5.13 Add and subtract fractions with models

Write the addition that describes the image.

Add the two fractions to find the total fraction shaded.

\text{Red}+\text{Blue}=\dfrac{1}{2}+\dfrac{1}{4}

What is the total fraction shaded?

Count how many parts are shaded and how many parts there are in total.

There are 2 red squares shaded and 1 blue square shaded.

The total number of squares in the image is 4.

So the total fraction shaded is \dfrac{3}{4}.

What is the equivalent fraction in fifteenths?

\dfrac{1}{3}=\dfrac{⬚}{15}

To find the numerator of the fraction, count the number of parts shaded.

There are 15 squares in total and 5 of them are shaded.

So the images also shows \dfrac{5}{15} of a rectangle shaded.

\dfrac{1}{3}=\dfrac{5}{15}

We now want to take away \dfrac{4}{15}.

What is the answer to \dfrac{1}{3}-\dfrac{4}{15}?

Use the equivalent fraction we found in part (a).

We can also count the number of shaded squared left after 4 are taken away.

In the image, 4 squares are shaded lighter to suggest that they are being taken away. Then we would only have 1 shaded square left out of 15.

So again: \dfrac{1}{3}-\dfrac{4}{15}=\dfrac{1}{15}

Complete the statement to make an equivalent fraction for \dfrac{1}{2}.

\dfrac{1}{2}=\dfrac{⬚}{8}

Use this a fraction wall showing halves and eighths.

By looking on the fraction wall, we can see that there are 4 eighths in 1 half.

So the complete statement is:

\dfrac{1}{2}=\dfrac{4}{8}

Plot \dfrac{4}{8} on the number line.

To plot \dfrac{4}{8}, we want to start at zero and jump right four spaces. So we have:

Choose the image below that represents the addition \dfrac{1}{2}+\dfrac{3}{8}.

A

B

C

D

Use the equivalent fraction found in part (a).

Remember when adding an amount on a number line we move to the right.

We have found that \dfrac{1}{2}+\dfrac{3}{8} is the same as \dfrac{4}{8}+\dfrac{3}{8}.

So we should start at \dfrac{4}{8} then jump right 3 eighths.

The correct answer is option B.