Addition & Subtraction

Let's practice this column method with a real example. We'll solve a problem step by step. Our example is: two thousand four hundred fifteen plus one thousand three hundred sixty-two. Here as 2,415 + 1,362. The first step is to write the numbers in columns, aligning by place value. Make sure thousands line up, hundreds line up, tens line up, and ones line up. Step two: we add from the rightmost column to the left. Five plus two equals seven. Ones first, just like we practiced. Then tens: one plus six equals seven. Hundreds: four plus three equals seven. Thousands: two plus one equals three. Our final step is to write the answer from our calculations. Two thousand four hundred fifteen plus one thousand three hundred sixty-two equals three thousand seven hundred seventy-seven. Let's review the key points from this example. First, always align numbers by their place value. Second, always add from the rightmost column—the ones column—to the left. That's the method that guarantees we get the right answer every time.

Excellent, class. This will help us practice addition with regrouping on larger numbers. We are going to add one thousand, seven hundred sixty-eight and two thousand, five hundred ninety-seven. Out for you. Let's set it up neatly with our place value columns. Step one. We start from the ones column. What is eight ones plus seven ones? Fifteen ones is the same as one ten and five ones. We write down the five ones in the ones place, and we carry the one group of ten over to the tens column. Step two. We add the tens column. We have six tens, plus nine tens, plus the one ten we carried over. Six plus nine is fifteen, plus one more is sixteen tens. Sixteen tens is the same as one hundred and six tens. We write the six in the tens place and carry the one group of a hundred to the hundreds column. Our final answer is four thousand, three hundred sixty-five. Great work following each step!

Let's dive into our third worked example. This time, we're going to tackle a more challenging subtraction: 4,052 minus 1,768. Let's break it down together, step by step. Here is our problem. We have 4,052 and we need to subtract 1,768 from it. Before we begin, let's check if this requires regrouping. At the ones column: we have 2 ones on top and 8 ones on the bottom. Can we subtract 2 minus 8? We need to borrow from the tens place. Since 2 minus 8 is not possible, we must borrow from the tens column. Wait, look at the tens column in our original number: we have 5 tens. That's enough to borrow from, right? Let's set up our problem neatly in vertical form. We'll write 4,052 on top and 1,768 below it, making sure each digit is correctly aligned in its place value column: thousands, hundreds, tens, and ones. Let's focus on the tens column. We have 5 tens. We borrow 1 ten from the 5 tens. What happens? The 5 tens become 4 tens. What do we do with the 1 ten we borrowed? We exchange it for 10 ones and add them to the ones place. Our 2 ones become... 12 ones! We can solve the ones column. We have 12 ones minus 8 ones. What is 12 minus 8? We write 4 in the ones column of our answer. Here is the calculation for the ones column: 12 minus 8 equals 4. Let's move to the tens column. Remember, after borrowing, our top number in the tens column is now 4. We need to subtract 6. Can we do 4 minus 6? What must we do? We need to borrow again, this time from the hundreds column. We look at the hundreds column. We have 0 hundreds. We cannot borrow from 0! We must go all the way to the thousands column. We borrow 1 thousand from the 4 thousands. The 4 thousands become 3 thousands. We exchange that 1 thousand for 10 hundreds and put them in the hundreds place. Our 0 hundreds become 10 hundreds. From these 10 hundreds, we can borrow 1 hundred for the tens place. This is the complete process of borrowing. After all the borrowing, we can finally subtract column by column. In the tens column, we borrowed 1 hundred, which is 10 tens, and added it to our 4 tens. We have 14 tens. We subtract 6 tens. 14 minus 6 is 8. Write 8 in the tens place. In the hundreds column, after lending to the tens, we have 9 hundreds left. Subtract 7 hundreds. 9 minus 7 is 2. Write 2 in the hundreds place. Finally, in the thousands column, we have 3 thousands left. Subtract 1 thousand. 3 minus 1 is 2. Write 2 in the thousands place. Here is our final answer: two thousand, two hundred and eighty-four. 4,052 minus 1,768 equals 2,284. Fantastic work, everyone! You've successfully solved a subtraction problem with multiple borrowings. Remember, the key is to work column by column, from right to left, and borrow whenever you need to.

Let's practice using addition in a real situation. This slide shows a word problem about a shopping list. John wants to buy a book. It costs KSh 1,250. He also needs a pen. The pen is KSh 350. Finally, he wants a bag. The bag is KSh 2,100. First, we read the problem carefully. Next, we identify what we are looking for. The problem asks: Find the TOTAL cost. We set up the addition: 1,250 plus 350 plus 2,100. We can solve this using column addition. It's helpful to write the numbers neatly in columns. We start by adding the units column, then the tens, then the hundreds. Remember to regroup if needed. The total cost is KSh 3,700. John needs to have this amount to buy all three items.