DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 2: Fractions and Core Number Skills

Fractions and Core Number Skills

Understand fractions as numbers, not just procedures with numerators and denominators.

Junior Maths Book 1 pages 19-328 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 19-32

Simplify, compare, order and calculate with fractions, mixed numbers and improper fractions.

AI explanation

The AI teacher uses fraction bars and number lines to show equivalence, then connects the visual model to efficient written methods for adding, subtracting, multiplying and dividing fractions.

  1. 1The denominator names the size of the parts.
  2. 2Equivalent fractions are the same value written with different-sized parts.
  3. 3For addition and subtraction, use common denominators.
  4. 4For multiplication, multiply parts of parts.
  5. 5For division, ask how many groups fit.

Animated teaching

See the method

Fraction bars resize into common denominators, then a number line shows the same values in order.

Fraction bars converting to common denominators2/34/6

Same value, same line

Common denominators make the pieces the same size, so addition and subtraction become fair.

Why this method works

  • You can only add or subtract fractions directly when the pieces have the same size.
  • Multiplication of fractions represents a fraction of a fraction.
  • Dividing by a fraction is the same as multiplying by its reciprocal because it asks how many of that fraction fit in the amount.

Common mistakes

  • Adding denominators.
  • Forgetting to simplify the final answer.
  • Changing mixed numbers without converting them to improper fractions first.
  • Using the reciprocal for multiplication instead of division.

Multiple methods

  • Fractions can be compared by common denominators, common numerators, decimals or a number line.
  • Mixed-number operations can be done by converting to improper fractions or by separating whole-number and fractional parts when appropriate.
  • Simplification can happen at the end or by cross-cancelling before multiplying.

Worked examples

Add unlike denominators

Calculate 5/6 - 1/4.

Method: Use a common denominator.

  1. 1.The lowest common denominator of 6 and 4 is 12.
  2. 2.5/6 = 10/12.
  3. 3.1/4 = 3/12.
  4. 4.10/12 - 3/12 = 7/12.

Answer: 7/12

Multiply fractions

Calculate 15/16 x 8/25.

Method: Cross-cancel before multiplying.

  1. 1.Cancel 8 with 16 to get 1 and 2.
  2. 2.Cancel 15 with 25 to get 3 and 5.
  3. 3.Multiply the remaining numerators and denominators.

Answer: 3/10

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Simplify 18/42.

Question 2

Calculate 2/3 + 1/6.

Question 3

Calculate 3/5 divided by 6.

Review prompt

Explain why 1/3 + 1/4 is not 2/7.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

A student says 2/5 + 3/7 = 5/12. Explain the error and find the correct answer.

Hint: Use a common denominator before adding.