SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS
SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS
SUBJECT: MATHEMATICS
CLASS: BASIC FOUR / / PRIMARY 4
WEEKLY TOPICS
- multiplication of whole numbers by two digit numbers
- Square of numbers one or two-digit numbers
- Division of 2 digit or 3-digit by number up to 9 with or without a remainder
- Common multiples of numbers
- Factors of numbers: Highest Common Factor
- Estimation
- Money: Addition and subtraction of money
- Money: multiplication and division of money by a whole number
- Money: division of money by whole number
- Profit and loss
- Open sentences
WEEK ONE
MULTIPLICATION OF NUMBERS BY 2-DIGIT NUMBERS
Example 1 multiply 48 by 36
Method 1: column form method 2: Expanded form
36, x, 48, = 1728. Th H T U
3 6
x 4 8
_________________
2 8 8
+ 1 4 4
_______________________
1 7 2 8
_________________________
Please take note of the following steps Multiply the ones on the bottom …
Step 1. Put the ones in the ones place and regroup the tens x. 3 6 above the tens and units column place …
Step 2. Add the two numbers x. 3 tens 6. units and do likewise for 48 = 4 tens and 8 units
Step 3 Add the answers from the first calculation to the answer of the second calculation
Step 4 : Write out your final answer
Regroup
3 2 4
Step 2: Multiply the tens
+ 1 0 8 0 = 54 × 20 Regroup
1 4 0 4 = 54 × 26
EXERCISES 1: Multiply the following
- 53 x 50 11. 84 x 10
- 97 x 10 12. 96 x 40
- 67 x 50 13. 67 x 50
- 87 x 20 14. 64 x 30
- 57 x 40 15. 64 x 40
- 56 x 10 16. 95 x 20
- 86 x 20 17. 84 x 50
- 99 x 50 18. 75 x 10
- 89 x 30 19. 43 x 87
- 75 x 40 20. 69 x96
EXERCISE 2: multiply the following
- 89 x 46
- 45 x 37
- 56 x 17
- 88 x 32
- 36 x 35
- 78 x 18
- 76 x 26
- 29 x 27
- 79 x 49
- 75 x 46
Example
25 × 34 = (20 × 34) + (5 × 34)
= 680 + 170
= 850
Exercise 3
Copy and fill the boxes with the correct numerals.
1. 24 × 33 = ( 20 × 33) + ( × 33) = 2. 35 × 48 = ( × 48) + ( × 48) =
3. 47 × 18 = ( × 18) + ( × 18) = 4. 45 × 35 = (40 × 35) + (5 × 35) =
5. 41 × 25 = (40 × 25) + ( × 25) = 6. 29 × 49 = ( × 49) + ( × 49) =
7. 57 × 16 = ( × 16) + ( × 16) = 8. 61 × 25 = ( × 25) + ( × 25) =
9. (12 × 7) + (30 × 7) = 10. 7 × 82 = (7 × ) + (7 × 2)
11. (20 × 8) + (2 × 8) = 12. 8 × 82 = (8 × ) + (8 × 2) =
13. 20 × 42 = (20 × 40) + (20 × 2) = 14. 50 × 28 = (50 × 20) + (50 × ) =
WEEK TWO
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to
discover what squares and square roots mean
solve problems involving the calculation of squares of numbers.
SQUARES AND SQUARE ROOTS OF NUMBERS ( 1- digit and 2 – digit numbers)
Example: 1: find 2^{2} = 4 ^{2}
=( 2 x 2) + ( 4 x 4) = 4 + 16 = 20 |
Example 2: find 4^{2} – 2^{2}
= (4×4) – (2 x 2) = 16 – 4 = 12 |
Example 3: find 3^{2} + 3^{2}
= (3 x 3) + (3 x 3) = 9 + 9 = 18 |
Example 4: 10^{2} – 4^{2}
= (10 x 10) – (4 x 4) = 100 – 16 = 84 |
Exercise 1
Find the value of:
- 4^{2} + 6^{2}
- 5^{2} – 2^{2}
- 5^{2} + 7^{2}
- 10^{2} – 5^{2}
- 8^{2} + 10^{2}
- 8^{2} – 6^{2}
- 2^{2} x 5^{2}
- 3^{2} x 4^{2}
- 4^{2} x 3^{2}
- 5^{2} x 2^{2}
- 6^{2} x2^{2}
- 2^{2} x 3^{2} x 5^{2}
- 2^{2} x 3^{2} x 5^{2}
- 3^{2} x 2^{2} x 5^{2}
SQUARE OF 2-DIGIT NUMBER
The squares of two-digit numbers are (in short form) 102, 112, 122, 133, … 992.
To calculate the squares of two digit numbers we may use any of these methods.
a) Multiply the number by itself, i.e. using multiplication method.
b) Find the square from the square table.
c) Count the dots from the square pattern.
(This method may be too cumbersome at a later stage
Examples
Study the workings to find 142.
