6T Maths Homework - 3/3/17 Order of Operations (BracketsOrderDivideMultiplyAddSubtract) tells us the order in which calculations in a sum should be done. 1(a) Emma works out 40 − 10 ÷ 2 Her answer is 15 The correct answer is 35 Explain the mistake that Emma has made. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ (b) Put +, −, × or ÷ in each of the following to make them true. 2 (a) Work out the answer. 2 + (16 ÷ 2) + 6 = .................... (b) Put brackets in the calculation below to make it correct. 2 + 16 ÷ 2 + 6 = 4 3) Write in the boxes what the missing numbers could be. + + = 15 × = 15 – = 15 × + = 15 4(a) Write the answers. (4 + 2) × 3 = ........................ 4 + (2 × 3) = ........................ (b) Work out the answer to (2 + 4) × (6 + 3 + 1) (c) Put brackets in the calculation to make the answer 50 4 + 5 + 1 × 5 (d) Now put brackets in the calculation to make the answer 34 4 + 5 + 1 × 5 5(a) List the first five multiples of 11 Answer _____; _____; _____; _____; _____; (b) Is 109 a multiple of 11? Give a reason for your answer. ______________________________________________________________ ______________________________________________________________ Factors, Multiples, Squares, Cubes and Primes Factor - A number that divides exactly into another number Multiple - A number that may be divided by another number a certain number of times without a remainder Square Number - The answer when an integer has been multiplied by itself Cube Number - The answer when an integer is multiplied by itself and by itself again. Prime - A number that has exactly 2 factors, 1 and itself 6 (a) What is the highest common factor (HCF) of 18 and 24? Answer ______________________________ (b) The least common multiple (LCM) of two numbers is 20 Give an example of what the numbers could be. Answer ____________ and ______________ 7)Three prime numbers add up to 30 Give an example of what the three prime numbers could be. Answer ______ and ________ and ________ 8) A number has eight factors. Five of the factors are 1, 2, 3, 5 and 10. What are the other three factors? Answer ______ and ________ and ________ 9) What is the only number that is 1 more than a square number and 1 less than a cube number? Answer ______________________________ 10) Write down all the numbers which are multiples of 3 and factors of 45 Answer ______________________________ 11) 70 written as the product of prime factors is 2 × 5 × 7 (a) Write 84 as the product of prime factors. Answer _____________________________ (b) Work out the highest common factor (HCF) of 84 and 70 Answer _____________________________ (c) Work out the lowest common multiple (LCM) of 84 and 70 Answer _____________________________ 12) Write down a number which is • a multiple of 4 • a factor of 400 • not 4 or 400 13) Here is a list of numbers. 6 9 11 27 30 36 90 From the list, write down (a) the multiple of 12 (b) the two factors of 30 (c) the prime number (d) the cube number 14) Mark is thinking of a square number whose digits add up to seven. Write down two numbers he could be thinking of. Answer ____________ and _____________ 15) The word ‘prime’ spelt backwards is ‘emirp’. An emirp is a prime number that makes a different prime number when its digits are reversed. For example, 13 and 31 are a pair of emirps. (a) Write down another pair of emirps between 10 and 100 Answer _____________________________ (b) Explain why 19 and 91 are not a pair of emirps. ______________________________________________________________ ______________________________________________________________ 16) The product of two whole numbers is an odd number. Explain why the sum of the two numbers must be an even number. ______________________________________________________________ ______________________________________________________________ 17) Three positive whole numbers add up to 34 One of the numbers is a multiple of 9 The other two numbers are equal. What are the three numbers? Answer _________ , _________ , _________ 18) Lena’s phone number has six digits. They are all different. She remembers it as three 2-digit numbers. The first 2-digit number is a factor of 118 The second 2-digit number is a prime number less than twenty. The third 2-digit number is a square number which is not a cube number. What is her phone number? ___________________________________________________________________ Homework due in by Wednesday 8th March .