Solution: Show Assume any one number to be a variable and form a linear equation by using the relationships between the two numbers mentioned in the problem statement. Let one of the numbers be x. Then the other number is 95 - x. If we assume x to be larger among two of them, ⇒ x - (95 - x) = 15 (as one exceeds the other by 15) ⇒ 2x = 15 + 95 ⇒ x = 110 / 2 = 55 The other number is (95 - x) which is 95 - 55 = 40 Thus, the two numbers are 40 and 55. ☛ Check: NCERT Solutions for Class 8 Maths Chapter 2 Video Solution: NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.2 Question 4 Summary: If the sum of two numbers is 95 and if one exceeds the other by 15, the numbers are 40 and 55. ☛ Related Questions: Math worksheets and
See also: Special Numbers and Concepts Standard numbers, anything greater than zero, are described as ‘positive’ numbers. We don’t put a plus sign (+) in front of them because we don’t need to since the general understanding is that numbers without a sign are positive. Numbers that are less than zero are known as 'negative' numbers. These have a minus sign (−) in front of them to indicate that they are less than zero (for example, -10 or 'minus 10'). Visualising Negative and Positive NumbersProbably the easiest way to visualise negative and positive numbers is using a number line, a tool with which you may well be familiar, especially if you have children at primary school. It looks something like this:
A number line can help you to visualise both positive and negative numbers and the operations (adding and subtracting) that you can do with them. When you have an addition or subtraction to calculate, you start at the first number and move the second number of places either to the right (for an addition) or left (for a subtraction). This number line is a simplified version, but you can draw them with every number included if you wish. The big advantage of a number line is that it is very easy to draw for yourself on the back of an envelope or a piece of scrap paper, and it is also quite hard to go wrong with the calculation. As long as you are careful to count the number of places that you are moving, you will reach the correct answer. Subtracting Negative NumbersIf you subtract a negative number, the two negatives combine to make a positive. −10−(−10) is not −20. Instead, you can think of it as turning one of the negative signs upright, to cross over the other, and make a plus. The sum would then be −10+10 = 0.
A Quick Note on Brackets For clarity, you would never write two negative signs side by side without brackets. So if you are asked to subtract a negative number, it will always have brackets around it so that you can see that the use of two negative signs was intentional. -10--10 is incorrect (and confusing) -10-(-10) is correct (and clearer) Multiplying and Dividing with Positive and Negative NumbersWhen multiplying or dividing with combinations of positive and negative numbers, you can simplify the process by first ignoring the signs (+/-) and just multiplying or dividing the numbers as if they were both positive. Once you have the numerical answer, then you can apply a very simple rule to determine the sign of the answer:
So: (positive number) × (positive number) = positive number (negative number) × (negative number) = positive number But: (positive number) × (negative number) = negative number As a side issue, this goes some way to explaining why you cannot have the square root of a negative number (there is more about this in our page on Special Numbers and Concepts). The square root is the number that is multiplied by itself to get the number. You cannot multiply a number by itself to get a negative number. To get a negative number, you need one negative and one positive number. The rule works the same way when you have more than two numbers to multiply or divide. An even number of negative numbers will give a positive answer. An odd number of negative numbers will give a negative answer.
Worked examples What is −5 × 25? 5 x 25 is 125. But here you have one negative and one positive number, so the sign of the answer will be negative. The answer is therefore −125. What is −40 ÷ 8? 40 ÷ 8 is 5. Again, you have one positive and one negative number, so the sign of the answer will be negative. The answer is −5. What is −50 ÷ −5? 50 ÷ 5 is 10. This time, you have two negative numbers, so the sign of the answer will be positive. The answer is 10. What is −100 × −2? 100 x 2 is 200. Again, you have two negative numbers, so the answer is positive. It is 200. What is 10 x −2 × 3? To begin with, consider the first part of the calculation. 10 x 2 = 20. You have one positive and one negative number, so the sign of the answer will be negative, making it −20. Now take the second part of the calculation: −20 × 3. So 20 × 3 = 60 but again, you have a negative and a positive number, so the answer will be negative: −60.
Why does multiplying two negatives give a positive answer? The fact that a negative number multiplied by another negative number produces a positive result can often confuse and seem counterintuitive. To explain why this is the case, think back to the number lines used earlier in this article since these help to explain this visually.
In both of these examples, you have moved forwards (i.e. the direction you were facing), a positive move.
ConclusionNegative signs can look a bit daunting, but the rules that govern their use are simple and straightforward. Keep these in mind, and you will have no problems. |