Solution: (Multiplication method)
14^{2}=14×14
(10+4)× (10+4)
10(10+4) + (10+4)
100+40+40+16
=196
Exercise
Solve each of the following:
1. 42 2. 92 3. 102 4. 122
5. 112
6. 152 7. 172 8. 162 9. 182 10. 202
Unit 2
WEEK THREE
DIVISION
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to
CONTENT
Division of 2-digit and 3-digit numbers by numbers up to 9 without remainder
Example 1: 78 ÷ 6 = 13
OR 6 x ___ = 78
Ans = 13
Example 2: 81 ÷ 3
81 ÷ 3 = 21
OR 21 x ___ = 81
Ans = 3
Exercise
A. Calculate and give the remainder.
1. 21 ÷ 9
2. 38 ÷ 4
3. 87 ÷ 4
4. 82 ÷ 6
5. 78 ÷ 7
6. 72 ÷ 7
7. 29 ÷ 9
8. 57 ÷ 7
9. 68 ÷ 8
10. 73 ÷ 6
11. 35 ÷ 3
12. 64 ÷ 6
13. 88 ÷ 9
14. 73 ÷ 4
15. 89 ÷ 2
16. 77 ÷ 4
17. 87 ÷ 9
18. 97 ÷ 8
19. 98 ÷ 6
20. 99 ÷ 5
B. Solve the following:
1. 39 nuts are shared among five children. Each child receives the same number of nuts:
a) How many nuts did each child receive? b) How many nuts remain?
2. Elijah shared out 65 among 8 pupils. Each pupil is given the same amount of money:
a) How much did each pupil receive? b) How much is remaining?
3. Joy bought a sack of sweet potatoes weighing 50 kg. He divided the potatoes into bags, so that each bag held 3 kg of potatoes.
a) How many complete bags of sweet potatoes did he get from his sack?
b) How many kg of sweet potato remains?
4. A box contains 87 notebooks. They are given out to 9 pupils equally.
a) How many notebooks did each pupil receive?
b) How many notebooks are remaining
Division of 3-digits numbers without remainder
Example
834 ÷ 3 means ‘how many threes are there in 834? To find 834 ÷ 3 start with the hundreds:
8 (hundreds) ÷ 3 = 2 (hundreds), remainder 2 (hundreds)
Take the remainder, 2 (hundreds), and add to the tens:
2 (hundreds) = 20 (tens); 20 (tens) + 3 (tens) = 23 (tens)
23 (tens) ÷ 3 = 7 (tens), remainder 2 (tens)
Take the remainder, 2 (tens) and add to the units:
2 (tens) = 20 (units); 20 (units) + 4 (units) = 24 units
24 (units) ÷ 3 = 8 units
” 834 ÷ 3 = 278
Solution
278
3 834
– 600 (2 hundreds × 3)
234
– 210 (7 tens × 3)
24
– 24 (8 units × 3)
Example
Calculate the following:
205 ÷ 5
Solution
2 (hundreds) ÷ 5 = 0 (hundred), remainder 2 (hundreds)
Take the remainder, 2 (hundreds) and add to the tens:
2 hundreds = 20 (tens); 20 (tens) + 0 (ten) = 20 (tens)
20 (tens) ÷ 5 = 4 (tens), remainder 0
5 (units) ÷ 5 = 1 unit, remainder 0
” 205 ÷ 5 = 41
Working
41
5 205
– 200 (4 tens × 5)
5
– 5 (1 unit × 5)
Exercise
A. Calculate the following.
1. 153 ÷ 3 2. 126 ÷ 6 3. 185 ÷ 5 4. 177 ÷ 3 5. 156 ÷ 6
6. 132 ÷ 4 7. 144 ÷ 4 8. 148 ÷ 4 9. 138 ÷ 6 10. 152 ÷ 4
11. 171 ÷ 9 12. 224 ÷ 4 13. 105 ÷ 7 14. 102 ÷ 3 15. 465 ÷ 5
16. 8 984 17. 5 555 18. 9 399 19. 9 981 20. 6 828
21. 7 777 22. 4 712 23. 2 516 24. 4 636 25. 8 888
B. Solve the following.
1. The money contributed by a group of 6 pupils for cake baking is 426. How much
did each pupil contributes?
2. Kelvin is paid 705 for a five day working week. How much is she paid for each day?
3. How many 8-litre kegs can be filled from a drum of water containing 928 litres?
4. A log of wood 522 metres long is sawn into pieces 9 m long. How many such pieces are there?
5. A book has 312 pages. How many days will it take to read
i) 8 pages a day? ii) 6 pages a day?
Exercise
- Divide 70 by 5
- Divide 78 by 6
- Divide 304 by 4
- Divide 981 by 9
- Divide 205 by 3
- Divide 420 by 9
- A box holds 30 tins. How many boxes can be filled with 810 tins?
- One packet contains 10 pencils. How many packets do 470 pencil fill?
- How many minutes are there in 720 seconds
- The product of three numbers is 540. The first number is 5 and the second number is 9. What is the third number?
