TOPIC 2: ADDITION AND SUBTRACTION OF WHOLE NUMBERS – MATHEMATICS STANDARD THREE NOTES
Adding whole numbers without regrouping A) Adding whole numbers horizontally
Example 1.
3246 + 2312 =
Solution
Align the numbers according to the place value of each digit
Add the digits from right to left
STEPS
1. Add the ones and write the answer in the ones place
2. Add the tens and write the answer in the tens place
3. Add the hundreds and write the hundreds in the one place
4. Add the thousands and write the answer in the thousands place
Therefore, 3246 + 2312 = 5558
Example 2.
68942 + 30051 =
Solution
Add the digits from right to left
Steps
1. Add the ones 2 + 1 = 3, write 3 in the ones place
2. Add the tens 4 + 5 = 9, write 9 in the tens place
3. Add the hundreds 9 + 0 = 9, write 9 in the hundreds place
4. Add the thousands 8 + 0 = 8 write 8 in the hundreds place
5. Add the ten thousands 6 + 3 = 9, write 9 in the 9 ten thousand place
Therefore, 68942 + 30051 = 98993
Example 3.
352411 + 136587 =
Steps
1. Add the ones and write the answer in the ones place
2. Add the tens and write the answer in the tens place
3. Add the hundreds and write the hundreds in the one place
4. Add the thousands and write the answer in the thousands place
5. Add the ten thousands and write the answer in the ten thousand place
6. Add the hundred thousands and write the answer in the hundred thousand place
Therefore 352411 + 136587 = 488998
Exercise 1.
Adding whole numbers vertically
Example 1
Solution
Align the numbers vertically according to their place value This can be done as follows:
Steps
1. Add the ones 8 + 1 = 9, write 9 in the ones place
2. Add the tens 1 + 1 = 2, write 2 in the tens place
3. Add the hundreds 1 + 2 = 3, write 3 in the hundreds place
4. Add the thousands 6 + 1 = 7 write 7 in the hundreds place
Therefore, the answer is 7329
Example 1
Steps
1. Add the ones 8 + 1 = 9, write 9 in the ones place
2. Add the tens 4 + 3 = 7, write 7 in the tens place
3. Add the hundreds 2 + 2 = 4, write 4 in the hundreds place
4. Add the thousands 5 + 0 = 5 write 5 in the hundreds place
5. Add the ten thousands 4 + 2 = 6 write 6 in the hundreds place
Therefore, the answer is 97456
Example 3.
Solution
Align the numbers vertically according to their place value as follows
Therefore, the answer is 693995.
Example 4
Solution
Exercise
ADDITION OF WHOLE NUMBERS BY REGROUPING
Adding whole numbers horizontally
Example 1
6327 + 3496 =
Solution
Add the digits from left to right
Steps
1. Add the ones. 7 + 6 = 13. Write three in the ones place. Regroup 10 ones into 1 tens and shift it to the tens place
2. Add the tens 1 + 2 + 9 = 12. Write 2 into the tens place. Regroup 10 tens into 1 hundreds place and shift it to the hundreds place
3. Add the hundreds. 1 + 3 + 4 = 8. Write 8 into hundreds place
4. Add the thousands 6 + 3 = 9. Write 9 into thousands place
Therefore, 6327 + 3496 = 9823
Example 2
472395 + 134826 =
Solution
Therefore, 472395 + 134826 = 607221
Exercise 3
ADDING WHOLE NUMBERS VERTICALLY
Example 1
Solution
Align the given numbers vertically according to the place value if each digits Steps
Example 2
Steps
Therefore, the answer is 603085.
Exercise 4
WORLD PROBLEMS INVOLVING ADDITION OF WHOLE NUMBERS
Exercise 5
1. Two printing companies produced books for primary schools. If the first company produced 5,900 books and the second 3,600 books, how many books did the two companies produced in total?
2. A farmer sold 35,752 litres of milk in january. Also, he sold 27,888 litres in february. How many litres of milk were sold in the two months?
3. A farmer has 1,982 timber trees and 7,291 fruit trees. How many trees does the farmer have in total?
4. In a certain hospital, 4,681 malaria patients and 689 eye patients were treated. Hoe many patients were treated in total?
5. A farmer stored 25,677 kilograms of maize in the first season, she stored 21, 913 kilograms. How many kilograms of maize were stored by the farmer in the two seasons?
6. In a certain year, 9,436 cars were inspected in mtwara region, while in ruvuma region 10, 170 cars were inspected. How many cars were inspected in the two regions?
7. Kakali primary school has 2,588 desks, dadawa primary school has 8, 813 desks, while Rukuku primary school has 10,554. How many desks are there in all three primary school?
8. Juma harvested 5,630 mangoes from the first tree. He then harvested 480 mangoes from the second tree. How many mangoes did he harvested in total?
