Real numbers

Real numbers are all the numbers on the number line: whole numbers, negatives, fractions, decimals, and numbers like $\pi$ and $\sqrt{2}$ whose decimals never end. In this topic you'll use all four operations with negative numbers, sort numbers into rational and irrational, find out which fractions give recurring decimals, and learn the index laws that make big powers easy to handle.

What you'll learn

• 1.01 Add and subtract integers: a refresher on adding and subtracting positive and negative whole numbers.
• 1.02 Multiply and divide integers: the sign rules, and why a negative times a negative is positive.
• 1.03 Four operations with integers: the order of operations with negative numbers, powers and brackets.
• 1.04 Negative fractions: adding, subtracting, multiplying and dividing fractions and mixed numbers that are negative.
• 1.05 Negative decimals: all four operations with negative decimals, including money and temperature problems.
• 1.06 Rational and irrational numbers: which numbers can be written as fractions, and which ones, like $\sqrt{2}$ and $\pi$, can't.
• 1.07 Recurring and terminating decimals: dot notation, and how to tell which fractions give decimals that go on forever.
• Investigation: the golden ratio. Find this famous irrational number in a number pattern, a five-pointed star and a rectangle.
• 1.08 Index laws: multiplying and dividing powers, a power of a power, and the zero index.

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 numbers and multi-step problems, 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.