WEEK FOUR
LEAST COMMON MULTIPLES (LCM)
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to
find the multiples of numbers
find common multiples of numbers
find the lowest common multiple by listing the multiples of numbers
find the lowest common multiple by calculation.
CONTENT
LEAST COMMON MULTIPLES (LCM)
Revision of multiples of numbers
Multiples of a number e.g. 4 are those numbers that 4 can divide without remainder.
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 etc. The first multiple of a number
is the number itself. Other multiples are obtained by repeated addition of the number.
Every number has unlimited number of multiples.
Example 1:
Find the least common multiples of 2 and 3
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
Thus the common multiples of 2 and three are 6, 12, 18 and 24
Examples
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 …
3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …
5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 …
We can use repeated addition or multiplication to find the multiples. Here the first five multiples of 6 and 7 are found by using addition. Multiples of 6 are 6, 6 +6, 6 + 6 + 6, 6 + 6 + 6 + 6, 6 + 6 + 6 + 6 + 6
= 6, 12, 18, 24, 30…
Multiples of 7 = 7, 7 +7, 7 + 7 + 7, 7 + 7 + 7 + 7, 7 + 7 + 7 + 7 + 7
= 7, 14, 21, 28, 35…
Here the first five multiples of 6 and 7 are found by using multiplication.
Multiples of 6 = 6 1 6 2 6 3 6 4 6 5
= 6, 12, 18, 24, 30
Multiples of 7 = 7 1 7 2 7 3 7 4 7 5
= 7, 14, 21, 28, 35 …
Here the sixth multiple of 3 and 8 are found by using multiplication.
6th multiple of 3 = 3 6 = 18
6th multiple of 8 = 8 6 = 56
Exercise
A. Write down the first ten multiples of
1. 9 2. 10 3. 12 4. 7 5. 14
B. Find the 5th multiple of
1. 4 2. 11 3. 6 4. 15 5. 20
C. Copy and complete the statements with the correct numerals.
1. 12 is a multiple of 4 and 2. 84 is a multiple of 7 and
3. 90 is a multip2le of 9 and 4. 108 is a multiple of 9 and
5. 45 is a multiple of and
Example
Here the first three common multiples of 3 and 4 have been found.
Solution
Multiples of:
3 are: 3 6 9 12 15 18 21 24 27 30 33 36…
4 are: 4 8 12 16 20 24 28 32 36 40…
The first three common multiples of 3 and 4 are: 12, 24, 36.
Exercise 1
Write down the first three common multiples of these series of numbers:
1. 6 and 9 2. 4 and 8 3. 2, 4 and 6 4. 8 and 16 5. 10 and 15
6. 7 and 14 7. 3, 6 and 9 8. 5 and 10 9. 4 and 12 10. 5 and 20
Exercise 2
Look at the following numbers in the box.
2 3 4 8 10 12 18 24 27 30 32 36
Which of these numbers are common multiples of:
1. 2 and 3 2. 3 and 4 3. 3 and 6 4. 4 and 8 5. 5 and 10
LCM of numbers from common multiples
EXAMPLES
1. The LCM of 4 and 6 has been found here.
Multiples of:
4 = 4 8 12 16 20 24 28 32 36…
6 = 6 12 18 24 30 36…
Common multiples of 4 and 6 are 12 24 36…
From 12, 24 and 36, the smallest or least of the common multiple is 12.
Therefore, LCM of 4 and 6 = 12
2 . The LCM of 8 and 12 has been found here.
8 = 8 16 24 32 40 48 56 …
12 = 12 24 36 48 60 …
Common multiple: 24 48…
From 24 and 48, the least of the common multiple is 24
LCM = 24
3. The LCM of 6 and 9 has been found here.
6 = 6 12 18 24 30 36…
9 = 9 18 27 36…
Common multiples are: 18 36…
From 18 and 36, the least of the common multiple is 18
LCM = 18
Exercise
Find the LCM of these pair of numbers by first finding their common multiples.
1. 3 and 4 2. 4 and 8 3. 3 and 5 4. 2 and 9 5. 4 and 6
6. 6 and 5 7. 2 and 3 8. 3 and 8 9. 4 and 5 10. 6 and 9
11. What is the least weight of garri that can be weighed into 3 kg or 5 kg bags without any remainder?
12. What is the smallest length of a string that can be cut into pieces of 2 cm or 9 cm without any remainder?
The smallest of these multiples (i.e. the least) is 6
We say that the least common multiples of 2 and 3 is 6.
That is L.C.M of 2 and 3 is 6
LCM of numbers by calculation (Using Prime Number
Division Method)
What is a prime number? A prime number is a number that has two factors, one and
itself. In other words any number that can be divided by only one and itself is a prime
number.
Prime numbers are: 2 3 5 7 11 13 17 19 …
We will discuss this in detail when we come to factors. Note that 1 is a factor of every
number but not a prime number.
Finding LCM by calculation
Method 1: Prime number division (by prime factors)
Divide the given numbers by prime numbers. If the prime number can divide only one
number, start until the numbers are completely divided without remainder. The LCM is the
product of the prime numbers.
