1. Operations with Fractions

We've divided fractions and whole numbers, but what does it look like to divide a fraction by another fraction?

Let's look at \dfrac{8}{9} \div \dfrac{2}{9}.

We can also apply the method of rewriting division as multiplication by the reciprocal like we did when dividing with whole numbers.

\displaystyle \dfrac {8}{9} \div \dfrac {2}{9} | \displaystyle = | \displaystyle \dfrac {8}{9} \cdot \dfrac {9}{2} | Multiply \dfrac{8}{9} by the reciprocal of \dfrac{2}{9} |

\displaystyle = | \displaystyle \dfrac {8\cdot 9}{9\cdot 2} | Multiply the numerators together and denominators together | |

\displaystyle = | \displaystyle \dfrac {8}{2} | Evaluate the multiplication | |

\displaystyle = | \displaystyle 4 | Divide |

Both methods give us the same result.

We can apply the same process to dividing with mixed numbers, because remember a mixed number is just a different form of a fraction. We just have to convert the mixed number into an improper fraction first.

Use the dropdown boxes to create a division expression.

Press the 'Start animation' button to see a model of the division.

Continue pressing 'Show next step' until the animation is complete.

Observe the animation for several different division expressions then answer the following questions:

- Explain how the model is showing the division.
- How does the model relate to the final fraction?
- What is the relationship between the numbers in the original division expression and the numbers in the final fraction?
- What do you notice about dividing a fraction or mixed number by a fraction between 0 and 1?

When a fraction or mixed number is divided by a fraction between 0 and 1, the result is larger than the original fraction or mixed number.

Evaluate each expression.

a

\dfrac{1}{8}\div\dfrac{1}{5}

Worked Solution

b

\dfrac{4}{5}\div\dfrac{11}{10}

Worked Solution

Evaluate and write your answer in its simplest form.

a

2 \dfrac {3}{5} \div 2 \dfrac {7}{10},

Worked Solution

b

1 \dfrac{1}{3} \div \dfrac{1}{8}.

Worked Solution

A 8 \dfrac{1}{4} meter long roll of fabric is to be cut into sections of equal length 2 \dfrac{3}{4}. How many pieces of fabric will there be?

Worked Solution

Idea summary

To divide one fraction by another, multiply the first fraction by the reciprocal of the second.