1.) Numbers

Question 1

What are rational and Irrational numbers?

Answer 1

• Rational numbers can be written as fractions (which includes integers)
• While irrational numbers cannot be written as neat fractions (have never-ending and non-repeating decimals)

Question 2

How do you find the LCM of two numbers?

Answer 2

• List each number’s prime factors
• The answer includes each prime factor and its MOST FREQUENT occurrence
• Example: 18 (2 * 3²) and 30 (2 * 3 * 5), the LCM would be 2 * 3² * 5
• Extra hint: LCM, you’d expect a number bigger than the two most of the time (exception being when the LCM is equal to one of the two numbers, LCM can never be smaller)

Question 3

How do you find the HCF of two numbers?

Answer 3

• List each number’s prime factors
• The answer includes ONLY THE OVERLAPPING factors
• Example: 180 (2² * 3² * 5) and 84 (2² * 3 * 7), the HCF would be 2² * 3
• Extra hint: HCF, you’d expect a number smaller than the two

Question 4

How is a number written in standard form?

Answer 4

• A x 10^x
• Where A has to be between 1 and 10
• A can also be thought of as a number that can only have 1 digit in front of its decimal point

Question 5

How do you add/subtract and multiply/divide by standard form?

Answer 5

• For adding/subtracting: make the powers of 10 the same. Then add the numbers in front together
• For multiplying/dividing: compartmentalise the two; multiply/divide the front numbers and then separately, do the same for the back numbers
• If the front number becomes >10 or <1, convert the power of 10 appropriately