50
Examples
Study how the LCM of the following numbers has been found.
1. 8 and 12 = 2 8, 12
2 4, 6
2 2, 3
3 1, 3
1, 1
LCM = 2 2 2 3
= 24
2. 6, 8 and 16 = 2 6, 8, 16
2 3, 4, 8
2 3, 2, 4
2 3, 1, 2
3 3, 1, 1
1, 1, 1
LCM = 2 2 2 2 3
= 48
Exercise 1
Find the LCM of:
1. 12 and 18 2. 10 and 12 3. 12 and 24 4. 6, 8 and 12 5. 12, 18, and 24
6. 6, 8 and 10 7. 4, 6 and 8 8. 9 and 27 9. 3, 4 and 9 10. 8, 10 and 12
Method 2
Examples
Study how the LCM of the following numbers has been found.
1. 8 and 12
8 = 2 8
2 4
2 2
1
12 = 2 12
2 6
3 3
1
8 = 2 ×2 ×2
12 = 2 ×2 ×3
LCM = 2 ×2 ×2 ×3
= 24
Pick all the prime factors of the first and the second numbers. Find the product.
2 . 8, 9 and 15
8 = 2 ×2 ×2
9 = 3 ×3
15 = 3 ×5
LCM = 2 ×2× 2× 3×3 ×5
= 360
51
Exercise 2
Find the LCM of:
1. 10 and 20 2. 5 and 15 3. 14 and 21 4. 8 and 9 5. 8 and 9
6. 14, 21 and 28 7. 24 and 30 8. 12, 16 and 24 9. 15, 20 and 30 10. 9, 15
EXERCISE
Find the by listing the multiples of:
- 2 and 5
- 3 and 4
- 3 and 5
- 4, 2 and 6
- 2 and 7
- 2 and 12
- 3 and 7
- 3 and 12
- 2, 3 and 5
- 2 and 10
- 2, 4 and 6
- 3 and 15
- 4 and 7
- 4 and 7
WEEK FIVE
HIGHEST COMMON FACTOR (HCF)
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to
find the factors of numbers
identify prime numbers
Work out the common factors and highest common factors of numbers
CONTENT
HIGHEST COMMON FACTOR (HCF)
REVISION OF FACTORS OF NUMBERS
Factors are just the numbers that divide into another number exactly without a remainder.
Examples
Factors of 6
To find the factors, begin multiplying two numbers starting with 1.
1 × 6 = 6 nothing else can be multiplied
2 × 3 = 6 to give 6.
$ Factors of 6 are 1, 2, 3, 6
6 can be divided by all the factors exactly without a remainder.
Factors of 12
1 × 12 = 12 2 × 6 = 12 3 × 4 = 12
No other numbers can be multiplied to give you 12. So the factors of 12 are 1, 2, 3, 4, 6, 12.
So 12 can be divided by all the factors exactly without a remainder.
Exercise 1
Write down all the factors of these numbers using the examples to guide you.
1. 9 2. 10 3. 12 4. 16 5. 18 6. 20
7. 56 8. 63 9. 70 10. 32 11. 60 12. 96
Common factors of numbers
Study the example carefully.
The factors of 12 are: 1 , 2 , 3 , 4, 6 and 12
The factors of 18 are: 1 , 2 , 3 , 6 , 9 and 18
The common factors are 1, 2, 3, 6 because these factors are
factors of both numbers as you can see.
Exercise
1. Find all the common factors of both numbers.
a) 25 and 30 b) 18 and 27 c) 12 and 24 d) 9 and 27
2. Copy and complete this table in your notebook.
Numbers Common factors
a) 6 and 21
b) 14 and 21
c) 8 and 20
d) 10 and 25
e) 10 and 30
3. Find the common factors of these numbers.
a) 12 and 15 b) 15 and 25 c) 14 and 28 d) 6, 8 and 10 e) 28, 24 and 30
f) 12 and 28 g) 18, 24 and 42 h) 56, 80, 72 i) 4, 8 and 12 j) 8, 16 and 24
54
Unit 3
HCF of numbers from common factors
Examples
1. Study the examples to find the HCF of 12 and 16.
12 = 1 × 12 16 = 1 × 16
2 × 6 2 × 8
3 × 4 4 × 4
Factors are 1 , 2 , 3, 4 , 6, 12 Factors are 1 , 2 , 4 , 8, 16
Common factors = 1, 2, 4
Highest Common Factor is 4 because it is the highest factor among the common factors.
