From cooking to budgeting, fractions are everywhere. Our guide breaks down the process into simple, relatable steps. Let's turn fractions from a mystery into a tool you can use every day!

How To Add Fractions by Robin Yeats
How To Add Fractions by Robin Yeats

Understanding Fractions: The Basics

At its core, a fraction represents a part of a whole. It's composed of two numbers: the numerator, located above the line, and the denominator, below the line. The numerator indicates how many parts of the whole you have, while the denominator tells you how many parts the whole is divided into.

For example: in the fraction 1/2, the numerator 1 signifies one part of the whole that's split into two, indicated by the denominator 2.

Step by Step: How To Add Fractions

Navigating through the realm of fractions can seem daunting at first, but with a step-by-step approach, adding fractions becomes a breeze. In the upcoming sections, we'll break down the process for adding fractions with the same and different denominators, as well as mixed numbers, into simple, manageable steps to ensure you grasp each concept with ease and confidence. Let’s go!

Adding Fractions with the Same Denominator

Adding fractions might seem a bit like trying to mix oil and water at first glance, but once you get the hang of it, you'll see it's more like blending your favourite smoothie - smooth and straightforward, especially when the denominators are the same.

Let's dive into the simple steps that make adding such fractions as easy as pie (or should we say, as easy as adding slices of pie!).

  1. Step 1: Check the Denominators: Ensure that the fractions you are adding have the same denominator. This tells you they're divided into the same number of parts, making them ready to combine.
  2. Step 2: Add the Numerators: Simply add the numerators and keep the denominator the same. This is how many parts you have in total now.
  3. Step 3: Simplify if Necessary: Sometimes your answer can be reduced to a simpler form. Keep an eye out in the question to see if you’re asked to do this or if it’s easier to represent the fraction this way.

You can also imagine you and a friend have slices of the same pizza which has been cut into 8 slices. You have two slices of it 2/8, and your friend offers you their three slices 3/8. Combine the slices, and voila, you have five slices out of the total of 8 slices - 5/8 of a whole pizza.

How To Add Fractions With The Same Denominator

Try it for yourself!

  • Add 1/4 + 2/4

  • Add 3/8 + 5/8

Solutions

  • 1/4 + 2/4 = 3/4. The denominators are the same, so we just add the numerators: 1 + 2 = 3. The fraction is already in its simplest form.
  • 3/8 + 5/8 = 8/8 or 1. Again, with the same denominators, we just add the numerators: 3 + 5 = 8. Since 8/8 is equivalent to 1, the answer is 1 whole.

Feeling more confident? Fantastic! To get even more practise and reinforce what you've learned, check out our worksheet on adding fractions with the same denominators. It's packed with exercises designed to turn you into a fraction-adding wizard in no time.

Remember, every fraction adds up to your growing maths skills, and with each step, you're piecing together a bigger picture of mathematical understanding. Keep practising, and soon, adding any fractions will feel like second nature.

Adding Fractions with Different Denominators

When fractions have different denominators, it’s a little tricker. Before when the denominators were the same, it was really easy, so essentially, that’s what we’re trying to achieve here! The key to adding them is to make the denominators the same, known as finding the lowest common denominator (LCD). This process ensures that the fractions are speaking the same mathematical language, making addition straightforward and simple. Let's dive into how to navigate this essential skill with a step-by-step guide.

Step-by-Step Guide to Adding

Using our example of 1/3 + 2/5

  • Step 1: Find the LCM: We look at the times tables of 3 and 5 and find the 15 is the lowest common multiple.
  • Convert to Equivalent Fractions:
    • To convert 1/3
      • Denominator: 3 x 5 = 15
      • Numerator: 1 x 5 = 5
      • Answer = 5/15
    • To convert 2/5
      • Denominator: 5 x 3 = 15
      • Numerator: 2 x 3 = 6
      • Answer = 6/15
  • Step 2: Add the Fractions: Now that both fractions have the same denominator (15), simply add the numerators:
    • 5/15 + 6/15 = 11/15
  • Step 3: Simplify if Necessary: If the fraction can be simplified, do so. In our case, 11/15 is already in its simplest form.

Now try some for yourself…

  • Add 1/4 and 2/8.
  • Add 1/2 and 2/5.

Solutions

  • 1/4 + 2/8 = 1/2. The LCD of 4 and 8 is 4, so you can just convert 2/8 to its simplest form, 1/4. This makes it 1/4 + 1/4 = 2/4, which simplifies to 1/2.
  • 1/2 + 2/5 = 5/10 + 4/10 = 9/10.

 

 

Step by Step: Adding Mixed Numbers

Mixed numbers are a blend of whole numbers and fractions, representing quantities greater than one. Adding them might seem like juggling apples and oranges at first, but with a straightforward process, it's as easy as pie. Let's slice through this mathematical challenge together, transforming mixed numbers into improper fractions, adding them up, and then neatly converting them back.

Converting Mixed Numbers to Improper Fractions

  • Step 1: Multiply the Whole Number by the Denominator: Take the whole number part of the mixed number and multiply it by the denominator of the fraction part.
  • Step 2: Add the Numerator: To the product, add the numerator of the fraction part.
  • Step 3: Write as a Fraction: The sum becomes the numerator and you keep the original denominator to get your improper fraction.

Adding Improper Fractions

With your mixed numbers now in the form of improper fractions (where the numerator is larger than the denominator), you simply add them as you would with any fractions, ensuring you have a common denominator first.

For example, 17/5 + 6/5 would simply become 23/5.

Converting the Result Back to a Mixed Number

  • Divide the Numerator by the Denominator: This will give you the whole number part of your mixed number.
  • The Remainder Becomes the New Numerator: Place this over the original denominator to form the fractional part of your mixed number.

Now give these a try:

  • Add 1 1/2 and 2 2/3.
  • Add 2 1/3 and 3 1/4.

Solutions

  • 1 1/2 add 2 2/3 = 4 1/6. Convert to improper fractions: 3/2 and 8/3. Find a common denominator (6), giving 9/6 and 16/6. Add them to get 25/6, which converts back to 4 1/6.
  • 2 1/3 add 3 1/4 = 5 7/12. Convert to improper fractions: 7/3 and 13/4. Find a common denominator (12), giving 28/12 and 39/12. Add them to get 67/12, which converts back to 5 7/12.

 

Test Your Skills

  1. Add 1/8 + 3/8.
  2. Add 2/3 + 5/6.
  3. Add 1 1/4 + 2 3/4.
  4. Add 7/10 + 2/5.
  5. Add 3 1/2 + 2 2/3.

 

Solutions

  • 1/8 + 3/8 = 4/8, which simplifies to 1/2.
  • To add 2/3 and 5/6, convert to a common denominator of 6, giving 4/6 + 5/6 = 9/6, which we can convert to 1 1/2.
  • Convert mixed numbers to improper fractions, giving 5/4 + 11/4 = 16/4, which simplifies to 4.
  • Convert 7/10 and 2/5 to a common denominator of 10, resulting in 7/10 + 4/10 = 11/10, which is an improper fraction equal to 1 1/10.
  • Convert to improper fractions, resulting in 7/2 + 8/3. Finding a common denominator of 6, we get 21/6 + 16/6 = 37/6, which simplifies to 6 1/6.

 

As we wrap up our fraction-filled journey, it's clear that mastering the addition of fractions is a critical skill that opens up a world of problem-solving and analytical thinking, essential both in academic settings and in everyday life. From baking to budgeting, fractions are everywhere, making their understanding and application universally valuable.

 

Test your knowledge using our worksheets below, and adding fractions will soon be a breeze!