5.12 Fraction patterns

Use area models.

\dfrac{1}{12} means means one twelfth or 1 part out of 12 parts should be shaded in an area model.

Here is the area model of \dfrac{1}{12} + \dfrac{1}{12}.

We can see that adding the two shaded parts means we get 2 shaded parts out of 12 parts.

This can be written as the fraction \dfrac{2}{12}.

\dfrac{1}{12}+\dfrac{1}{12}= \dfrac{2}{12}

Add \dfrac{1}{10} to the last given value to complete the pattern.

This picture shows \dfrac{4}{10} blocks shaded blue. If another 1 block were shaded, 5 out of 10 would be shaded in total. So the next number is \dfrac{5}{10}.

\dfrac{4}{10} + \dfrac{1}{10} = \dfrac{5}{10}

We can see that the numerator increased by 1 and the denominator stayed the same. Similarly doing this for the following numbers we can complete the pattern:\dfrac{3}{10}, \,\dfrac{4}{10}, \,\dfrac{5}{10}, \, \dfrac{6}{10}, \,\dfrac{7}{10}

Notice how the number of shaded parts changes each time.

In the first shape, 3 out of 3 parts are shaded.

In the second shape, 2 out of 3 parts are shaded.

In the third shape, 1 out of 3 parts are shaded.

The number of shaded parts are decreasing by 1 each time. So the next shape should have \\ 1-1=0 parts shaded.

So option C is the answer.

Find how much the numbers are increasing by each time and add that to the last given value to complete the pattern.

To work out how much the numbers are increasing by each time, you can count up or find the difference between two fractions.

So we need to add \dfrac{1}{7} to each number to complete the pattern.

The complete pattern is \dfrac{1}{7},\,\dfrac{2}{7},\,\dfrac{3}{7},\,\dfrac{4}{7},\,\dfrac{5}{7},\,\dfrac{6}{7}