Calculations with Fractions and Mixed Numbers

Differentiated Learning Objectives

  • All students should multiply and divide with mixed numbers and top-heavy fractions.
  • Most students should efficiently evaluation calculations with fractions and mixed numbers.
  • Some students should substitute mixed numbers and top-heavy fractions into a formula and evaluate the result. 

Links to Lesson Resources (Members Only)

Starter/Introduction

Students recap ordering fractions and mixed numbers by arranging a series of values along a number line. The fractions could be written with a common denominator or converted to decimals using a calculator to differentiate for the less able students.

Calculations with Fractions and Mixed Numbers

 Prompts / Questions to consider

  • What is the lowest common multiple of 3, 4, 5, 6 and 8?
  • How do we convert mixed numbers to top-heavy fractions?
  • Which fractions are greater than one?
  • Which fractions are less than one?

Calculations with Fractions and Mixed Numbers

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TThe key points when working through the questions are:

  • When adding and subtracting fractions with different denominators, write them with a common denominator using equivalent fractions.
  • To multiply fractions, look to cross-simplify whenever possible, as this will make the question simpler overall. Mixed numbers need to be converted to top-heavy fractions when multiplying and dividing.
  • To divide by a fraction, we multiply by its reciprocal.

Work through the first couple of questions to demonstrate for the class. Students could then try the following question on mini-whiteboards and give feedback on their workings.

Calculations with Fractions and Mixed Numbers

 Prompts / Questions to consider

  • What is the order of operations?
  • Are equivalent fractions needed to add or subtract fractions?
  • Can I cross-simplify any products?
  • How do I write a division as a multiplication using its reciprocal?

Plenary

The plenary takes between 8 and 12 minutes. Encourage students to work in pairs to share their ideas and question each other’s methods. Students should check their workings using a calculator before feeding back to the teacher or class.

Calculations with Fractions and Mixed Numbers

 Prompts / Questions to consider

  • How can I use the formula to work out the calculation?
  • Can I use a pair of brackets to make the calculation simpler?
  • How can I use the fraction and mixed number button on a calculator to check my solution?

Differentiation

More able students could substitute known fractions and mixed numbers into complex formulae. Less able students may benefit from recapping how to multiply and divide with fractions before including addition and subtraction.

Additional Resources

Problem Solving
Fractions
Revision
Adding and Subtracting Fractions with the same Denominator
4 Part Lesson
Calculations with Fractions and Mixed Numbers

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