2. Rational numbers

Lesson

Previously, we worked on multiplying and dividing fractions. Now, we'll apply the same rules to multiply and divide mixed numbers.

Recall that a mixed number is a number consisting of an integer and a unit fraction. A mixed number can also be expressed as an improper fraction or a fraction where the numerator is larger than the denominator.

Watch the video below, where we discuss how to multiply and divide mixed numbers.

- In what ways are the steps the same as multiplying and dividing other fractions?
- In what ways are the steps different?

Notice that we can use the same steps for multiplying and dividing fractions that we previously saw, with one added step. That is, we can convert mixed numbers to improper fractions first.

Evaluate $2\frac{2}{5}\times1\frac{3}{5}$225×135, giving your answer as a mixed number in simplest form.

Evaluate $3\frac{3}{7}\div1\frac{3}{5}$337÷135, giving your answer as a mixed number in simplest form.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = (8/9) because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = (ad/bc). How much chocolate will each person get if 3 people share 1/2lb of chocolate equally? How many (3/4) cup servings are in (2/3) of a cup of yoghurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?