# JSS 1 FIRST TERM LESSON NOTE MATHEMATICS

GENERAL MATHEMATICS

Jss 1 SCHEMES OF WORK FOR ALPHA TERM

*WEEK 1**WHOLE NUMBER (COUNTING AND WRITING IN MILLIONS,& TRILLIONS)*

*WEEK 2**WHOLE NUMBER (CONTD.,)*

*WEEK 3**FRACTIONS (TYPES OF FRACTIONS)*

*WEEK 4**FRACTIONS (EQUIVALENTFRACTIONS AND PROBLEMS SOLVING)*

*WEEK 5**FRACTIONS (CONVERTION FROM PERCENTAGE TO DECIMAL VICE-VERSA*

*WEEK 6**FRACTIONS (ADDITION, SUBTRACTION)IRST *

*WEEK 7**REVIEW OF THE FIRST HALF TERM WORK AND PERIODIC TEST*

*WEEK 8**FRACTIONS (MULTIPLICATION AND DIVISION)*

*WEEK 9**L.C.M AND H.C.F (LOWEST AND HIGHEST COMMON FACTOR*

*WE EK 10**ESTIMATION*

*WEEK 11**REVISION OF THE FIRST TERM AND EXAMINATION*

*WEEK 12**EXAMINATION*

**WEEK 1 TOPIC: WHOLE NUMBERS (COUNTING IN M ILLINS, BILLINS AND TRILLIONS)**

*CONTENTS:*

The figures 0,1,2,3,4,5,6,7,8,9 are called digits or unit. Numbers 10, 11,12,13,14,…. 99 are called Tens, numbers 100,101,… 999 are called hundred. One thousand is written as 1 with 3 zeros.

LARGE NUMBERS

NAME VALUE

One thousand 1000

Ten thousand 10000

One hundred thousand 100000

One million 1000000

Ten million 10000000

One hundred million 100000000

One billion 1000000000

Ten billion 10000000000

One hundred billion 100000000000

One trillion 1000000000000

In our everyday life, we often come across large numbers such as 75800074890.

75 800 074 8 9 0

Billion million thousand hundred ten unit

** Example 1**: write this in figures: twenty five trillion, three hundred and five billion, six hundred and sixty nine million, one hundred thousand and forty one.

** Example 2**: ninety billion, three hundred and nine million, ninety one thousand seven hundred and six three.

**Solution**

- 25 000 000 000 000

305 000 000 000

669 000 000

1 000

41

*25 305 669 001 041*

- 19 000 000 000

309 000 000

91 000

763

**19 309 091 763**

**Order large numbers**

** Example 1**: arrange these numbers in order of size stating with the smallest: 28980579, 18967547, 2897871, 36497871, 36479568, 18898069, 36478967

** Note that** 🙁 This arrangement is also called ascending order. The reverse is known as descending order).

*NB: Always group large numbers in threes.*

**Solution**

18 898 069, 18 967 547, 28 978 951, 28 980 579, 36 478 967, 36 479 568, 36 497 871

**DO THESE**

**Write the following in words (a) 567256789, (b) 18000901234**

**Write in figures (a) three hundred and twenty – nine billion, five hundred and sixty two million, eight hundred and one thousand, four hundred and thirty three**

**(b) fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.**

**Arrange the following numbers in ascending order 1009085941, 1288890563, 102458001, 999999999, 10009002, 105879894167**

**Assignment **

**Page 23 exercise 3.1 No 2 page 25 exercise 3.3 No (a, b c)**

*WEEK 3AND 4* *FRACTIONS (TYPES OF FRACTIONS)*

*WEEK 3AND 4*

*FRACTIONS (TYPES OF FRACTIONS)*

CONTENT:

A Fraction is a portion or part of a whole. Imagine a whole as a complete object. For example, the pie below is a whole which can be cut into sectors (or slices) representing different fractions as follows:

