Fractions are numbers that express partial quantities of numbers. To know fractions, it's important to understand the two categories of numbers that make up fractions. A fraction is a way of expressing how the two basic parts of a fraction -- the numerator and the denominator -- relate to each other. Once you understand numerators and denominators, you'll be able to use fractions easily.
Numerator and Denominator
The numerator and denominator of a fraction are the two numbers that make the fraction. The numerator is the top number of a fraction. The denominator is the bottom number. Suppose you have the fraction 2/3. The numerator is 2, and the denominator is 3. A common trick for remembering numerator and denominator is to associate the n in the word numerator with north, to remember that the numerator is on top, and the d in the word denominator to signify that the denominator is down or below the numerator.
Sometimes, when using fractions, you’ll see two fractions that have different denominators that you have to add or multiply. Two or more fractions that have different denominators are known as unlike denominators. When you work with fractions that have unlike denominators, you have to convert them to a common denominator.
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What Do the Numerator and Denominator Signify?
The denominator of a number shows what fraction of 1 a fraction is counting. For example: 1/4 means one-quarter. The 4 signifies that you are splitting 1 into four parts. Similarly, 1/2 is one-half, and 1/3 is one-third. The numerator shows how many divisions are being counted. So, 2/4 is two quarters, 3/4 is three quarters and 4/4 is four quarters.
Numerator and denominator also signify division. A fraction is equal to its numerator divided by its denominator. Usually, doing this division will produce a decimal. For example, 1/4 is equal to 0.25. This also means that a fraction like 4/4, which has the same number as the numerator and denominator, is equal to 1.
The numerator of a fraction can be larger than the denominator. If the numerator is larger, then the fraction is larger than 1 -- and is called an improper fraction. For example, the fraction 7/4 is 7 fourths. If you can divide an improper fraction's numerator evenly by its denominator, then the improper fraction is equal to a whole number. For instance, the improper fraction 18/6 is equal to the whole number 3.
An improper fraction that has a denominator of 1 will always be equal to its numerator. So, the improper fraction of 7/1 = 7. This is true because dividing a number by 1 will always give you the original whole number.
Since an improper fraction is larger than 1, you can also express it as a mixed fraction, such as 4 3/5. A mixed fraction is equal to the whole number outside of the fraction plus the fraction. For example, take the fraction 7/4. If you divide the fraction, you find that 4 goes into 7 once, and has a remainder of 3. Place the quotient of the division outside the fraction, and set the remainder as the new numerator. The denominator stays the same. So, since 4 went into 7 one time with a remainder of 3, then the improper fraction 7/4 equals the mixed fraction 1 and 3/4.
You can convert a mixed fraction into an improper fraction, using the reverse process. To convert a mixed fraction into an improper fraction, multiply the number outside the fraction by the denominator, then add it to the numerator. For example, take the mixed fraction 3 and 1/6. First, multiply 3 times 6 to get 18. Then, add 3 to the numerator of 18, which results in 19. So, the mixed number 3 and 1/6 equals the improper fraction 19/6.