# What is a fraction?

Table of Contents

### What is a fraction?

A fraction is a number that represents a part of a whole. It is written as a number followed by a slash (/), and the number after the slash represents how many parts there are in total. For example, if someone cuts a cake into four equal pieces, each piece would be one fourth, or 1/4, of the cake.

### What is a mixed fraction?

A mixed fraction is a fraction that has a whole number and a fractional part. For example, if someone has two and one half pieces of cake, it would be written as 2 1/2.

### How do you solve fractions?

The easiest way to solve fractions is to use a calculator, and type in the fraction you want to solve. For example, if you want to solve 1/4, you would type in “1 divided by 4”, which would give you the answer of 0.25 on the calculator.

Another way to solve fractions is to convert the fraction into an equivalent fraction with a denominator of 10, 100, or 1000. This is called renaming the fraction, and it can be done by multiplying the numerator and denominator by the same number. For example, if you want to solve 1/4, you could rename it as 2/8, 4/16, 8/32, 16/64, or 32/128. All of these fractions are equivalent to 1/4, and they can be solved by simply looking at the numbers and finding the answer.

To solve a fraction, you need to find the value of the numerator (the number before the slash) divided by the denominator (the number after the slash). For example, if someone has two and one half pieces of cake, it would be written as 2 1/2. To solve this fraction, you would take the value of the numerator (2) and divide it by the denominator (1), which would give you the answer of 2.

### How do you divide fractions?

To divide fractions, you first need to invert (or “flip”) the second fraction, and then multiply the two fractions together.

So, if we wanted to divide 1/2 by 1/4, we would flip the second fraction (1/4) to become 4/1, and then multiply the two fractions together:

1/2 Ã— 4/1 = 4/2 = 2

Here’s another example. Let’s say we wanted to divide 3/4 by 1/6. We would first flip the second fraction (1/6) to become 6/1, and then multiply the two fractions together:

3/4 Ã— 6/1 = 18/4 = 4 1/2

Remember, when you’re dividing fractions, you’re really just multiplying one fraction by the inverse (or “flipped”) version of the other fraction. So, if you can remember how to multiply fractions, you can easily divide them too!

### How do you multiply fractions?

To multiply fractions, you first need to find the product of the numerators and then the product of the denominators. This will give you the answer in its simplest form. For example, to multiply 1/4 by 1/3, you would first multiply 1 by 1 to get 1, then multiply 4 by 3 to get 12. Therefore, 1/4 multiplied by 1/3 is equal to 1/12.

If you’re multiplying mixed fractions, the process is similar. First, multiply the whole number portion of each fraction together, and then multiply the fractional portions together. Finally, add these two products together to get your answer. So, if you were to multiply 1 1/2 by 2 3/4, you would first multiply 1 by 2 to get 2, then multiply 1/2 by 3/4 to get 3/8. Adding these two products together gives you the final answer of 2 3/8.

### What is a common denominator?

A common denominator is a number that is a multiple of all the denominators in a set of fractions. This allows you to add or subtract the fractions without having to convert them to different forms first. For example, if you are adding 1/4 and 1/6, their common denominator would be 12. This means that you would be adding the fractions in the form of 12/12 and 6/12, which are both equal to 1/2.

### How do you find a common denominator?

To find a common denominator, you need to find the least common multiple (LCM) of all the denominators in a set of fractions. The LCM is the smallest number that is a multiple of all the numbers in a set. To find the LCM of two numbers, you can use the Greatest Common Factor (GCF) method.

To find the GCF of two numbers, you need to list out all the factors of each number and then find the largest number that appears on both lists. For example, to find the GCF of 12 and 18, you would list out all the factors of each number:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

The largest number that appears on both lists is 6, so the GCF of 12 and 18 is 6. To find the LCM, you would then take the product of the two numbers and divide it by the GCF. In this case, that would be (12)(18)/6 = 36. Therefore, the LCM of 12 and 18 is 36.

### content:How do you simplify fractions?

There are a few different ways to simplify fractions. One way is to factor both the numerator and denominator and cancel out any common factors. For example, if you have the fraction 12/18, you can factor both the numerator and denominator to get (2)(6)/(3)(6). The common factor of 6 can then be cancelled out, leaving you with the simplified fraction of 2/3.

Another way to simplify fractions is to use the Greatest Common Factor (GCF) method. To do this, you would list out all the factors of both the numerator and denominator and then find the largest number that appears on both lists. This number is the GCF, and it can be used to simplify the fraction.

For example, if you have the fraction 12/18, you would list out all the factors of each number:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

The largest number that appears on both lists is 6. This means that 6 is the GCF of 12 and 18. You can then use this number to simplify the fraction by dividing both the numerator and denominator by 6. This gives you the simplified fraction of 2/3.

### What is a unit fraction?

A unit fraction is a fraction where the numerator is 1 and the denominator is a whole number. For example, 1/4 is a unit fraction because the numerator is 1 and the denominator is 4. Unit fractions are a type of proper fraction, which means that the numerator is less than the denominator.

Unit fractions can be used to help simplify other fractions. For example, if you have the fraction 3/4, you can simplify it by using a unit fraction. This can be done by dividing both the numerator and denominator by 4, which gives you the unit fraction 1/4. You can then add this to the original fraction to get the simplified fraction of 4/4, which is equal to 1.

### What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than the denominator. For example, 3/2 is an improper fraction because the numerator (3) is greater than the denominator (2). Improper fractions are a type of top-heavy fraction, which means that the numerator is larger than the denominator.

Improper fractions can be converted to mixed numbers by dividing the numerator by the denominator. This will give you the whole number part of the mixed number. The remainder can then be used as the numerator of a new fraction, with the denominator staying the same. For example, if you have the improper fraction 3/2, you can convert it to a mixed number by dividing 3 by 2. This gives you 1 as the whole number part of the mixed number. The remainder of 1 can then be used as the numerator of a new fraction, with the denominator staying 2. This gives you the mixed number 1 1/2.

### What is the greatest common factor?

The greatest common factor (GCF) is the largest number that can be evenly divided into both the numerator and denominator of a fraction. The GCF can be used to simplify fractions. For example, if you have the fraction 12/18, you would list out all the factors of each number:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

The largest number that appears on both lists is 6. This means that 6 is the GCF of 12 and 18. You can then use this number to simplify the fraction by dividing both the numerator and denominator by 6. This gives you the simplified fraction of 2/3.

### What is a mixed number?

A mixed number is a whole number and a fraction that are combined together. For example, 3 1/2 is a mixed number because it is made up of the whole number 3 and the fraction 1/2. Mixed numbers are usually written with the whole number first, followed by a space, then the fraction.

Mixed numbers can be converted to improper fractions by multiplying the whole number part by the denominator of the fraction, and then adding this to the numerator of the fraction. For example, if you have the mixed number 3 1/2, you can convert it to an improper fraction by multiplying 3 by 2 (the denominator of the fraction), which gives you 6. You would then add this to 1 (the numerator of the fraction), which gives you 7. This means that 3 1/2 is equal to the improper fraction 7/2.