Flashcards · J560 · Topic 1

Number operations and integers flashcards

18 cards on Topic 1, subtopics 1.01 to 1.04. Pick a subtopic or study them all.

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Adding and subtracting negative numbers: Subtracting a negative is the same as adding: 5 − (−3) = 8. Adding a negative is the same as subtracting: 5 + (−3) = 2.
Signs when multiplying or dividing: Same signs give a positive answer; different signs give a negative answer. With many factors, an even number of negatives gives a positive.
Work out (−4) × (−9) + (−20) ÷ 5: Multiply and divide first: 36 + (−4) = 32.
How do you check a whole-number calculation quickly?: Estimate first by rounding (18 × 23 ≈ 20 × 20 = 400, so 414 fits). Reverse a division by multiplying back and a subtraction by adding back.

Prime number, and the primes under 20: A number with exactly two factors. 1 is neither prime nor composite. Primes under 20: 2, 3, 5, 7, 11, 13, 17, 19.
Factor compared with multiple: A factor divides exactly into the number, so it is smaller than or equal to it. A multiple is in the number’s times table, so it is larger than or equal to it.
How do you write a number as a product of prime factors?: 1. Divide by the smallest prime that fits. 2. Keep dividing until you reach 1. 3. Collect repeats into powers and multiply back to check. Example: 150 = 2 × 3 × 5².
HCF and LCM of 72 and 60 from prime factors: 72 = 2³ × 3², 60 = 2² × 3 × 5. HCF: shared primes, lowest powers = 2² × 3 = 12. LCM: all primes, highest powers = 2³ × 3² × 5 = 360.
Divisibility tests for 3, 4 and 9: 3: the digit sum is a multiple of 3. 4: the last two digits form a multiple of 4. 9: the digit sum is a multiple of 9.
Uniqueness of prime factorisation: Every whole number above 1 has exactly one prime factorisation, apart from the order of the factors. Different factor trees always give the same result.

Priority of operations: 1. Brackets, including fraction bars and the line of a root sign. 2. Powers, roots and reciprocals. 3. × and ÷, from the left. 4. + and −, from the left.
Work out 20 − 12 ÷ 4 + 2: Divide first: 20 − 3 + 2, then left to right: 19.
Work out 2 × (3 + 4)² − 5 × 6: 2 × 49 − 30 = 98 − 30 = 68
Work out 5 + 2 × (√100 − 4)²: Root inside the bracket first: 5 + 2 × 6² = 5 + 2 × 36 = 5 + 72 = 77.

Inverse operations: Add ↔ subtract. Multiply ↔ divide. Square ↔ square root. Cube ↔ cube root.
How do you solve a "think of a number" puzzle?: 1. Write the steps in the order given. 2. Reverse the order. 3. Replace each step with its inverse. 4. Check by running the original steps forward.
I square a positive number and add 11 to get 92. What was the number?: Reverse: 92 − 11 = 81, and √81 = 9. Check: 9² + 11 = 92.
Use inverse operations to work out 17 × 25 mentally: × 25 is the same as × 100 ÷ 4: 1700 ÷ 4 = 425.