We write HCF = 4
2. Study the examples to find the HCF of 16 and 24.
16 = 1 × 16 24 = 1 × 24
2 × 8 2 × 12
4 × 4 3 × 8
4 × 6
Factors are 1 , 2 , 4 , 8 , 16 Factors are 1 , 2 , 3, 4 , 6, 8
The common factors of these numbers 16 and 24 are 1, 2, 4, 8
The Highest Common Factor (HCF) for 16 and 24 is 8
We write HCF = 8
Exercise
1. Using the above method find the HCF of each pair of numbers.
a) 8 and 10 b) 12 and 20 c) 25 and 35 d) 20 and 50 e) 18 and 36
f) 60 and 100 g) 18 and 20 h) 25 and 50 i) 27 and 63 j) 20 and 100
2. Find the highest common factors of these pairs of numbers.
a) 9 and 12 b) 5 and 15 c) 12 and 15 d) 12 and 16 e) 16 and 20
f) 10 and 12 g) 16 and 18 h) 5, 10, and 15 i) 4, 5 and 30 j) 18, 21 and 27
The product of 2 and 3 is; 2 x 3 = 6
2 and 3 are factors of 6
The factors of a number are numbers that divide the number without a remainder
EXAMPLE
Find the common factors of 24 and 36
24 = 1 x 24 36 = 1 x 36
= 2 x 12 = 2 x 18
= 3 x 8 = 3 x 12
= 4 x 6 = 4 x 9
= 6 x 6
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors of 24 and 36 are: 1, 2, 3, 4, 6, 12
The highest common factor is 12.
EXERCISE
Find the HCF of:
- 6 and 9
- 6 and 27
- 21 and 14
- 12 and 18
- 6 and 21
- 6 and 15
- 24 and 60
- 18 and 30
- 14 and 16
- 6 and 10
WEEK SIX
ESTIMATION
Rounding off decimals to the nearest whole number
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to
round whole numbers to the nearest 10, 100
Round decimals to the nearest whole numbers
estimate the sums and differences of whole numbers and decimals
estimate the product of two numbers
solve word problems involving estimation
CONTENT
ESTIMATION
Rules for rounding off decimals to the nearest whole number
When the rounding off decimals to the nearest whole number, look at the digit in the tenths place.
- If this digit is 5 or greater than 5, replace the digits after the decimal point by zero and add 1 to the digit in the units place
- If this digit is less than 5, replace the digits after the decimal point by zero.
Note: ‘≈’ means ‘is approximately equal to’
ROUNDING WHOLE NUMBERS
Consider these numbers:
10 20 30 40 50 60 70 80 90
Each of these numbers are multiples of 10 and each number has zero in its unit place. These numbers (i.e. multiples of 10) are round numbers.
Consider these numbers:
11 12 13 14 15 16 17 18 19 21 24 25 etc
These numbers are called non-rounded because the digits in the unit place is greater than zero.
Non-rounded numbers can be replaced by the nearest multiples of 10, 100. This is called rounding.
We can use the number line to round numbers to the nearest 10 and 100. We can also round without using the number line.
Rounding to the nearest 10
Examples
Round to the nearest 10.
1. 46 2. 22
Rounding decimals to nearest whole numbers
Decimals can also be rounded to the nearest whole numbers with and without using a number line.
Examples
Example: round off the following decimal numbers to the nearest whole numbers.
6.7 ≈ 7 to the nearest whole number
6.3 ≈ 6 to the nearest whole number
17 ≈20 to the nearest ten
EXERCISE 1.
Write to the nearest whole number
- 4.7
- 1.1
- 7.9
- 8.6
- 0.9
- 13.2
WEEK SEVEN
Money
Addition of money
BEHAVIOURAL Objectives: At the end of the lesson, pupils should be able to
Convert money from one unit to another
Shop and collect the correct change
Add money
Subtract money
Solve word problems involving money.
CONVERSION INVOLVING UNITS OF MONEY
Note
100 k = 1.00
When changing kobo to Naira we divide the given amount by 100.
Examples
1. 520k = 520/100 = 5.20k 2. 890k = 890/100 = 8.90k
= 5.20 = 8.90
Exercise 1
Convert the following to Naira.
1. 638k = 2. 750k = 3. 430k = 4. 970k = 5. 257k =
6. 1 008k = 7. 3 450k = 8. 1 520 = 9. 17 000k = 10. 28 640k =
Examples
When converting Naira to kobo, we multiply by 100.
1. 8.00 = 8 × 100 = 800k 2. 17.50 = 17.50 × 100 = 1750k
or 8.00 = 800k
Example: find the sum of N4.36, N3.79 and N4.82
N K
4. 36
+ 3. 7 9
+ 4. 8 2
12. 9 7
EXERCISES
Add up
- N56.00, N24.70 and N32.55
- N32.20, N174.30 and N132.30
- N91.00, N152.10 and N184.20
- N241.80, N378.35 and N29.46
- Fin the sum, of N168.00 and N276.00
- Find the sum of N128.10, N78.30 and N8.05
- I have N1000 in my pocket and my father gave me N174.20 more. How much do I have altogether?
Subtraction of money
Example 1
What is the difference between N167.50 and N345.00?
N K
345.00
-167. 50
177.50
EXERCISE 2
- Find the difference between N406.60 and N322.20
- Find the different between N270 and N162.30
- Subtract N236.44 from N475.00
- I have N150.00 and I bought a spoon for N85. How much is my change?
