**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

- 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.

- – 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

- 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

- 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

- - 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

- – 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

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

Also, (+8) – (-6) = + 8 +6 = +14

- 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)

- 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**

- Simplify the following the number line: (a) ( +6) (-4) (b) (+6) + (-13) (c) -3 +7-10
- 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?
- What number must be subtracted from -7 to obtain 12.
- Work out 15-7-5-6+6-10

Solving problems on quantitative reasoning in basic operation

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

**Reading Assignment**

Essential Mathematics for JSS1 pages 112 – 120

NGM for West Africa JSS1 pages 72-79

**General Evaluation**

Work out the following:

- (a) +3 + (-3) (b) +10 + (-10)
- Draw a suitable horizontal number line to help answer these questions

- -4 -5+4
- – 3 + 8- 5

- Put the following numbers in order with the smallest first:

- -12, 4, 0, -15, 0.5, -5, 10.
- 14, -20, 42, -12, -8, 1, 5.

**Weekend Assignment**

- Simplify ( +7) –(-3) (a) 7 (b) 3 (c) 4 (d) 10
- Simplify -8- (-3) + (+5) + (-8) (a) 8 (b) 16 (c) -8 (d) -24
- What is the additive inverse of -8? (a) +4 (b) + 2 (c) +8 (d) +7
- 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
- Simplify ( +5) + (-7)-4. (a) 2 (b) -2 (c) -6 (d) 8

**Theory**

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

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