Number Using Column Addition and Subtraction for Whole
Number Using Column Addition and Subtraction for Whole Numbers
Learning Objective Success Criteria
Starter See how many of these you can get right in the set time. Your teacher will tell you how long you have: 1+7= 8 19 – 8 = 11 3 + 15 = 18 17 – 8 = 9 12 + 5 = 17 14 – 8 = 6 14 + 5 = 19 10 – 3 = 7 2+4= 6 7– 3= 4 9 + 5 = 14 19 – 10 = 9 7 + 5 = 12 1– 0= 1 2 + 9 = 11 18 – 9 = 9 9 + 7 = 16 11 – 8 = 3 15 + 5 = 20 14 – 8 = 6 12 + 7 = 19 10 – 4 = 6 12 + 3 = 15 13 – 3 = 10 16 + 4 = 20 17 – 3 = 14 9 + 9 = 18 19 – 18 = 1 1+6= 7 20 – 5 = 15 18 + 2 = 20 19 – 9 = 10
Column Addition When we want to add two numbers together but cannot work out the answer mentally, we can do so using column addition. Suppose that we want to add 464 to 2335. We begin by writing the numbers one above the other (you’ll usually be told to write the larger number first, but it doesn’t really matter). It is important that units are lined up vertically, tens are lined up vertically and so on. This gives us: + 2 3 4 3 6 5 4 2 7 9 9 Beginning on the right-hand side in the units column, we add. 5 + 4 = 9 and the 9 is written underneath in the units column. 3+6=9 3+4=7 2+0=2 2335 + 464 = 2799
Column Addition Where Carrying Is Required Let’s try 4095 + 598; we set this out in the same way. Again, columns are lined up so that units are above units, tens are above tens and so on. + 4 0 5 9 9 5 8 4 6 9 3 1 1 Beginning on the right-hand side in the units column, we add. 5 + 8 = 13 Because 13 is a 2 -digit number, we need to carry the 1 over into the tens column, while keeping the 3 in the units column. When we add the numbers in the tens column, we must also add on the 1. 9 + 1 = 19 0+5+1=6 4+0=4 4095 + 598 = 4693
Now Try These Use column addition to answer the following: 352 + 2324 5408 + 5499 2 3 3 2 5 4 2 2 6 7 6 + 5 5 4 9 4 0 9 8 1 0 9 0 7 1 1 + 1
Column Subtraction We can use column subtraction when we cannot work out the answer, mentally. Suppose that we want to subtract 253 from 9857. Write the number you’re subtracting from above the number which is being subtracted. Again, it is important that the place values are lined up vertically. This gives us: - 9 8 2 5 5 7 3 9 6 0 4 Beginning with the units column, we subtract. 7 – 3 = 4 and the 4 appears underneath in the units column. 5– 5=0 8– 2=6 9– 0=9 9857 – 253 = 9604
Column Subtraction Where Borrowing is Required When subtracting, if a smaller number in a column is over a bigger number, we must use borrowing. Only the digits on the top row can borrow and lend. As always, write the numbers with the place values lined up vertically. Let’s have a go with 59 834 – 3957. This gives us: 8 7 2 - 5 5 9 3 5 1 8 9 8 1 3 5 14 7 7 7 Begin in the units column. Because 7 is larger than 4, we’re not going to take 7 from 4. Instead, we borrow from the 3 in the tens column; it becomes a 2 and the 4 becomes 14. 14 – 7 = 7 We don’t subtract 5 from 2 because 5 is bigger than 2. Instead, we borrow from the 8, which becomes a 7 and so the 2 becomes a 12. 12 – 5 = 7 We don’t do 7 – 9 so must borrow from the 9 which becomes an 8, making the 7 into a 17. 17 – 9 = 8 8– 3=5 5– 0=5 59 834 – 3957 = 55 877
Column Subtraction Where Borrowing is Required Sometimes, when borrowing is required, the number which we are trying to borrow from is a zero. Here is what happens then: 0 9 9 1 10 10 11 - 4 7 5 5 2 6 The zero 5 inisthe tensthan column now has aborrow left-hand can borrow Because larger 1, the 1 must fromneighbour the digit that in theit tens column; from. We cross out 10, isreplace it with 9 and put a 1 next to the can zeroonly in the tens from however, this the digit a zero and hasanothing to lend. As digits borrow column, to make it a 10. the 1 cannot get a loan. their left-hand neighbours, Finally, the in the units hascolumn a neighbour can borrow from. Instead, the 1 zero in the tens can tryit to borrow from its left-hand neighbour. We cross out the 10, isreplace with anotherthe 9 and 1 next to thecolumn 1 in thecan units Unfortunately, this also a it zero. However, zeroput in athe hundreds column, from making it 11. borrow its left-hand neighbour, the 1 in the thousands column. 11 – 5 = 6 This 1 becomes a zero and a 1 is placed next to the zero in the hundreds column, 9 – 7 = 2 it a 10. making 9– 4=5 1001 – 475 = 526
Now Try These Use column subtraction to answer the following: 3968 – 234 5423 – 786 200 – 56 4 - 3 9 2 6 3 8 4 3 7 3 4 - 5 4 2 9 0 5 10 1 4 4 1 - 0 6 13 11 4 7 2 8 6 3 1 3 6 7
Activity Sheet Now work through the activity sheet.
Plenary Fill in the gaps in the following calculations: 4 4656 + 43 = 4699 56 + 43 = 6 86 2884 + 982 = 3866 48 5 – 322 = 4 5 4875 – 322 = 4553 28 4 + 982 = 45 – 6 7 = 2825 3452 – 627 = 2825
- Slides: 13