Fractions

A fraction describes part of a whole: a slice of pizza, a section of a road trip, a share of the money from a fundraiser. In this topic you'll learn to read, compare and simplify fractions, place them on a number line (including to the left of zero), and use all four operations with fractions and mixed numbers. Fractions turn up in recipes, measurements, sport and money, so these skills will keep coming back.

What you'll learn

• 4.01 Identify, order and compare fractions: naming fractions from pictures and number lines, mixed numbers and improper fractions, and putting fractions in order.
• 4.02 Negative fractions: fractions to the left of zero, opposites, and comparing negative fractions on a number line.
• 4.03 Equivalent and simplified fractions: fractions that look different but are worth the same, and writing fractions in simplest form.
• Investigation: fraction flowers. Fill in petals with equivalent fractions, find the weed, and plan a flower garden.
• 4.04 Add and subtract fractions: finding a common denominator, and adding and subtracting mixed numbers.
• Investigation: Egyptian fractions. Share loaves the way the ancient Egyptians did, using fractions with a numerator of 1.
• 4.05 Fractions of a quantity: finding a fraction of an amount, and working backwards to the whole.
• 4.06 Multiply fractions: multiplying numerators and denominators, cancelling first, and area models.
• 4.07 Divide fractions: reciprocals, and dividing by multiplying by the reciprocal.
• 4.08 Order of operations with fractions: brackets first, then powers, then × and ÷, then + and −.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: harder fractions and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.