- How much more is N147.50 greater than N112.80
- How much more is N36.00 than N278.00
WEEK EIGHT
PROBLEM ON MULTIPLICATION OF MONEY
BEHAVIOURAL Objectives: At the end of the lesson, pupils should be able to
Find the costs of more than one commodity using a shopping centre
Multiply money by a whole number
CONTENT
PROBLEM ON MULTIPLICATION OF MONEY
EXAMPLE
Multiplication involving money
Examples
1. 65k × 8 = 520k 2. #11.24
= 5 Naira 20 kobo × 6
= #5.20 #67.44
Note: The naira sign has two digits to the right of the decimal point in these examples.
Exercise 1
Simplify these. Follow the examples.
1. 199k × 6 2. 186k × 8 3. 159k × 4 4. 167k × 7
5. 148k × 13 6. 137k × 21 7. 167k × 18 8. 154k × 19
9. # K 10# K 11.# K 12.# K
4 32 8 66 13 26 16 13
× 6 × 8 × 9 × 7
13. #12.62 × 8 14. #27.04 × 5 15. #31.78 × 6 16. #76.21 × 10
17. #17.83 × 6 18. #48.56 × 4 19. #29.37 × 7 20. #81.42 × 8
169
Exercise 2
Find the cost of these items.
1. 5 meters of white poplin at 320.00 per meter.
2. 20 kg of yam flour at 150.00 per kg.
3. Taxi fare for 16 people at 150.00 per person.
4. 9 school chairs at 300 Naira per chair.
5. 8 school uniforms at 955.00 per uniform.
A man earns 535.00 a day. How much does he earn in
6. 2 days 7. 6 days 8. 9 days 9. 10 days
A trader sells a packet of rulers for 625.00 each. How much money does he receive if he sells
10. 3 packets of rulers 11. 5 packets of rulers
12. 8 packets of rulers 13. 10 packets of rulers
Find the cost of 3 books at N91.55 each.
Solution
N91. 55
× 3
N274.65
EXERCISE
- N5.52 x 4
- N4.75 x 6
- N4.75 x 6
- N5.91 x 8
- N12.37 x 6
- A bag of salt costs N585.40. how much will I pay for 5 bags?
- What is the cost of 6 meters of while poplin at N212. 85 per meter?
- Find the cost of 7 chairs if one chair costs N423.50
WEEK 9
DIVISION OF MONEY
BEHAVIOURAL Objectives: At the end of the lesson, pupils should be able to
Divide money by a whole number.
CONTENT
DIVISION OF MONEY
Examples
1. #1.68 ÷ 7 =
#0.24
or 168/ 7 k =
24k
2. Divide 18.24 by 8
#2.28
8 #1 8.2 4
– 1 6/
2 2
– 1 6
6 4
6 4
0 0
Unit 3 Division involving money
Exercise 1
Follow the examples and work out the following problems.
1. 119 ÷ 7 2. 2 Naira 25 kobo ÷ 9 3. 16.50 ÷ 30
4. 38.40 ÷ 6 5. 42 ÷ 20 6. 1 610k ÷ 5
7. 29.04 ÷ 4 8 . 10 Naira 23 kobo ÷ 3 9. 17 Naira ÷ 10
10. 98 Naira 1 kobo ÷ 9 11. #11.76 ÷ 7 12. 84.32 ÷ 8
13. 52.32 ÷ 6 14. 73.25 ÷ 5 15. 90.16 ÷ 4
Find the cost of one item.
16. 10 lollipops cost 150.00 17. 8 eggs 240.00 18. 9 safety pins cost 27.63
19. 7 sports shorts cost 1 520.20 20. 20 cups of garri cost 650.00
21. Six children paid the same amount of money totaling 1 605.00 to travel on a bus. How much did each child contribute?
22. The cost of petrol for eight return journeys from village to a town is 2 000.00. What is the cost of petrol for one return journey?
Puzzle corner
A hen and 7 chickens cost 1 720.00. The same hen and 10 similar chickens cost 2 140.
Find the cost of:
23. 3 chickens 24. a hen and a chicken 25. 7 chickens
26. a hen 27. 10 chickens 28. a chicken
Mixed exercises on multiplication and division of money
Exercise 2
Copy and complete this table.
Money Multiply by Divide by
1. 185 kobo 6 7
2. 13 naira 5 kobo 8 5
3. 16.24 4 8
4. 25.40 20 10
5. 9 Naira 90 kobo 7 9
Find the cost of these.
6. 5 notebooks at 45.00 each 7. 20 litters of petrol at 97 per liter
8. 38 meals at 300.00 per meal
9. 8 pens at 250 each and 4 bottles of ink at 120 per bottle
10. 6 pairs of shorts 1 850 per pair of shorts and 5 shirts at 1 950.00 per shirt
Find the cost of one item.
11. 10 torch batteries at 125.00 12. 9 metres of chino material costs 1 774.80
13. 7 head ties cost 2 200.00 14. 6 pieces of plantain cost 420 Naira 50 kobo
15. 4 erasers cost 42.80
Two pencils cost 16.36 and three baskets cost 335.00.
