# Lesson Notes By Weeks and Term - Junior Secondary School 1

BASIC OPERATIONS

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 2nd TERM

REFERENCE BOOKS

• New General Mathematics, Junior Secondary Schools Book 1
• Essential Mathematics for Junior Secondary Schools Book 1

WEEK SEVEN

TOPIC: BASIC OPERATIONS

Content

• Addition and subtraction of positive(+ve)and negative(-ve)integers on the number line
• Solving problems on quantitative reasoning in basic operations

Addition and subtraction of Positive and Negative integers on the number line

Integers are positive and negative numbers including zero. Directed numbers are positive numbers greater than zero and negative numbers less than zero.

Number line: This is a picture that shows the arrangement of numbers according to their values, zero being the starting point.Numbers arranged to the left of zero are negatives (-ve)and decrease in value  while numbers to the  right of zero are positive(+ve)and increase in value.

Negative numbers decrease in value                                 Positive numbers increase in value

 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

The values of numbers increase from left to right.

Considering the number line, -12 is to the left of 0 while +12 is to right of 0. Therefore,-12 is less than +2

Inother words, +2 is greater than -12. Mathematically, symbol (<)and (>)are respectively used to denote “less than”and “greater than” respectively. It should be noted that the ADDITIVE INVERSE of a number add up with the number to zero. For instance, +1 is the additive inverse of -1,+2 is the additive inverse of -2, etc.

Example 1

Replace the sign between the following pairs of numbers with any of the signs(<)and(>).

(a)-18… +8  (b)-20… -50 (c)23… 15

Solution

(a)-18<8 (-18 is to the left of zero and 8 is to the right of zero)

(b)-20>-50

(c)23>15

Example 2

Arrange the following in ascending order (a)0,1,-2,-1,-9,-18,-5,2.

Solution

Arranging these numbers on a number line will make the number easier.

 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

Since the numbers increase from left to right on the number line,we have the answer thus:

-18,-9,-5,-2,-1.0.+1,+2

Example 3

Use the number line to find the values of the following.  (a)5+3 (b)-5+3(c)5-3(d)3-5 (e)-3-5 (f)-4-5+12

Solution

1. 5+3
 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from + 5, move three times in the positive ( +ve) direction. This gives 8.

1. – 5 + 3 = -2
 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from -5 , move 3 times in the positive direction and this gives 2

1. 5- 3 = 2

 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from 5 and move 3 times in the negative direction, this gives 2

1. 3 – 5 = -2
 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from 3 and move 5 times in the negative direction, this gives -2

1.  - 3 – 5 = - 8
 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from -3 and move 5 times in the negative direction, this gives – 8

1. – 4 -5 + 12 = 3
 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Method: Start from – 4 and move 5 times in the negative direction, then move 12 times in the positive direction, this gives 3.

Rules for addition and subtraction of positive and negative integers

1. If the same sign appear together, then replace them by a positive sign.

Also, (+8) – (-6) = + 8 +6 = +14

1. If different signs appear together, replace them by a negative (-ve) sign.

For instance, (+4) +(-7) = -3.

(Note, 7 cannot be subtracted from 4. So, subtract 4 from 7 and place the –ve sign of 7)

1. When there is a combination of positive and negative integers, the easiest way to simplify them is to add all positive together and also add all negative number together. For instance, 8-7+5-3+2 = 8+5+2-7-3 =5.

Evaluation

1. Simplify the following the number line: (a) ( +6) (-4) (b) (+6) + (-13) (c) -3 +7-10
2. A man can withdraw N 2500.00 more than what he has in his account as overdraft. If he takes this amount from his account instead of N 350.00 which he has in his account, what is the balance in his account?
3. What number must be subtracted from -7 to obtain 12.
4. Work out 15-7-5-6+6-10

Solving problems on quantitative reasoning in basic operation

1. What sign is attached to numbers which are to the left of zero on the number line?
2. In solving -3-7, which of the numbers will I start counting from and how many times will I move and to which direction?
3. When two numbers have different signs, what would you do to simplify them?
4. When two similar signs are together, they should be replaced by what sign?
5. When there is a combination of both positive and negative numbers, what method could be used to simplify them?

Essential Mathematics for JSS1 pages 112 – 120

NGM for West Africa JSS1 pages 72-79

General Evaluation

Work out the following:

1. (a) +3 + (-3)    (b) +10 + (-10)
2. Draw a suitable horizontal number line to help answer these questions
1. -4 -5+4
2. – 3 + 8- 5
1. Put the following numbers in order with the smallest first:
1. -12, 4, 0, -15, 0.5, -5, 10.
2. 14, -20, 42, -12, -8, 1, 5.

Weekend Assignment

1. Simplify ( +7) –(-3) (a)  7   (b)  3  (c) 4   (d) 10
2. Simplify -8- (-3) + (+5) + (-8)  (a) 8   (b)  16    (c) -8   (d)  -24
3. What is the additive inverse of -8? (a) +4  (b) + 2  (c) +8  (d) +7
4. Two students were seen entering an empty classroom by an observer. A few minutes later, three students were seen coming out. If one more student should enter the classroom again, how many students would be left in the class? (a) 0   (b) 1   (c)  2   (d)  3
5. Simplify ( +5) + (-7)-4.  (a) 2   (b) -2   (c) -6  (d) 8

Theory

1. Use the number line  to add the following: (a) -3+7   (b)  -4 -3   (c) – 5 + 8 – 2
2. Work out – ( +7) – (6) – (-8) + 6- (+5)