Numbers in Grade IV

Hello friends, in today's session we are going to learn about the number sense – positive numbers and negative numbers. And of course we are going to do some addition and subtraction on these numbers. So let's start without wasting any time.

What is a number?

A Number is just a mathematical term used for counting and measuring. The definition of number has been long extended from so many years to include various new topics in it.

Mathematical operations are some steps that we follow which include one or more numbers (read this for more information) as input and give a number as an output. The most simple and basic operations that we perform are addition, subtraction, multiplication and division. Every number is either positive or negative, and has a sign in front of it. The sign before the number decides whether it is positive or not.

A positive number in general is a number greater than zero.

For Example – 1, 2, 3, 10, 100, 1000, 2.9, 3.14, 0.5 etc.

What we have studied in mathematics in our previous grades, we were considering the positive numbers.

A natural number which is not positive is negative. In a more proper way we can say that any real number which is less than zero is known as a negative number.

For Example – -1, -2, -3, -10, -100, -1000, -2.9, -3.14, - 0.5 etc. In general it is used to represent the absence or loss of something. The Negative number is written with a minus sign “-” in front of it.

To understand it more properly we can use a number line.

like in this number you can see that at the center we have a zero and the same numbers on both sides of it, but with different signs. The numbers which are right to the number line without any sign are known as the positive numbers while the numbers to the left of the zero with minus sign are known as the negative numbers.

We should also know that the numbers which are farther to the right are greater than each of the number to its left and similarly the one farther to the left is smaller to the one from the right.

For positive numbers the number with with large magnitude is greater, but for the negative number the number higher in magnitude is less than the one lower in magnitude.

Like if we take example for positive number the number 8 is greater than 5, we represent it as 8 > 5.

For negative numbers minus 8 is considered less than minus 5, and we represent it as – 8 < - 5.

But when we take a positive and a negative number, we should remember that we do not take the magnitude into consideration, the positive number is always greater than the negative number.

Like if we take -8 and 5 into consideration, then 5 will be greater than – 8, for second example we take -5 and 8, then 8 will be greater than -5. and we represent these two situations as 5 > - 8 and 8 > - 5.

Now we have compared both the numbers, so we know which one is greater and which one is smaller. So we move forward to the absolute values of these numbers. The absolute value in general means how far the number is from zero on the number line. The absolute value of any number is always positive. Like in general if we have to see the absolute value of n, then we represent it by putting two vertical bars across it : |n|.

you will better understand it with the help of an example.

|6| = 6

|-0.004| = 0.004

|0| = 0

|3.44| = 3.44

|-3.44| = 3.44

|-10000.9| = 10000.9

So, now it would be very much clear what an absolute value is.

Now we are going to perform some simple arithmetic operations on positive numbers and negative numbers.

For Example -

2 + 5.7 = 7.7

4 + 8 = 12

14 + 32 = 46

80 -12 = 68

42 – 4 = 38.

This is what you have already learnt, so let's now move to the arithmetic operations on negative numbers. which is of more importance as this topic is new for you. Let's start with the addition process.

The addition of two positive numbers is similar to the addition of the two negative numbers like

-4 + -5 = -9

(-$420) + (-$200) = -$620

The concept is like when two profits are added together to make bigger profit same way two losses are added to together to represent the whole loss. While adding a positive number and a negative number we should take the problem like two positive quantities being subtracted.

For Example –

8 + (-3) = 8 – 3 = 5.

$420 + (-$200) = $220

So for understanding it practically we can say it as the loss being subtracted from the profit. In this case the profit was higher so our total was also a profit.

Now what if the loss is greater than the profit. Then our result will also be a loss.

For Example -

-8 + 3 = -5, as said above it is negative.

(-$420) + $200 = -$220

Now we move over to Subtraction

For Example -

5 – 8 = 5 + ( -8 ) = -3

In general we can say that subtraction of positive number is the same thing as the addition of two negative terms.

And

( -3 ) – 5 = ( -3 ) + ( -5 ) = -8

For subtracting a positive number, it could be considered as the addition of positive numbers.

3 - (-5) = 3 + 5 = 8

and (-5) - (-8) = (-5) + 8 = 3.

(-$420) - (-$200) = -$220

(-$200) - (-$420) = $220

Now you will be able to perform some basic operations on it.

So let's now move towards the another topic which is negation.

A negation in general is a referred to as a reverse of our positive number. If we take 3 as our given number then -3 will be its negation. What we you should keep in mind while negation is that the sum of the given number and its negation term is always equal to zero. In general algebra we write it as

x + -x = 0.

It has two properties -

1. the negation of 0 is always 0
2. the negation of any number will be its corresponding positive number.

Let's move to the reciprocal of negative numbers.

Reciprocal of a positive or negative number is obtained by switching the numerator and denominator, but the sign of the new fraction that is formed always remains same.

For Example -

What is the reciprocal of -2/7?

We just switch the numerator and denominator, and keep the same sign then our answer is -7/2.

Now after solving them you will be very much capable of doing the math word problem help.

1. Steve has taken $27 from his pocket from the total of $100 which he was having, so now what is left with him?

Total is $100, from which he has taken $27, so now the left money is $100 - $27 = $73.

2. Find the difference in height between the top of a hill 973 feet high and a crack caused by an earthquake 79 feet from the ground.

The total height is 973 feet, from which we have reduced the 79, so now it becomes 973 – 79 = 894.

3. The given data shows the temperature of a city for 5 different days, find the lowest temperature.

-12°, -8°, -3°, 6°, -15° among these.

The lowest among the following is -15°.

4. Solve y = 5 - (3.750 - 0.500) - 2.375 ?

by doing simple subtraction we get y = 4.125.

5. In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

So the temperature now will be (-14) + (-7) = -21. so the temperature would be -21°F.

6. In the Sahara Desert one day it was 136°F. In the Gobi Desert a temperature of -50°F was recorded. What is the difference between these two temperatures?

The temperature would be 136 - (-50) = 186, which is the answer.

7. John has $36.00 to spend. He bought a CD player for $26.75. How much money does John have left?

The left money would be $36.00 - $26.75 = $ 3.25.

8. Mary overspent this month and her bank account has a negative balance of $27.00. The bank charged her $25.00 for overspending. What is the new balance in her account?

She already has a balance of - $27, with this the bank reduced it by -$25, so the remaining balance would be (-27) + (-25) = -52.

Now I can say that you would be able to understand what Numbers are and how to perform some simple operations on Negative Numbers and Positive Numbers.

In upcoming posts we will discuss about Fractions and Decimals in Grade IV and Tools to record observations. Visit our website for information on CBSE board fashion studies syllabus for class 11