lesson
Use the operation's meaning
1 · Learn
Adding fractions combines equal-sized parts, so rewrite them with a common denominator. Multiplication takes a fraction of a fraction. Division asks how many of one quantity fit into another and can be checked by multiplication.
For division by a non-zero fraction, multiplying by its reciprocal gives the same result. Explain the meaning before treating the reciprocal as an unexplained trick.
2 · Worked example
3/4 ÷ 1/8 = 6 because six eighths make three quarters. The reciprocal method gives 3/4 × 8/1 = 6 too.
3 · Your turn
Calculate 2/3 + 1/4, 2/3 × 1/4 and 2/3 ÷ 1/4.
Check your answer
11/12; 1/6; 8/3 or 2 2/3.
4 · Apply your learning
Represent one quotient using equal-length fraction strips, then verify it by multiplication.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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