Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice!

Adding and Subtracting Mixed Numbers with Common Denominators—Let's Practice! exercise

• Workout the fraction problems using addition or subtraction.

  Hints

  First we need to add the whole number.

  Next we add across our numerators.

  Lastly, as the denominators (bottom number) are the same, our answer should have the same too. Remember sometimes our answers can be simplified

  Use the images to help you. You can count the whole cakes and the slices.

  Has your answer been simplified?

  In this example $\frac{1}{4}$ + $\frac{1}{4}$ = $\frac{2}{4}$

  $\frac{2}{4}$ can be simplified. Both the numerator and denominator can be divided by 2, so our answer would be simplified from $\frac{2}{4}$ to $\frac{1}{2}$

  $\frac{1}{4}$ + $\frac{1}{4}$ = $\frac{1}{2}$

  Solution

  2 $\frac{3}{5}$ + 1 $\frac{1}{5}$ = 3 $\frac{4}{5}$

  1 $\frac{1}{4}$ + 3 $\frac{2}{4}$ = 4 $\frac{3}{4}$

  2 $\frac{1}{2}$ + 2$\frac{1}{2}$ = 5

  1 $\frac{2}{6}$ + 1 $\frac{1}{6}$ = 2 $\frac{1}{2}$

• Solve the addition and subtraction fraction problems

  Hints

  First, we add or subtract the whole numbers.

  Next we add or subtract the numerators top numbers.

  When the denominators bottom number are the same in the question, they will also be the same for the answer.

  Solution

  2 $\frac{2}{6}$ + 2 $\frac{3}{6}$ = 4$\frac{5}{6}$

  2 $\frac{3}{6}$ - 1 $\frac{2}{6}$ = 1 $\frac{1}{6}$

  2 $\frac{1}{4}$ + 3 $\frac{2}{4}$ = 5 $\frac{3}{4}$

  1 $\frac{2}{3}$ - 1 $\frac{1}{3}$ = $\frac{1}{3}$

• Addition and subtraction

  Hints

  Firstly we need to add or subtract the whole numbers. How many whole cakes are there?

  Next we need to add or subtract the numerator. The numerator refers to the parts we have (slices of cake)

  The denominator bottom number is how many parts the cake has been split into.

  Solution

  1 $\frac{1}{3}$ + 1 $\frac{1}{3}$ = 2 $\frac{2}{3}$

  2 $\frac{1}{4}$ - $\frac{3}{4}$ = 1 $\frac{1}{2}$

  1 $\frac{2}{6}$ + 2 $\frac{3}{6}$ = 3 $\frac{5}{6}$

  2 $\frac{4}{5}$ - 2$\frac{3}{5}$ = $\frac{1}{5}$

• Solve the fraction problems.

  Hints

  First look to see what you need to do. Is it an addition or a subtraction question?

  When you have done this, you can then add or subtract the whole numbers.

  Then look at the numerators and either add or subtract these.

  Finally look at the denominator bottom number. This will be the same for the answer. So we can write this in the blank denominator space.

  Solution

  2 $\frac{1}{5}$ + 3 $\frac{2}{5}$ = 5 $\frac{3}{5}$

  3 $\frac{5}{7}$ - 1 $\frac{4}{7}$ = 2 $\frac{1}{7}$

  4 $\frac{2}{7}$ - 1 $\frac{1}{7}$ = 3 $\frac{1}{7}$

  1 $\frac{2}{5}$ + 1$\frac{3}{5}$ = 3

• Solve the equation to create a new fraction.

  Hints

  First we need to add the whole numbers, these are also shown as the whole pizzas. Then add this to the whole number box.

  Next, we can add the parts of the fraction, these are the slices of pizza. Put your answer in the numerator top number box.

  How many slices has the pizza been split into? This is our denominator bottom number.

  Solution

  2 $\frac{1}{3}$ + 1 $\frac{1}{3}$ = 3 $\frac{2}{3}$

• Work out the missing numbers.

  Hints

  Look at the questions. If the denominator (bottom number) is blank, we can look at the denominators in the question as they will all be the same.

  If the numerator (top number) is blank we can use the inverse to help work it out. Look at this example.

  Solution

  2 $\frac{2}{4}$ + 1 $\frac{1}{4}$ = 3 $\frac{3}{4}$

  2 $\frac{5}{7}$ - 1 $\frac{2}{7}$ = 1 $\frac{3}{7}$

  1 $\frac{2}{5}$ + 2 $\frac{2}{5}$ = 3 $\frac{4}{5}$

  4 $\frac{2}{3}$ - 2 $\frac{1}{3}$ = 2 $\frac{1}{3}$