Here we will learn about multiplying and dividing negative numbers including what negative numbers are and how to multiply and divide them. Show
There are also negative number worksheets and exam questions at worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. What are negative numbers?Negative numbers are any numbers less than zero and have a negative sign (−) in front of them. Numbers greater than zero are referred to as positive numbers. If there is no sign in front of a number the number is positive. On the number line below we can see some positive and negative integers (whole numbers): The numbers in orange are negative and the blue numbers are positive. Just like you can multiply and divide positive numbers, you can do the same with negative numbers. In order to multiply or divide negative numbers you must remember: If the signs are the same, the answer is positive. If the signs are different, the answer is negative. When multiplying negative numbers: The same rules apply for dividing negative numbers:
Click here to learn about adding and subtracting negative numbers. What do you need to remember when multiplying and dividing negative numbers?How to multiply and divide negative numbersIn order to multiply and divide negative numbers:
Explain how to multiply and divide negative numbers in 2 stepsMultiplying and dividing negative numbers worksheetGet your free multiplying and dividing negative numbers worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE Multiplying and dividing negative numbers worksheetGet your free multiplying and dividing negative numbers worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE Multiplying and dividing negative numbers examplesExample 1: multiplication of negative numbersMultiply: \[ -3\times5\]
\[ 3\times5 = 15\] 2Change the sign using the rules of multiplying and dividing negative numbers: \[-3\times5\] In this case we have a number that is positive multiplied by a negative number (minus times positive gives a minus). The signs are different so we must have a negative answer: \[= -15\] Example 2: division of negative numbersDivide: \[ -24\div-6 \] Multiply or divide numbers normally. Change the sign using the rules of multiplying and dividing negative
numbers: \[-24\div-6\] In this case we have a negative number divided by a negative number. The signs are the same so we must have a positive answer: \[= 4\] Example 3: order of operationsSolve: \[ -12\div(-6) +4\times(-2)\] Multiply or divide numbers normally. In this case we are dealing with three different operations (+, x and ÷). We need to use BIDMAS to determine the order to calculate. Let’s temporarily ignore the negative signs. If we start with division: \[12\div6 = 2\] Next multiplication: \[4\times2 = 8\] There is an add sign in between so we must add the two numbers once we have dealt with the negatives. Change the sign using the rules of multiplying and dividing negative numbers: For the first part, −12 ÷ (−6), the signs are the same. For the second part 4 x (−2), the signs are different. We are left with 2 + (−8), which is the same as 2 − 8: \[= -6\] Example 4: powersSolve: \[ (-2)^3\] Multiply or divide numbers normally. 23 = 2 × 2 × 2 = 8
Change the sign using the rules of multiplying and dividing negative numbers: Remember (−2)3 is the same as (−2) × (−2) × (−2). If we start with just (−2) × (−2) the resulting answer = 4. It is positive because the signs are the same. If we take that 4 and times is by the final (−2), 4 × (−2) is −8 as a negative multiplied by a positive results in a negative answer. \[= -8\] Example 5: worded problemThe table below shows the temperatures recorded in Manchester at different times of the day. What is the product of the highest and lowest temperatures?
Multiply or divide numbers normally. The highest temperature was at 1pm of 2℃. The lowest temperature was at 2am of −6℃. \[2\times6 = 12\] Change the sign using the rules of multiplying and dividing negative numbers: \[2\times-6\] In this case we have a positive number multiplied by a negative number. The signs are the same so our answer has to be negative. \[= -12\] Common misconceptions
Multiplying and dividing negative numbers is part of our series of lessons to support revision on negative numbers. You may find it helpful to start with the main negative numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Practice multiplying and dividing negative numbers questions12 \times 6=72 The signs are the same therefore the answer is positive: 60 \div 12 = 5 The signs are different therefore the answer is negative: We must
remember to apply BIDMAS here. 7 \times 8=56 The calculation becomes
-2 – – 56 . \begin{aligned} -2 – – 56 &= – 2 + 56\\ &=54 \end{aligned}
(-3)^{4} means (-3) \times (-3) \times (-3) \times (-3) Starting from the left,
The calculation we need to do is 3 \times -8 The signs are different so the answer is negative. Multiplying and dividing negative numbers GCSE questionsThe table shows the temperature in different cities across Canada.
(a) Which city has the lowest temperature? (b) Find the product between the warmest and the coldest cities. (3 marks) Show answer a) Calgary (1) b) Identifying the warmest and coldest temperatures (Ottawa and Calgary). (1) Correctly multiplying 2 and −12 to give −24 (1) 2. Mary has the following 6 cards:
She is going to choose 2 cards and multiply them. (a) What is the largest possible number she can make? (b) What is the smallest possible number she can make? (4 marks) Show answer a) For identifying −9 or −8. (1) Correctly multiplying −9 and −8 or 72 seen. (1) b) For identifying −9 or 7. (1) Correctly multiplying two numbers or −63 seen. (1) 3. The temperature in London was −6℃ on Wednesday. On the same day the temperature at the north pole was 4 times as cold as
it was in London. (2 marks) Show answer (−6) x 4 seen. (1) −24℃ (must have negative and celsius sign). (1) Learning checklistYou have now learned how to:
Still stuck?Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths revision programme. How do you multiply negative and positive integers?There are two simple rules to remember: When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive.
What are the 4 rules for multiplying and dividing integers?What are the Four Rules for Multiplying Integers?. Rule 1: Positive × Positive = Positive.. Rule 2: Positive × Negative = Negative.. Rule 3: Negative × Positive = Negative.. Rule 4: Negative × Negative = Positive.. |