9. A bus baried two baskets of oranges. The first basket has 2,376 oranges and the second had 4,638 oranges. How many otanges did the bus carry?
10. In a certain region, 6, 523 pupils joined standard one in 2015. In 2016, 7,212 pupls joined standard one, and in 2017, a total of 7,430 joined standard one. How many pupils joined standard one in the three years?
SUBTRACTION OF WHOLE NUMBERS
Subtraction of whole numbers without regrouping
1. Subtracting whole numbers vertically
Example 1
6874 – 2430 =
Steps
1. Subtract the ones: 4 – 0 = 4. Write 4 in the ones place.
2. Subtract the tens: 7 – 3 = 4. Write 4 in the tens place
3. Subtract the hundreds: 8 – 4 = 4. Write 4 in the hundreds place
4. Subtract the thousands: 6 – 2 = 4. Write 4 in the thousands place
6874 – 2430 = 4444
Example 2
46781 – 1041 =
Steps
1. Subtract the ones: 1 – 1 = 0. Write 0 in the ones place.
2. Subtract the tens: 8 – 4 = 4. Write 4 in the tens place
3. Subtract the hundreds: 7 – 0 = 7. Write 7 in the hundreds place
4. Subtract the thousands: 6 – 1 = 5. Write 5 in the thousands place
5. Subtract the ten thousands 4 – 0 = 4. write 4 in the ten thousands place
Therefore, 46781 – 1041 = 45740
Exercise 6
Subtracting whole numbers vertically
Example 1
Align the numbers according to their place value of each digit. This can be done as shown in the table.
Therefore, the answer is 1111
Example 2
Steps
1. Subtract the ones: 7 – 6 = 1. Write 4 in the ones place.
2. Subtract the tens: 9 – 2 = 7. Write 4 in the tens place
3. Subtract the hundreds: 5 – 3 = 2. Write 4 in the hundreds place
4. Subtract the thousands: 6 – 4 = 2. Write 4 in the thousands place
5. Subtract the ten thousand 8 – 5 = 3. Write 3 in the ten thousand place
Therefore, the answer is 32271.
Example 3.
Solution
Therefore, the answer is 352122
Exercise 7
SUBTRACTION OF WHOLE NUMBERS BY REGROUPING
a. Subtracting whole numbers horizontally
Example 1.
5371 – 3282 =
Steps
Therefore 5371 – 3282 = 2089.
Exercise 8
SUBTRACTING WHOLE NUMBERS VERTICALLY
Example 1
Steps
Example 2
Solution
Exercise 9
Word problems involving subtraction of whole numbers
Example 1
The total number of cattle and goats in a district is 2,139,500, the number of cattle is 1,104,563. How many goats are there in the district?
Solution
Total number of cattle and goats 2139500
Number of cattle 1104563
Number of goats
Therefore, there are 1, 034,937 goats in the district
Exercise 10.
1. Maria shop has 2,972 mobile phones and landlines, if there are 1,235 mobile phones, how many landlines are there?
2. A mango vender had four thousand three hundred and eighteen mangoes. He sold one thousand four hundred and thirty-five mangoes to a merchant. How many mangoes did he remained with?
3. A fisherman caught seven thousand three hundred and eighty-one fish. He sold five thousand deven hundred and ninety-two fish. How many fish did he remained with?
4. Remi bought two boxes containing six thousand four hundred and forty tomatoes. One thousand three hundred and two tomatoes were rotten. How many tomatoes were not rotten?
5. A school needs three thousand seven hundred forty-nine desks. Parents contributed two thousand mime hundred and ninety-seven desks. How many desks are still needed by the school?
6. The school bought seven thousand two hundred and fifty-two exercise books. Juma and Tatu were asked to carry the exercise books to the store. Juma carried three thousand and thirty-nine exercise books. How many exercise books were carried by Tatu?
7. Pupils planted three thousand four hundred and eighty trees in a certain year. After two years, five hundred and eighty-seven trees had dried up. How many trees remained healthy?
8. A cooperative union produced 287,891 bricks out of the required 482,674 bricks. How many bricks were not produced?
9. A contractor was paid 845,750 shillings for the construction of a school toilet. If the construction cost was 974,500 shillings, how much money was needed to complete her payments?
10. A certain ward has six thousand eight hundred and seventy-four voters. Three thousand and eighty-seven voters turned up to vote. How many voters did not turn up to vote?
11. A company was assigned to deliver two thousand eight hundred and seven iron sheets. The comp[any delivered two thousand three hundred and ninety-eight iron sheets. How many iron sheets were not derived?
12. Kulwa harvested five thousand and forty-seven bags of beans in the first year. He harvested three thousand four hundred and thirty-eight bags in the second year. Find the difference of the two harvests in the two years?
Revision exercise
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