GCSE Maths: Primes, Factors and Fraction Calculations

Number work without a calculator is the backbone of the non-calculator paper at both GCSE tiers, and it is where many easy marks are lost. This material trains the structure-and-calculation content of the GCSE subject content for England: primes, factors and multiples, prime factorisation in index form, the highest common factor and lowest common multiple, the four operations with fractions and mixed numbers, the conventional order of operations, and systematic counting with the product rule.

The quiz has thirteen questions. You identify primes in a list that includes the usual traps, write a number as a product of prime factors, find an HCF from prime factorisations and an LCM from a Venn diagram of prime factors described in words, and solve a timetable problem where two buses leave together again. Four questions cover adding, subtracting, multiplying and dividing fractions and mixed numbers, one evaluates an expression with a negative number raised to a power, one counts the combinations of a three-course menu, and one finds a fraction of an amount of money. The wrong options are built from real slips: treating 1 as prime, adding denominators, subtracting the fractional parts the wrong way round, multiplying instead of dividing, and confusing the HCF with the LCM.

The flashcards define prime, factor, multiple, HCF, LCM, prime factor decomposition, reciprocal, mixed number and improper fraction, explain the order of operations with division and multiplication (and addition and subtraction) taken from left to right, and state the product rule for counting and the uniqueness of prime factorisation.

The printable written work has eight problems to answer with full working: a prime factorisation used to make a square number, HCF and LCM from prime factors, a flashing-lights timing problem, a sum and a quotient of mixed numbers, a multi-step fraction problem about a garden, two order-of-operations calculations with explanations, and counting four-digit codes with and without repeated digits. Exam questions at this level usually award marks for method, so each item asks you to show it.

The content is common to Foundation and Higher tiers and suits Year 10 and Year 11 students who want secure, fast number skills before tackling longer problems.

• Identify prime numbers and write a number as a product of prime factors in index form
• Find the HCF and LCM of two numbers, including with a Venn diagram, and use them in context
• Add, subtract, multiply and divide fractions and mixed numbers without a calculator
• Apply the order of operations with negative numbers and powers
• Count outcomes systematically with the product rule

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Number: structure and calculation (N1, N2, N3, N4, N5).