Reduce / simplify any fraction to its lowest terms by using our Fraction to the Simplest Form Calculator. Find the answer to questions like: Simplify 3/4 or what is 3/4 reduced to the simplest form?
Step 1: (5.2 - 4.5) - 5.5 + 4.8 Step 2: 5.2 + ( - 4.5 - 5.5) + 4.8 (identity property) Step 3: 5.2 - 10 + 4.8 Step New Questions Winston Churchill's reaction to the 1938 Munich Agreement was. Pomodoro technique app. For example, 3/4 is in lowest form, but 6/8 is not in lowest form (the GCD of 6 and 8 is 2) and 6/8 can be written as 3/4. You can do this because the value of a fraction will remain the same when both the numerator and denominator are divided by the same number. 3 / 4 is already in the simplest form. It can be written as 0.75 in decimal form (rounded to 6 decimal places). Steps to simplifying fractions. Find the GCD (or HCF) of numerator and denominator GCD of 3 and 4 is 1; Divide both the numerator and denominator by the GCD 3 ÷ 1 / 4 ÷ 1; Reduced fraction: 3 / 4 Therefore, 3/4 simplified to lowest. The coefficients and variables of terms can be multiplied or divided together in the process of simplifying equations. For examples: 3 × 4b = 3 × 4 × b = 12b. 5a × 3a = 5 × a × 3 × a = 5 × 3 × a × a = 15a 2 (using exponents) Be careful! A × a = a 2 a + a = 2a. Example 1: Simplify: 4a × 5a ÷ 2a = 60.
How to reduce a fraction
Among different ways simplifying a fraction, we will show the two procedure below: Song editing and mixing software free download for pc.
Method 1 - Divide by a Small Number When Possible
Start by dividing both the numerator and the denomiator of the fraction by the same number, and repeat this until it is impossible to divide. Begin dividing by small numbers like 2, 3, 5, 7. Art text 3 graphic design software 3 2 6. For example,
Simplify the fraction 42/98
- First divide both (numerator/denominator) by 2 to get 21/49.
- Dividing by 3 and 5 will not work, so,
- Divide both numerator and denominator by 7 to get 3/7. Note: 21 ÷ 7 = 3 and 49 ÷ 7 = 7
In the fraction 3/7, 3 is only divisible by itself, and 7 is not divisible by other numbers than itself and 1, so the fraction has been simplified as much as possible. No further reduction is possible, so 42/98 is equal to 3/7 when reduced to its lowest terms. This is a PROPER FRACTION once the absolute value of the top number or numerator (3) is smaller than the absolute value of the bottom number or denomintor (7). Textmate 2 0 rc16.
Method 2 - Greatest Common Divisor
Can You Simplify 1 6
To reduce a fraction to lowest terms (also called its simplest form), just divide both the numerator and denominator by the GCD (Greatest Common Divisor).
For example, 3/4 is in lowest form, but 6/8 is not in lowest form (the GCD of 6 and 8 is 2) and 6/8 can be written as 3/4. Episodes 2 2 – manage all of your tv shows. You can do this because the value of a fraction will remain the same when both the numerator and denominator are divided by the same number.
Note: The Greatest Common Factor (GCF) for 6 and 8, notation gcf(6,8), is 2. Explanation:
Simplify 3 2 8
- Factors of 6 are 1,2,3,6;
- Factors of 8 are 1,2,4,8.
So, it is ease see that the 'Greatest Common Factor' or 'Divisor' is 2 because it is the greatest number which divides evenly into all of them.
See also:
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Simplifying Fractions. Some Examples:
Let's learn by an example, let's simplify the fraction: 12/16
- Numerator of the fraction. The number that is above the fraction bar, 12, is called the numerator of the fraction;
- Denominator of the fraction. The number that is below the fraction bar, 16, is called the denominator of the fraction;
- The value of the fraction. Fraction 12/16 shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:
- 12 ÷ 16 = 0.75
- We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
- 12/16 = (12 ÷ 2)/(16 ÷ 2) = 6/8
- The value of the fraction 6/8 is calculated as:
- 6 ÷ 8 = 0.75
- We notice that the value of the fraction 6/8 is equal to that of the fraction 12/16, namely 0.75
- Reduced (simplified) fraction, Equivalent fraction. The new fraction, 6/8, is equivalent to the original one, 12/16, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.
- Common factor (divisor). The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.
- The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
- We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
- 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
- The value of the fraction 3/4 is calculated as:
- 3 ÷ 4 = 0.75
- The new fraction, 3/4, is a reduced fraction (a simplified fraction) and an equivalent of the fractions 12/16 and 6/8
- Irreducible fraction. Fraction 3/4 is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.
Simplify 3 4 2
How to reduce the fraction 12/16 to the lowest terms? Irreducible fraction
- Greatest common factor, GCF. To reduce a fraction to the lowest terms (or, in another words, to its simplest form, irreducible), we must divide both the numerator and the denominator of the fraction by their greatest common factor, gcf (12; 16).
- Prime Factors. One way to calculate the greatest common factor, GCF, is to break down each of the two numbers to prime factors and then write them as products of those primes, in exponential form. After that, multiply all the common primes by their lowest exponents, see it below.
- The prime factorization of the numerator and the denominator:
- 12 = 2 × 2 × 3 = 22 × 3
- 16 = 2 × 2 × 2 × 2 = 24
- The greatest common factor, GCF (12; 16), is calculated by multiplying all the common prime factors of the numerator and the denominator, by their lowest exponents:
- GCF (12; 16) = (22 × 3; 24) = 22 = 4
- To reduce the fraction to its lowest terms, divide the numerator and the denominator by their greatest common factor, GCF:
- 12/16 = (12 ÷ 4) / (16 ÷ 4) = 3/4
- Irreducible fraction. The end fraction 3/4 is called a reduced fraction, simplified. Since the numerator and the denominator are coprime numbers (prime to each other), their greatest common factor is 1, so this fraction is in its simplest form (it cannot be reduced anymore). This fraction is called an irreducible fraction.
- The fraction 3/4 is also an equivalent of the original fraction 12/16, representing the same value or proportion of the whole. As we saw above:
- 3/4 = 6/8 = 12/18 - all these are equivalent fractions, calculated by reducing the original one.
- Equivalent fractions can be calculated not only by reducing but also by expanding a fraction, that is, by multiplying the numerator and denominator by the same number other than zero, that is, the inverse of the process of simplification, but this is another discussion.
Why reducing fractions to lower terms (simplifying)?
Simplify 4 3 4 5
- In order to do calculations with fractions, sometimes we are also required to build them up to the same denominator or the same numerator. Sometimes both the numerators and the denominators are large numbers. Doing calculations with such large numbers could be time and resource consuming.
- By simplifying, by reducing a fraction to lower terms, both the numerator and denominator of the fraction are reduced to smaller values which are easier to work with.