16. Find the cost of 1 pencil. 17. What is the cost of 3 pencils?
18. What is the cost of 5 pencils? 19. What is the cost of 5 baskets?
20. Find the cost of 7 baskets. 21. What is the cost of 1 b
Example
Four children were given n624.40 to share equally. how mcuch will each of them. Get?
Solution
Note that N624.00 = 62400k
= N624.00 x 4
= N156.10
EXERCISES
- Divide N1.68 by 4
- Divide N2.25 by 9
- Divide N44.80 by 8
- Divide N11.76 by 7
- 610k by 5
- Five boys are to share N615.55 equally. How much will each receive?
WEEK TEN
PROFIT AND LOSS
BEHAVIOURAL Objectives: At the end of the lesson, pupils should be able to:
1. Discover the meaning of cost price and selling price
2. Find the profit of any given item sold
3. Find the loss of any given item sold.
CONTENT
Meaning of cost price and selling price
When you go to the market, you see some people buying and some are selling. A farmer produces rice, beans, vegetables etc to sell. The market woman buys from the farmer to resell. The price at which the market woman buys from the farmer is the cost price and the price at which the market woman sells in the market is the selling price.
Cost price = Price at which the article is bought (C.P)
Selling price = Price at which article is sold (S.P)
There is profit or gain when the selling price is more than the cost price.
There is loss when the cost price is more than the selling price.
Activity
Provide a few items that can be bought and sold in the market.
Group the pupils into those buying.
Group the pupils into those selling
Let them do buying and selling to discover the concept of gain and loss.
Copy and fill in the table to show the amount gain or loss
Item Cost Price Selling Price Gain Loss
1.
2.
3.
4.
5.
6.
Profit
Examples
1. Goods which cost # 560.50were sold for #784.30. Find the profit.
C.P = #560.00
S.P = #784.30
Profit = S.P – C.P
= #784.30
– 560.50
223.80
2. Bola bought five tubers of yams for #2 670.50 and sold it for #3 000.80. What
is the profit?
C.P = #2 670.50
S.P = #3 000.80
Profit = S.P – C.P
= #3 000.00
– 2 670.00
330.00
A man bought a leather bag for N350.00 and sold it for N360.00. Will he have more money or less money with him?
Solution
Selling price = N460.oo
Cost price = – N350.00
Profit(gain) = N110.00
Note: profit or gain = selling price – cost price
Exercise 1
Copy and complete the table.
Cost Price Selling Price Profit
1. 358.30 #420.80
2. 518.40 #602.50
3. 1750.48 50.02
4. 7623.14 8100.60
5. 6350.39 6948.40
6. 2150.70 2370.60
7. 5340.35 354.45
8. 960.50 990.30
9. 4330.75 4542.13
10. 8956.45 155.90
Exercise 2
Word problems on profit
1. A trader bought 30 eggs for 225. Two of the eggs were broken. She sold the rest of the eggs at 15.00 each. What was her profit?
2.A woman bought a bunch of 15 plantains for 840.00. She gave three to a friend and sold the rest at 80.00 each. How much did she gain?
3. A chicken was bought for 500.00. A profit of 105 was made when it was sold. What is the selling price?
4. A basketful of pawpaws was sold for 1 500.00 at a profit of 400.00. What was the cost price?
5. Margarine bought at 5 000.00 for 50 kg was sold at 120.00 per kg. What was the profit on the 50 kg?
6. I bought fifty kilograms of pineapples for 7 500. I sold them at 220.00 a kilogram. Find my profit.
7. Mr Ojo bought a bicycle for 9 080. He sold it at a profit of 1 080. How much was paid for the bicycle?
8. A woman bought two hundred eggs at two for 25. Five of them were broken. She sold the rest at three for 50. What was her gain?
9. A carpenter built a cupboard and sold it for 3 060. The materials cost him 1 286. He calculated the labor at 1 047.75. What was his profit?
10. A bookshop manager bought 200 books at 370 each. He sold half of them at 400.00 each, a quarter at 410.00 each and the rest at 430.00 each. What was his profit?
Loss
Examples
A loss is realized when the selling price is less than the cost
1. A trader bought goods for 2 500 and sold them for 2 000.
Find his loss
C.P = 2 500
S.P = 2 000
loss = C.P – S.P
= 2 500 – 2 000
= 2 500
– 2 000
500
2. If a lady bought a wrist watch for N800 and sold it for N600. Will he have money or less money with her?
Solution
The selling is price is less than. Therefore, she will have less money with her. That is, she sold at a loss.
Cost price of wrist watch = N800.00
Selling price = N600.00
Loss N200.00
3. A piece of cloth was bought for 10 200. It was sold out after a long time for 9 850. What was the loss?
C.P = 10 200
S.P = 9 850
loss = C.P – S.P
= 10 200
– 9 850
350
Exercise 1
Copy and complete the table.
