To simplify the fraction 7/21, find the greatest common factor (GCF) of both the numerator and the denominator. The GCF of 7 and 21 is 7. Divide both numbers by 7: 7 ÷ 7 equals 1, and 21 ÷ 7 equals 3. Therefore, the fraction 7/21 simplifies to 1/3.
To simplify 7/21, find the greatest common divisor (GCD) of 7 and 21, which is 7. Divide both the numerator (7) and the denominator (21) by 7. This results in 7 ÷ 7 = 1 and 21 ÷ 7 = 3. Thus, the fraction 7/21 simplifies to 1/3. This is its lowest term, as 1...
Yes, the ratio 14:21 can be simplified. Find the greatest common divisor (GCD) of 14 and 21, which is 7. Divide both numbers in the ratio by 7. So, 14 ÷ 7 equals 2, and 21 ÷ 7 equals 3. The simplified ratio becomes 2:3. This is its simplest form because 2 and 3 share...
To simplify a fraction like 15/21, first identify the greatest common divisor (GCD) of the numerator (15) and the denominator (21). In this case, the GCD is 3. Next, divide both the numerator and the denominator by this GCD. So, 15 divided by 3 is 5, and 21 divided by 3 is 7. The simplified...
To simplify (21x + 7) / 7, divide each term in the numerator by 7. 21x divided by 7 is 3x, and 7 divided by 7 is 1. Thus, the expression simplifies to 3x + 1. This represents the fully simplified form, as no further common factors exist to simplify the individual terms.
"Lowest terms" for a fraction means its numerator and denominator share no common factors other than 1. Once a fraction reaches this point, it cannot be further divided by any common integer to yield a simpler equivalent. For instance, 1/3 is in lowest terms, unlike 7/21, which can still be divided by 7.
Simplifying algebraic fractions involves factoring both the numerator and denominator to identify and eliminate common factors. This method mirrors numerical fraction simplification but extends to variables and polynomial expressions. By cancelling these common terms, the fraction reduces to its most basic, equivalent form. For example, (x^2 - 4) / (x - 2) simplifies to (x...
To simplify a square root like sqrt(21), look for perfect square factors within the number. The factors of 21 are 1, 3, 7, and 21. Since none of these, apart from 1, are perfect squares, sqrt(21) is already in its simplest radical form. It cannot be simplified any further.
Yes, the fraction 21/7 can be simplified. To do so, divide the numerator (21) by the denominator (7). 21 divided by 7 results in 3. Therefore, the fraction 21/7 simplifies directly to the whole number 3. This happens because 7 is a direct factor of 21, resolving it to a simple integer value.
Simplifying fractions and expressions makes them easier to understand, compare, and utilize in subsequent calculations. It reduces complex forms to their most fundamental representation, preventing errors and clarifying relationships between numbers or variables. Simplified forms are often the standard answer format in mathematics, promoting precision and efficiency in problem-solving.
A fraction is fully simplified when its numerator and denominator share no common factors beyond 1. You cannot divide both numbers by any integer greater than 1 to obtain a smaller, equivalent fraction. For example, 1/3 is fully simplified. However, 2/6 is not, as both 2 and 6 are divisible by 2.