction with a numerator over a denominator (could be stored as an ordered pair, or an ordered triple [for mixed numbers]). If the numbers are mixed numbers the first step is to convert them to improper fractions. To add rational numbers the denominators must be the same. If they are not the same then the fractions need to be converted into equivalent fractions with the same denominator. Then the fractions are added by adding together the numerators Finally the result is simplified by dividing the numerator and denominator by their Highest Common Factor (HCF). If the numerator is greater than or equal to the denominator, then the fraction is converted to a mixed number. To convert a mixed number to an improper fraction, the new numerator is the whole number multiplied by the denominator plus the original numerator; the new denominator is the original denominator. To find the new denominator for equivalent fractions it is best done by finding the lowest common multiple (LCM) of the denominators. To find the LCM, there are various methods, but I would suggest* using the fact that the product of the HCF and LCM of two number is the product of those two numbers; then the LCM is the product of the numbers divided by their HCF. The HCF of two numbers is easily found by using Euclid's method: to find the HCF of two numbers a and b: 1) find the remainder (r) of the first number (a) divided by the second (b) 2) If the remainder is 0, the HCF is the second number; otherwise 3) replace the first number (a) by the second number (b) 4) replace the second number (b) bu the remainder (r) 5) repeat from step 1. (If a < b the first time through the algorithm will swap a and b so that a > b.) There is no need to check for denominators being the same as the LCM will work out to be the current denominator. To convert a fraction with one denominator to an equivalent fraction with a new denominator, the new numerator is found by multiplying the old numerator by the new denominator and divide by the current denominator (which is the same as finding out how many times the current denominator divides into the new denominator and multiplying the numerator by this). I To do the addition, the numerators are added together and the denominator is kept. To simplify the fraction find the HCF of the numerator and denominator and divide each by this HCF. (No real need to check for HCF = 1 → fraction already as simple as possible but dividing by 1 will leave the numerator and denominator as they are!) To convert an improper fraction to a mixed number, divide the numerator by the denominator to get a whole number quotient and a remainder. The remainder is the numerator over the denominator for the fraction of the mixed number with the quotient as the whole number. If the whole number is zero, then the fraction is a proper fraction; if the remainder is zero, then the fraction is a whole number. ----------------------- * This suggestion means the LCM function becomes: LCM(a, b) = a * b / HCF(a, b) And only the HCF function need be worked out in a full algorithm. For two numbers Euclid's method provides an easy function. For more than 2 numbers I would use the prime factorization method.
How do you get the simplest form?
To find the simplest form of the fraction p/q first find the highers common factor of p and q. If HCF(p, q) = 1 then the fraction is already in its simplest form and there is nothing to be done. Otherwise, divide p by the HCF to give r, divide q by HCF to give s and the simplest form is r/s.
Why do you find LCM and HCF?
When simplifying fractions it's useful to know what is the HCF of the numerator and denominator is. When adding or subtracting fractions with different denominators it's useful to know what the LCM of them is.
What is the rule for reducing a fraction to its lowest term?
Find the highest common factor (HCF) of the numerator and denominator. If it is 1, then the fraction is already in its lowest term.If not, divide the numerator by the HCF for the new numerator.Divide the denominator by the HCF for the new denominator.The new numerator over the new denominator is the fraction in its lowest terms.
How do you find the quotient in simplest form?
Find the Highest Common Factor (HCF) of the numerator and denominator of the fraction. Divide both by their HCF and you will have the fraction in its simplest form.
What is the rule to change to lowest terms?
There are two equivalent ways: 1. Find the highest common factor (HCF) of the numerator (top) and denominator (bottom) of the fraction. If it is 1, the fraction is already in its lowest terms. If not, divided both, numerator and denominator, by the HCF. The fraction is now in its lowest form. 2. Find any common factor of the numerator (top) and denominator (bottom) of the fraction. If the only common factor is 1, the fraction is already in its lowest terms. If not, divided both, numerator and denominator, by the HCF. Repeat the process until the only common factor is 1. The fraction is then in its lowest form.