Cost Price Selling Price Loss
1. 4050.60 3580.30
2. 2014.50 1976.10
3. 19403.40 443.60
4. 2780 2250
5. 1780.40 1630.50
6. 2356.80 2068.30
7. 1740 66.00
8. 1367.04 1256.80
9. 8740.70 7350.90
10. 1740.61 539.30
11. 7350.40 7000.30
Exercise 2
Word problems
1. A carpenter sold a dining table at 3 060. Materials cost him 1 286 and workmanship was 1 047.75. What was his profit?
2. Mr. Chukwu bought a bicycle for 8 000 and sold it at a loss of 800 to Mr Onu. How much did Mr. Onu pay?
3. By selling a measure of garri for 125.00, a trader gained 35.00. What was the cost price of the garri per measure?
4. A keg of 15-litre kerosene was bought by a trader at the petrol station for 855.00. She sold it as 60.00 per litre. What was her profit or loss?
5. 15 litters of groundnut oil was bought for 1 500. The family used 2 litters for cooking. The rest was sold at 125 per litre. Calculate the profit or loss.
6. A lady sold some provisions for 274.05 at a profit of 20.30. What is the cost price?
7. A trader bought electric torches at 2 880 per dozen. He sold them at 220 each. How much profit or loss did he make?
8. If I sell for 60 some goods which cost 53 each, calculate my profit on 1 article and on 27 articles.
9. Mallam Jimoh bought 100 kg of sugar for 1 600. He sold it at 15 per kg. Find the profit or loss.
WEEK 11
OPEN SENTENCE
BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:
identify the meaning of open sentences
review work done on addition and subtraction involving open sentences
review work done on multiplication and division involving open sentences
use letters in replacing empty box to solve simple equations
solve word problems involving simple equation
Meaning of open sentences
Closed and open sentences
Study the following mathematical statements:
13 + 6 = 19 23 + 12 = 35
42 − 20 = 22 63 − 49 = 14
7 × 5 = 35 11 × 12 = 132
40 ÷ 5 = 8 120 ÷ 10 = 12
The mathematical statements above are called closed number sentences.
Closed number sentences can either be true or false.
Examples
15 + 7 = 22 (True mathematical statement) 18 + 3 = 19 (False mathematical statement)
3 × 6 = 12 (False mathematical statement) 42 ÷ 6 = 7 (True mathematical statement)
Study each of the following mathematical statements:
{}+ 9 = 13 11 +{} = 25 {}− 4 = 11 20 –{} = 7
{}× 5 = 15 4 ×{} = 24 {} ÷ 6 = 5 48 ÷{} = 12
In each of the statement above, there is a missing number called unknown represented by
. They are called open sentences.
An open sentence is a mathematical statement that involves equality signs and a missing
quantity represented by that the four arithmetic operations of addition, subtraction,
multiplication and division can be applied to solve.
Open sentences can either be true or false depending on the value .
Exercise
A. Write True (T) or False (F) for each of the following closed number sentences.
1. 15 + 16 = 31 2. 54 + 4 = 68 3. 18 + 10 = 38 4. 51 + 47 = 98
5. 29 + 60 = 82 6. 42 + 54 = 84 7. 55 − 23 = 33 8. 54 − 11 = 43
9. 64 − 43 = 21 10. 98 − 45 = 53
B. Write True (T) or False (F) for each of the following open sentences if is replaced by 4.
1. + 2 = 9 2. + 3 = 7 3. + 7 = 12 4. − 3 = 1
5. 12 − = 7 6. 8 − = 4 7. 4 × = 16 8. × 2 = 10
9. ÷ 2 = 2
Unit 2 Operation of addition and subtraction involving open
sentences (Revision)
Examples
Here the number represented by in each of the following has been found.
1. + 14 = 36 2. 12 + = 8 3. − 4 = 30 4. 15 − = 9
Solution
1. + 14 = 36 can be interpreted as “what can be added to 14 to get 36?”
+ 14 = 20 + 16
+ 14 = 20 + 2 + 14
+ 14 = 22 + 14
= 22
Check:
22 + 14 = 36
Short method
If + 14 = 36
then = 36 − 14
= 22
$ = 22
Check:
22 + 14 = 36
Exercise
1. When 79 is added to a number, we get 124. Find the number.
2. When 71 is added to a number, we get 214. Find the number.
3. When I subtract 19 12 from a certain number, the result is 9 12 . What is the number?
4. When 31 kg of meat is removed from the part of the cow, there is 25 kg left. What is the weight of the cow?
5. A poultry farmer took four crates of eggs to the market. He had 45 eggs left after market hour. How many eggs were sold?
6. When 564 is added to a certain number, the result is 801. Find the number.
7. 6 times an unknown number gives 72. Find the number.
8. When a number is multiplied by 12, we get 108. Find the number.
9. I think of a number, divide it by 8 and get 32. Find the number.
10. A certain number of oranges was shared equally among 6 children. Each child received 14 oranges. How many oranges were shared?