** **

**Whole (1)** ** ** ** half (1/2)** ** three- quarters (3/4)**

*Types of fraction*

r: ½, ¼, ¾, 3/8 and 5/8 are called fraction. One number over another. Numerator is the term given to the number on the top part of a fraction. De nominator is the term given to the number at the bottom part of a fraction.*Common fractions or vulga*

34=numeratordenominator

**Decimal fractions**: are simply called decimals example 0.897, 7.864 etc.**Proper fraction**: the numerator is less than the denominator. e.g. 2/5, ¼,ect**An improper fraction**the numerator is greater than the denominator e.g 8/3, 12/5 etc.

*CHANGING AN IMPROPER FRACTION TO A MIXED NUMBER*

**EXAMPLE 1**: Change 15/4 to a mixed number.

**Solution**

154 = 12+34 = 124 + 34 = 3+34= 334

**Example 2**: change 237 to improper fraction.

**Solution**:

237 = 2+37 =147+37 = 14+37= 177

**EQUIVALENT FRACTIONS**

Fraction that have the same value are said to be equivalent. Example are ½, 2/4, 3/6, 4/8, 5/10, 6/12 etc.

Example 1: convert 2/9 into an equivalent fraction with the denominator 54

Solution:

2/9 = /54 (divide the second denominator by the first denominator to obtain the multiplier)

54/9 =6

Therefore use the 6 to multiply 2/9= 12/54

2/9 =12/54

Finding the missing part of these fractions: /10 =12/= = 20/50 = / 80

Solution

Step 1 Use 20/50 as your reference fraction because both its numerator and denominator are given. 20/50 = 2/5

10/5 (use the 5 of denominator to get your numerator of /10) =2

Therefore use 2 to multiple both 2/5 =4/10

Step 2 use the 2 to divide the numerator of 12/ to get 6 and use the 6 to multiply 2/5 = 12/30

Step 3: use 5 to divide the denominator of 80 to get 16

Therefore use 16 to multiply 2 / 5 = 32 /80

So 4/10 = 12/30 = 20/50 =32/80.

*DO THESE*

- Express each of the following fractions as a mixed numbers: (a) 9/5 (b) 15/2
- Express each of the following fractions as improper fraction: (a) 11/2

(b) 43/8

- Copy and complete each of the following: 3/5 = /15 (b) 4/7 = 12/y = y/35 = y/49 = 44/y where y =

*ASSIGNMENT: EXERCISE 5.1 NO. 1, 2 & 3; EXERCISE 5.2 NO 4a-j PAGE 36 & 38*

##### WEEK 5 FRACTIONS (CONVERTION FROM PERCENTAGE TO DECIMAL AND DECIMAL TO FRACTION)

CONTENT: To convert a fraction into a decimal, first rewrite the numerator as a decimal, then divide it by the denominator.

Example 1 (a) change 34 into a terminating decimal number (b) 58 to decimal fraction

Solution:

- Numerator 3 can be written I decimal number as 3.0 or 3.00 0r 3.000

34 = 0.75 I,e 4 divide 3, then add zero, 4 goes in 30 is ,it remain 2, add 0 to make it 20 and 4 in 20 gives 5

Therefore 34 = 0.75

- 8 divies 5,it becomes 0,then add zero to make it 50,it gives 6, it remains 2, add zero it becomes 20, 8 divides 20 is 2, it remains 4, add zero to gives 40, 8 in 40 is 5

Therefore 58 = 0.625.

CONVERTING DECIMALS TO FRACTIONS

To change a decimal into a fraction, count the digits after the decimal, then divide by the appropriate power of 10,i.e 10,100,1000.

