How are fractions reduced to their lowest terms?
Reducing a fraction to its lowest terms means transforming it into an equivalent fraction having the smallest terms (numerator and denominator). This transformation occurs by simplifying all the common divisors between the numerator and denominator.
How to reduce a fraction to a minimum?
By applying this rule we can REDUCE a FRACTION to the MINIMUM TERMS DIVIDING the numerator and denominator by their GCD As we know, the GCD of two or more numbers is obtained by BREAKING these numbers into PRIME FACTORS and multiplying the PRIME COMMON FACTORS, each taken once, with the MINIMUM EXPONENT.
When is a fraction reduced to its lowest terms?
A fraction is said to be reduced to its lowest terms (or irreducible) when the numerator and denominator do not have common divisors greater than 1, that is, they are prime to each other.
Which term is not common to fractions?
A minimal or irreducible fraction is a fraction whose operators (dividend and divisor) are coprime to each other, that is, they have no common divisors other than unity. To identify this number, a series of simple simplifications are carried out on the numerator and denominator. ...
How do you calculate the greatest common divisor of fractions?
The least common denominator (gcd) is equal to the least common multiple (lcm) of the denominators.- (6: 3) x 1 = 2 x 1 = 2 ⇒ 1/3 is therefore equivalent to 2/6 ⇒ 1/3 = 2/6.
- (6: 2) x 1 = 3 x 1 = 3 ⇒ 1/2 is therefore equivalent to 3/6 ⇒ 1/2 = 3/6.
The reduction to a minimum
Find 18 related questions
How do you find the greatest common divisor of two numbers?
In summary: the GCD of two or more numbers is obtained by BREAKING these numbers into PRIME FACTORS and multiplying the PRIME COMMON FACTORS, each taken only once, with the MINIMUM EXPONENT.
How to add with fractions with different denominators?
The sum (or difference) of fractions with different denominators is equal to a fraction whose denominator is the lcm between the two denominators and the sum (or difference) of the numerators of the equivalent fractions as its numerator.
What is a fraction called if the numerator is a multiple of the denominator?
Proper fractions, improper fractions and apparent fractions are types of fractions where the numerator is less than the denominator, the numerator is greater than the denominator, the numerator is a multiple of the denominator, respectively. In particular, the apparent fractions can be expressed as whole numbers.
How do you say a fraction when the numerator and denominator are prime to each other?
Definition - A fraction is said to be irreducible or reduced to a minimum (not simplifying) when the numerator and denominator are prime numbers. Two numbers are prime to each other when: the two numbers have no divisor in common; the two numbers are consecutive (for example, 152 and 153);
How do you tell if a fraction is greater?
Between two fractions that have the same denominator, the one that has the greater numerator is greater. Between two fractions that have the same numerator, the one that has the smaller denominator is greater. An improper fraction is always greater than a proper fraction.
What is the difference between simplification and minimization?
The 2/9 fraction was obtained by SIMPLIFYING the 14/63 fraction. So we can say that to SIMPLIFY a fraction it is enough to DIVIDE both TERMS by the same COMMON DIVIDER. Therefore, a fraction is said to be REDUCED TO THE MINIMUM TERMS when the NUMERATOR and the DENOMINATOR are FIRST OF THEM.
How does two-thirds break down?
We divide both 4 (numerator) and 6 (denominator) by 2. We get a new fraction, two thirds, which is equivalent to the first (in fact if you try to do with the calculator 4 divided by six and then 2 divided by 3 you will get the same result ).
How do you compare fractions?
How to compare fractions- If the two fractions have the same numerator and denominator then they are equal. ...
- If the two fractions have the same denominator, just compare the numerators: the larger numerator corresponds to the larger fraction.
How to make an irreducible fraction?
irreducible or minimized fraction, fraction in which the numerator and denominator are prime.
What does it mean to simplify a fraction?
The simplification of algebraic fractions is a procedure by which it is possible to identify an algebraic fraction equivalent to the given one, which involves breaking down the polynomials that define the algebraic fraction and simplifying the terms in common.
How do you turn a fraction into a decimal number?
The simplest way to convert a fraction to a decimal number is to evaluate it as a division where the top number (numerator) must be divided by the one below (denominator). The fraction 2/3, for example, can also be thought of as "2 divided by 3".
What characteristics do two prime numbers have?
prime numbers between them or coprime numbers, a pair of integers that do not admit common divisors other than 1 or −1. For example, 14 and 15 are prime to each other. Two numbers can be coprime without they being singularly prime (these are in fact neither 14 nor 15).
When are 3 numbers prime to each other?
The prime numbers between them (or coprime numbers) are integers whose only common divisor is 1. In a completely equivalent way, two or more natural numbers are said to be prime numbers between them if their greatest common divisor is 1.
How do you turn fractions into natural numbers?
At this point we can enunciate another rule concerning apparent fractions: "If the numerator of a fraction is a multiple of the denominator, then the fraction is apparent and its value is a natural number". Thus summarizing the apparent fractions represent a natural number.
How do you calculate the value of an improper fraction?
The calculation of the improper fraction
The easiest and most immediate method is to divide the numerator by the denominator. Since the numerator is always greater than the denominator, we will always have a result greater than 1. In addition, the improper function will always give a remainder other than 0.
How are improper fractions made?
Improper fractions can also be represented with a simple straight line. Use the centimeters of the ruler as reference points. To make the same fraction of 9/5, then draw two straight lines of five centimeters and divide them with a small vertical stroke into five equal parts each.
How do you turn an apparent fraction into a whole number?
A fraction is said to be apparent if the numerator is equal to or multiple of the denominator, that is, it is equivalent to the whole number obtained by dividing the numerator by the denominator.
How do you add with fractions?
To add (or subtract) two fractions that have the same denominator, we write a fraction that has: as denominator the same denominator of the given fractions; • as numerator the sum (or the difference) of the numerators. The result is reduced to a minimum, if it is possible.
How do you add three fractions?
The operations we are going to do are therefore these:- 36: 12 = 3; 3 · 7 = 21. Let's write 21 in the numerator. ...
- 36: 9 = 4; 4 · 2 = 8. And we also write the number 8 in the numerator and rewrite the sign "+". ...
- 36: 4 = 9; 9 · 3 = 27. The 27 will be the last addend of our addition and we write it to the numerator.
When is the denominator different?
The only way to compare two fractions with different numerator and denominator is to make them have the same denominator. ... The operation we have to do is this: lcm (60) divided by the denominator of the first fraction (12) and the result by the numerator of the first fraction (5).