How do you simplify a fraction to a fraction?
By reducing it to its lowest terms which will be when the HCF of the numerator and denominator is 1
How do you tell if a fraction is simplest form?
A fraction is in its simplest form when the HCF of its numerator and denominator is 1
When the numerator and denominator of a fraction are relatively prime?
When they have no factor in common, or their HCF is 1.
What is the simplest form of the fraction?
When the HCF/GCF/GCD of the numerator and denominator equals 1 then the fraction is said to be in its simplest form.
What is 31.35 as an improper fraction?
Since this number goes out to the hundredths place, 31.35 is the same as the improper fraction 3135/100. Next we have to find the Highest Common Factor (HCF) for the numerator and denominator of this fraction - in this case the HCF is five. When we divide the numerator and the denominator by five we get 627/20, which is fully simplified. So, 627/20 is the fully reduced, improper fraction of 31.35.
How do you simplify fractions?
Divide the numerator and the denominator by a common factor. For example, 16/24 = 8/12 = 4/6 = 2/3 Find the GCF of the numerator and the denominator and divide them both by it. If the GCF is 1, the fraction is already in its simplest form.
How do you convert a fraction to its simplest form?
Divide numerator and denominator by their HCF eg 35/77: HCF is 7 so simplifies to 5/11.
How do you reduce the fraction 275 over 550 to lowest terms?
It is: 1/2 by dividing the numerator and denominator by the HCF
What algorithms will produce the correct result for the sum a b where a and b each represent rational numbers?
You are basically asking how to add two fractions together: Assuming your rational numbers are in the form of a fraction with a numerator over a denominator (could be stored as an ordered pair, or an ordered triple [for mixed numbers]). If the numbers are mixed numbers the first step is to convert them to improper fractions. To add rational numbers the denominators must be the same. If they are not the same then the fractions need to be converted into equivalent fractions with the same denominator. Then the fractions are added by adding together the numerators Finally the result is simplified by dividing the numerator and denominator by their Highest Common Factor (HCF). If the numerator is greater than or equal to the denominator, then the fraction is converted to a mixed number. To convert a mixed number to an improper fraction, the new numerator is the whole number multiplied by the denominator plus the original numerator; the new denominator is the original denominator. To find the new denominator for equivalent fractions it is best done by finding the lowest common multiple (LCM) of the denominators. To find the LCM, there are various methods, but I would suggest* using the fact that the product of the HCF and LCM of two number is the product of those two numbers; then the LCM is the product of the numbers divided by their HCF. The HCF of two numbers is easily found by using Euclid's method: to find the HCF of two numbers a and b: 1) find the remainder (r) of the first number (a) divided by the second (b) 2) If the remainder is 0, the HCF is the second number; otherwise 3) replace the first number (a) by the second number (b) 4) replace the second number (b) bu the remainder (r) 5) repeat from step 1. (If a < b the first time through the algorithm will swap a and b so that a > b.) There is no need to check for denominators being the same as the LCM will work out to be the current denominator. To convert a fraction with one denominator to an equivalent fraction with a new denominator, the new numerator is found by multiplying the old numerator by the new denominator and divide by the current denominator (which is the same as finding out how many times the current denominator divides into the new denominator and multiplying the numerator by this). I To do the addition, the numerators are added together and the denominator is kept. To simplify the fraction find the HCF of the numerator and denominator and divide each by this HCF. (No real need to check for HCF = 1 → fraction already as simple as possible but dividing by 1 will leave the numerator and denominator as they are!) To convert an improper fraction to a mixed number, divide the numerator by the denominator to get a whole number quotient and a remainder. The remainder is the numerator over the denominator for the fraction of the mixed number with the quotient as the whole number. If the whole number is zero, then the fraction is a proper fraction; if the remainder is zero, then the fraction is a whole number. ----------------------- * This suggestion means the LCM function becomes: LCM(a, b) = a * b / HCF(a, b) And only the HCF function need be worked out in a full algorithm. For two numbers Euclid's method provides an easy function. For more than 2 numbers I would use the prime factorization method.