Example : convert each of the following decimal numbers into a fraction in lowest term:

- 0.067 (b) 0.64

Solution

(a) 0.067 = 671000 (3 digits after the decimal point i.e divide by 1000)

(b) 0.64 = 64100 (as above information) divide through by 4 =1625

**CONVERTING PERCENTAGE TO FRACTIONS**

PERCENTAGE IS A SPECIAL TYPE OF FRACTION WITH 100 AS DENOMINATOR. THUS, TO CHANGE A PERCENTAGE TO A FRACTION, DIVIE BY 100.(%)

Example 1: express each of the following as a fraction in its simplest form:

- 30% (b) 45% (c)
**16**1/2 %

Solution

- 30% = 30/100 i.e the zeros cancel each other. the answer is 3/10
- 45% = 45/100 i.e 5 divide both it gives 9 / 20.
- 16 ½ = 39/200 i.e you change the mixed number to improper fraction and then multiply it by %.

*WEEK 6**OPERATIONS ON FRACTIONS *

**ADDITION AND SUBTRACTION**

Example 1: Find the value of the following (a) 49+59+79 (b) 58–38 (c) 1+47

Solution:

(a): 49+59+79 = 169 (since the denominator are the same we just add the numerator together)

(b): ) 58–38 = ) 28 (since the denominator are the same we just subtract the numerator from each other)

*Try question C yourself*

Example 2: simplify the following (a) 334+58+1712 (b) ) 2+425-535

Solution:

(a) 334+58+1712

(198 + 15 + 34)/24 = (find the L C m of the fraction then add the whole together, the L C M is 24)

= (247/24) = 10724 (convert the improper fraction to mixed numbers)

(b) 2+425-535

Solution:

2+4-5+25–35 (rearrange by separating the whole numbers from fractions)

5+2-35 = 45 (same denominator)

**MULTIPLICATION AND DIVISION OF FRACTION**

Example 1: Simplify the following (a) 4/5 * 2/3 (b) what is the product of 35/17, 2 5/6 and 4/8

- 3/5 ÷ 4/9 (d) 24/5 * 56/8 ÷ 51/9

Solution:

- 4/5 * 2/3 = 8/15( multiple the numerator and denominator together)
- (b) what is the product of 35/17, 2 5/6 and 4/8 = 56/17 * 17/6 *4/8

= 17 divides 17, 6 divides 56 also 4 divides 8

= 14/3 = 42/3

- 24/5 * 56/8 ÷ 51/9= 14/5 * 46/8 * 9/46(change to improper and also change the division sign to multiplication and also change the fraction up and down)

= 14/5 * 46/8 * 9/46 (46 divides 46 etc)

= 63/20 = 33/20

**ASSIGNMENT**

**EXERCISE 5.9; NO 23, 24, 25, 33, 35, 36, 37 AND 40 PAGE 45**

**EXERCISE 5.12; NO 1, 2, 6, 7, 13 AND 14 PAGE 49**

JSS 3 FIRST TERM LESSON NOTE MATHEMATICS

*WEEK 9**L.C.M AND H.C.F (LOWEST AND HIGHEST COMMON FACTOR)*

**COMMON MULTIPLES AND FACTOR**

A prime number is a number that can only divide itself. it has two factor which is 1 and itself. Examples of prime numbers are: 2 ,3, 5, 7, 11, 13, 17, 19 etc.

**Multiples:** A multiple of a number is obtained by multiplying it by any whole number. Example the multiple of 4 are 4, 8, 12, 16, 20 , 24 etc.

**Factors:** The factor of a number is the whole number that divides the number exactly.

**Example 1: **(a) find all the factors of 18

(b) State which of these factors are even

( c) state which of these factors are prime numbers

(d) Write the first three multiple of 18

**Solution**

- Factors of 18 are 1, 2, 3, 6, 9, and 18
- The even numbers are 2, 6, and 18
- The prime numbers are 2 and 3

**Example 2:** Find the factor pairs of 56

**Solution: **

1 × 56

2 × 28

4 × 14

7 × 8

**Therefore the factors of 56 are; **1, 2, 4, 7, 8, 14, 28, and 56.

**Product of a Prime Factor**

A prime factor is a factor that is also a prime number. You can find the product of prime factors of a number using a prime factor tree method or using the method of dividing repeatedly by the prime numbers.

