Adding two mixed numbers

When adding mixed numbers, you can use a similar method to adding two fractions, but this time you have to add whole numbers as well.

Remember, a mixed number is a combination of an integer (a whole number) and a fraction, like \( 3 \frac{1}{3} \).

What is \( 1 \frac{1}{3} + 2 \frac{2}{9}\)?

Let's break this calculation down into steps. The method below allows you to partition the mixed numbers into fractions and whole numbers, so that you can add them separately.

Step 1: Partition the mixed numbers, so you are left with the whole numbers together and the fractions together.

\( 1 + 2\)

and

\( \frac{1}{3} + \frac{2}{9} \)

You can quickly add the whole numbers together to make 3.

\( 1 + 2 = 3\)

Step 3: Now that the denominators are the same, you can add the numerators together.

\( \frac{3}{9} + \frac{2}{9} = \frac{5}{9}\)

Step 4: Finally, add the answers from the whole numbers and fractions together.

\( 3 + \frac{5}{9} = 3 \frac{5}{9}\)

Jeannie and Oliver ordered lots of pizzas. Jeannie ate \( 2 \frac{1}{4} \) pizzas and Oliver ate \( 1 \frac{1}{8} \). How much pizza did they eat altogether?

Let's write that as a calculation.

\( 2 \frac{1}{4} + 1 \frac{1}{8}\)

Step 1: Partition the fractions and whole numbers to add them separately.

\( 2 + 1 = 3\)

and

\( \frac{1}{4} + \frac{1}{8} \)

Step 2: Change one of the fractions so they both have the same denominator.

\( \frac{1}{4} = \frac{2}{8} \)

Step 3: Add the numerators together.

\( \frac{2}{8} + \frac{1}{8} = \frac{3}{8} \)

Step 4: Add the whole number answer and fraction answer together.

\( 3 + \frac{3}{8} = 3 \frac{3}{8} \)

So Jeannie and Oliver ate \( 3 \frac{3}{8} \) pizzas.

Have a go at solving these three problems involving addition of mixed fractions.

You may need a pen and paper.

1. Add these mixed fractions together. Can you give the answer in its simplified form?

   • 3 \(\frac {5}{8} \) + 9 \(\frac {1}{2} \)
   • 8 \(\frac {4}{9} \) + 2 \(\frac {2}{6} \)
   • 5 \(\frac {1}{6} \) + 6 \(\frac {1}{2} \)

2. On Saturday, there was 9 \(\frac {1}{6} \) hours of sunshine.On Sunday, there was 6 \(\frac {1}{5} \) hours of sunshine.How many hours of sunshine were there over the whole weekend?

3. Charlie has completed the calculation:

2 \(\frac {2}{6} \) + 4\(\frac{1}{4} \) = \(\frac {22}{6} \) + \(\frac{17}{4} \) = \(\frac{44}{12} \)+ \(\frac{51}{12} \) = \(\frac{95}{12} \) = 7 \(\frac{11}{2} \)

Frankie thinks he has spotted a mistake.

Can you:

• Explain the mistake Frankie has spotted.
• Find the correct answer, showing your working out.

Once you've had a go, check your answers here.