Fractions: Adding, Simplifying, and Converting to Decimals & Percents

Adding & Simplifying Fractions: Step-by-Step

Working with fractions means you need to know a few basic rules. This is especially true when you add them or make them simpler. For adding fractions, they must have the same bottom number. Other math like multiplying or dividing fractions has its own steps. When we simplify a fraction, we just make it as small as possible. This means the top and bottom numbers don’t share any factors other than 1.

Think of fractions as parts of a whole thing. The top number is called the numerator, and the bottom number is the denominator. Knowing how to do math with fractions is super helpful. You’ll use it in school and even in real life. This guide will show you how to add, subtract, multiply, and divide fractions. We’ll also cover how to change mixed numbers and how to simplify your answers. Finally, we’ll show how to convert fractions to decimals and percents, with handy reference charts.

How to Add and Subtract Fractions

When you add or subtract fractions, they need to have the same bottom number (denominator). If they don’t, you have to find a least common multiple (LCM). This LCM helps you make new fractions that are equal to the old ones but have the same bottom number. After that, you can add or subtract.

Formulas for Adding/Subtracting Fractions:

• If Denominators are the Same: a/b + c/b = (a+c)/b or a/b - c/b = (a-c)/b. You just add or subtract the top numbers.
• If Denominators are Different: First, find the LCM of b and d. Change a/b to a'/LCM and c/d to c'/LCM. Then, a'/LCM + c'/LCM = (a'+c')/LCM.

Let’s Try an Example: 1/4 + 2/3

1. Find a Denominator They Both Share: Our bottom numbers are 4 and 3. The smallest number that both 4 and 3 can divide into evenly is 12. This is our LCM.
2. Change Them to New, Equal Fractions:
   • For 1/4: We need the bottom number to be 12. Since 4 times 3 is 12, we multiply both the top and bottom by 3. So, 1/4 becomes (1*3)/(4*3) = 3/12.
   • For 2/3: We also need the bottom number to be 12. Since 3 times 4 is 12, we multiply both the top and bottom by 4. So, 2/3 becomes (2*4)/(3*4) = 8/12.
3. Add the Top Numbers: Now that both fractions have 12 at the bottom, we can add the top numbers: 3/12 + 8/12 = (3+8)/12 = 11/12.
4. Make it Simpler (if you can): Look at 11 and 12. They don’t share any common factors except for 1. So, 11/12 is already as simple as it gets.

So, 1/4 + 2/3 equals 11/12.

How to Multiply Fractions

Multiplying fractions is pretty easy! You just multiply the top numbers together and then multiply the bottom numbers together. You don’t need to find a common denominator for this.

Formula for Multiplying Fractions:

• a/b * c/d = (a*c)/(b*d)

Let’s Try an Example: 2/3 times 2/3

1. Multiply the Top Numbers: Take the numerators and multiply them: 2 * 2 = 4.
2. Multiply the Bottom Numbers: Take the denominators and multiply them: 3 * 3 = 9.
3. Put Them Together: Your new fraction is the new top number over the new bottom number: 4/9.
4. Make it Simpler (if you can): Check 4 and 9. They don’t have any common factors besides 1. So, 4/9 is already in its simplest form.

So, 2/3 times 2/3 equals 4/9.

How to Divide Fractions

To divide fractions, there’s a neat trick. You “flip” the second fraction upside down. This is called finding its reciprocal. Then, you just multiply the first fraction by this flipped second fraction.

Formula for Dividing Fractions:

• a/b / c/d = a/b * d/c = (a*d)/(b*c)

Let’s Try an Example: 3/4 divided by 4 (as a fraction)

1. Turn Whole Numbers into Fractions: A whole number like 4 can be written as a fraction: 4/1.
2. Flip the Second Fraction: Our second fraction is 4/1. When you flip it, it becomes 1/4.
3. Now, Multiply: We’ll multiply the first fraction by the flipped second one: 3/4 * 1/4.
4. Multiply the Top Numbers: 3 * 1 = 3.
5. Multiply the Bottom Numbers: 4 * 4 = 16.
6. Put Them Together: The answer is 3/16.
7. Make it Simpler (if you can): Look at 3 and 16. They only share 1 as a common factor. So, 3/16 is already as simple as it gets.

So, 3/4 divided by 4 equals 3/16.

Changing Mixed Numbers to Improper Fractions

A mixed number has a whole number and a fraction together (like 2 and 1/3). An improper fraction has a top number that is bigger than or equal to its bottom number (like 7/3).

Formula for Changing Mixed Number to Improper Fraction:

• Whole_Number and Numerator/Denominator = (Whole_Number * Denominator + Numerator) / Denominator

Let’s Try an Example: Change 2 1/3 to an improper fraction

1. Multiply the Whole Number by the Bottom Number: Take the whole number (2) and multiply it by the denominator (3): 2 * 3 = 6.
2. Add the Top Number to Your Result: Now add the numerator (1) to that result: 6 + 1 = 7.
3. Put This New Number Over the Old Bottom Number: The denominator stays the same (3). So, the improper fraction is 7/3.