**Example 2:** Express the following numbers, 56 and 108, as products of prime factors in index form.

**Solution:**

Method 1: dividing repeatedly by using prime numbers

2 56 2 108

2 28 2 54

2 14 3 27

7 7 3 9

1 Index form = 23 x 7 3 3

1 index form = 22 x 32

Method 2: Factor tree

56 108

2 28 2 54

2 14 2 27

2 7 3 9

3 3

*Note that the numbers must be a prime numbers*

**EXAMPLE 1:** Find the L C M of 18 and 24

**Solution:**

**METHOD 1** **METHOD 2**

**2** **18** **24** **18 = 2 ×3 ×3**

**2** **9** **12** **24 = 2 ×2 ×2 ×3**

**2** **9** **6** **L C M = 2 ×2 ×2 ×3 ×3 **

**3** **9** **3** **= 72**

**3** **3** **1**

**1** **1**

**L C M = 2 × 2 × 2 × 3 × 3 = 72**

Example 2: Find the L C M of 72 and 90

**Solution:**

**METHOD 1** **METHOD 2**

2 72 90 72 = 2 X 2X 2 X 3 X 3

2 36 45 90 = 2X 3 X3 X 5

2 18 45 L C M = 2 X 2 X 2 X 3 X 3 X 5

3 9 45 = 360

3 3 15

5 1 5

1 1

2 x 2 x 2 x3 x 3 x 5 = 360

Example 3: Find the H C F of 72 and 96

Solution: find the prime product of the number and pick the common ones

**72 = 2 ***** 2 ***** 2 ***** 3 ***** 3**

**96 = 2 ***** 2 ***** 2 ***** 2 ***** 2 ***** 3**

**H C F = 2 ***** 2 ***** 2 ***** 3 = 24**

*DO THESE: *

*EXERCISE 4.2; NO 8, 10, 11, 12 AND 18. PAGE 29 *

*EX 4.5; N0 2 (K L M). PAGE 32*

* *

*WEEK 10**ESTIMATION*

Estimation may be explained as a rough or sensible guess fo a value or calculation. Although, the estimated value is not correct, it gives us an idea of what the correct answer should be.

The common units of length are kilometer (km), meters (m), centimeters (cm), millimeters (mm).Mass = (Tonne, kilogram (kg) gramme (g). Capacity = (litre (l), centiliter (cl), militre(ml)

It is important to be able to choose the most appropriate metric units of measurement to use.

Example: To measure distance less than a metre, smaller units such as milimetre (mm), and centimeter are used to measure large distance, metre and kilometer (km) are used.

State the metric units of the length you would use to measure the following:

(a). Length of your class room = metre (m0

(b). Length of your fingers nail = milimetre (mm)

(c). your height = centimeter (cm)

(d) Distance between Lagos and kaduna = kilimetre (km)

(e). the height of a building = metre (m)

*SIGNIFICANT: TO ROUNDOFF A NUMBER CHANGE 0,1,2,3,4 TO 0 WHILE 5,6,7,8,9 TO 1 AND ADD IT TO THE NEXT NUMBER*

Example 1: round off 492.763 to (a) 3 s.f (b) 3 s.f (c) 2 d.p (d) 4 d.p

Solution:

(a). 492.763 = 49 (since the third number is 2 it has change to zero)

(b). 492.763 = 493 (the 2 as change to 3 because 7 as change to 1 and been added to 2 to become 3)

(c).492.763 = 492.76 (in decimal point we count after the point).

(d). 492.763 = 492.7630(since the number is not upto 4d.p we add zero to it.)

*DO THESE*

*PAGE 86 EXERCISE 8.3 N0 1(G TO I) , N0 2 (G TO I)*