So, 2 1/3 is the same as 7/3.

Simplifying Fractions (Making Them Smaller)

Simplifying a fraction means making it as small as possible. You do this by dividing both the top and bottom numbers by the biggest number they both can be divided by. Keep doing this until they only share 1 as a common factor.

Let’s Try an Example: Simplify 12/20

1. Find Common Factors: Both 12 and 20 are even numbers, so we know they can both be divided by 2.
   • 12 divided by 2 = 6
   • 20 divided by 2 = 10
   • Now our fraction is 6/10.
2. Keep Dividing by Common Factors: Both 6 and 10 are still even. So, we can divide them both by 2 again.
   • 6 divided by 2 = 3
   • 10 divided by 2 = 5
   • Our fraction is now 3/5.
3. Check if You Can Simplify More: Look at 3 and 5. They are both prime numbers, meaning they can only be divided by 1 and themselves. They don’t share any other factors. So, we’re done!

So, 12/20 simplified is 3/5.

Sometimes, fraction math can get a bit tricky, especially with mixed numbers or lots of steps. That’s when an online tool can really help. A good Fraction Calculator can do all these steps for you quickly. It makes sure your answers are right and saves you time.

More Examples and Conversions

Here’s a table to show you different ways fractions are used and simplified. It answers some common questions too:

Converting Fractions to Percents

Do you need to turn a fraction into a percentage? It’s easier than you might think! First, you divide the top number (numerator) by the bottom number (denominator). This gives you a decimal. Then, you simply multiply that decimal by 100.

For example, let’s take the fraction 2/5. You divide 2 by 5, which equals 0.4. Now, multiply 0.4 by 100. That gives you 40%. So, 2/5 is the same as 40%.

Fractions, decimals, and percentages are all ways to talk about parts of a whole thing. Knowing how to switch between them is a really useful skill. You’ll use it in math, when managing money, and even in everyday life.

A fraction like 1/2 shows a part compared to its whole (like half a pizza). A percentage like 50% shows that same part, but out of 100. Luckily, the steps to convert them are simple. It works for all kinds of fractions, even tricky ones!

How to Turn a Fraction into a Percent

Turning a fraction into a percentage is a two-step process. I’ll walk you through it.

1. Make it a decimal: Take the top number (numerator) and divide it by the bottom number (denominator).
2. Make it a percent: Take the decimal you just found and multiply it by 100. Don’t forget to add the percent sign (%) at the end!

The Formula

Here’s the math formula if you like to see it written out:

Want to keep going? See Converting Fractions to Decimals below.

Percent = (Numerator / Denominator) * 100

Step-by-Step Example: Changing 2/5 to a Percent

Let’s use our example of 2/5 again. I’ll show you exactly how to convert it.

1. Divide the top number by the bottom number:

   The top number is 2.

   The bottom number is 5.

   2 ÷ 5 = 0.4

   So, 2/5 as a decimal is 0.4.

2. Multiply the decimal by 100:

   0.4 × 100 = 40

   Now, add the percent symbol:

   40%

That means 2/5 is the same as 40%. See, it’s not so bad!

What About Mixed Numbers?

Sometimes you’ll see a mixed number. This is a whole number with a fraction next to it, like 1 1/3. Before you can convert it to a percent, you need to change it into an “improper fraction.”

To do this, you multiply the whole number by the bottom number of the fraction. Then, you add the top number of the fraction. Put this new total over the original bottom number.

Example: Converting 1 1/3 to a Percent

1. Turn the mixed number into an improper fraction:

   Our whole number is 1, the fraction’s top number is 1, and its bottom number is 3.

   (1 × 3) + 1 = 3 + 1 = 4

   So, our improper fraction is 4/3.

2. Divide the top number by the bottom number:

   4 ÷ 3 ≈ 1.3333 (This decimal goes on forever, so we’ll round it a bit.)

3. Multiply the decimal by 100:

   1.3333 × 100 ≈ 133.33

   Add the percent symbol:

   133.33%

So, 1 1/3 is about 133.33%. It’s more than 100% because it’s more than a whole!

Fraction to Percent Conversion Chart

I put together this table with common fraction to percent conversions. It includes some with decimals that repeat. You can use it to quickly find answers or to check if your own calculations are correct. You can also use a dedicated fraction to percent calculator for any fraction.

Fraction to Percent: Common Questions

What is 10/12 as a percent?

To change 10/12 to a percent, you divide 10 by 12. This gives you about 0.8333. Then, multiply that by 100. So, 10/12 is about 83.33%.

How do you convert 5/6 to a percentage?

First, divide 5 by 6. You’ll get about 0.8333. Next, multiply 0.8333 by 100. That means 5/6 is roughly 83.33%.

What is the percentage equivalent of 1/20?

1/20 is the same as 5%. I get this by dividing 1 by 20, which is 0.05. Then I multiply 0.05 by 100, which gives me 5%.

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top) by the denominator (bottom). For a mixed number such as “4 and 1/4”, keep the whole-number part. Convert only the fractional part to a decimal and then add it to the whole number.

For example, to change 4 and 1/4 to a decimal, divide 1 by 4 to get 0.25. Add 0.25 to the whole number 4. The result is 4.25.

How to Change Fractions to Decimals

Fractions show parts of a whole. Decimals also show parts of a whole but use base ten. Converting a fraction to a decimal is division and a decimal point. You will use this in math, science, and daily tasks. You use it when you compare numbers or include non-whole values in calculations.

You’ll usually see three types of fractions:

Want to keep going? See Converting Fractions to Percents below.

• Proper Fractions: The numerator is smaller than the denominator (for example, 1/2 or 3/4). These convert to decimals between 0 and 1.
• Improper Fractions: The numerator is equal to or larger than the denominator (for example, 5/4 or 7/2). These convert to decimals of 1 or more.
• Mixed Numbers: A whole number plus a proper fraction (for example, 1 1/2 or 3 3/4). Convert the fractional part and keep the whole number the same.

The Simple Formula for Fractions to Decimals

The main rule is short and direct.

Decimal = Numerator ÷ Denominator

For a mixed number, change the rule slightly.

Decimal = Whole Number + (Numerator ÷ Denominator)

Now see a worked example.

Step-by-Step Example: Changing 4 and 1/4 to a Decimal

We will apply the rules above to convert the mixed number 4 and 1/4 to a decimal.

1. First, find the parts:
   • The whole number is 4.
   • The numerator (top number of the fraction) is 1.
   • The denominator (bottom number of the fraction) is 4.
2. Next, change the fraction part to a decimal:

   Divide the numerator by the denominator:

   1 ÷ 4 = 0.25

3. Finally, add the decimal part to the whole number:

   4 + 0.25 = 4.25

So, 4 and 1/4 as a decimal is 4.25.

Some divisions produce digits that repeat forever. For example, 1/3 and 1/9 show repeating digits. In those cases, we usually round to a few decimal places. Common choices are two, three, or four digits. You may also see ellipses (…) or a bar over the repeating digits to show they continue.

Handy Chart: Fractions to Decimals

This chart lists common fraction-to-decimal conversions. It shows proper fractions, improper fractions, and mixed numbers for quick reference.

Things to Think About with Decimal Conversions

Not every fraction becomes a short decimal. Some produce repeating decimals, where one or more digits repeat forever. For example, 1/3 becomes 0.333… and 1/7 becomes 0.142857142857…. Choose the precision you need. For everyday use, rounding to two or three decimal places often suffices. For science and engineering, keep more digits or keep the fraction to avoid rounding errors.

Whether a decimal terminates or repeats depends on the denominator. First, simplify the fraction. If the denominator’s only prime factors are 2 and/or 5, the decimal terminates. If the denominator has other prime factors, such as 3, 7, or 11, the decimal repeats indefinitely.

When to Pick Fractions vs. Decimals

• Use fractions when:
  • You need an exact result (1/3 is exact while 0.333… is an approximation).
  • You work in algebra or with ratios.
  • Measurements come naturally in fractions (for example, 1/2 inch or 3/4 cup).
• Use decimals when:
  • You want to compare numbers quickly (0.75 and 0.8 are easier to compare than 3/4 and 4/5).
  • You deal with money, which uses cents (for example, $1.25).
  • You take scientific measurements, since instruments often give decimals.
  • You use calculators or computers, which usually work with decimals.

How to Round Repeating Decimals

When a decimal repeats, you often round it for practical use. Use the usual rounding rules.

• Look at the digit right after where you want to stop.
• If that digit is 5 or higher, round the last kept digit up.
• If that digit is less than 5, leave the last kept digit as it is.

For example, 1/9 as a decimal is 0.1111….

• If you round it to two decimal places, it becomes 0.11.
• If you round it to three decimal places, it becomes 0.111.

Fraction to Decimal: Common Questions

How do I change a mixed number into a decimal?

Convert the fractional part by dividing the numerator by the denominator. Then add that decimal to the whole number part.

What’s the difference between a decimal that stops and one that repeats?

A terminating decimal ends after a few digits (for example, 0.5 or 0.25). A repeating decimal has one or more digits that continue forever (for example, 0.333… or 0.142857…).

Can every fraction be turned into a decimal?

Yes. Any common fraction where the numerator and denominator are whole numbers and the denominator is not zero converts to a decimal. Some decimals terminate and some repeat.

Common Questions About Fractions

How do you make fractions simpler?

To simplify a fraction, divide both the top number and the bottom number by the biggest number they both share. Keep doing this until no other number besides 1 can divide into both of them.

What is an improper fraction?

An improper fraction is a fraction where the top number (numerator) is bigger than or equal to the bottom number (denominator). For example, 7/3 or 5/5 are improper fractions.

When do you need a common bottom number?

You need a common bottom number (denominator) when you are adding or subtracting fractions. This makes sure you are combining or taking away equal-sized pieces of something.

Can you multiply fractions if they don’t have a common bottom number?

Yes, you absolutely can! When you multiply fractions, you don’t need a common bottom number. Just multiply the top numbers together and the bottom numbers together.