Subtraction

CBC Grade 5 Mathematics — Subtraction

Lesson Objectives

By the end of this topic, a learner should be able to:

• Subtract up to two 6-digit numbers without regrouping
• Subtract up to two 6-digit numbers with regrouping
• Estimate differences by rounding before subtracting
• Perform combined addition and subtraction in one problem
• Create number patterns involving subtraction

Subtraction

Subtracting takes one number away from another. It tells you how many are left. It also shows how much bigger one number is.

a) Setting it out

Write the bigger number on top and the smaller one underneath.

Line up the columns from the right. Ones under ones, tens under tens.

Draw a line and work from the right, one column at a time.

b) Subtracting without regrouping

Sometimes each digit on top is bigger than the one below it. Then just subtract each column and write the answer.

c) Subtracting with regrouping

Sometimes the top digit is too small. Then you borrow from the next column to the left.

One ten becomes ten ones. So a 3 in the ones column becomes 13.

The column you borrowed from goes down by one. Cross it out and write the new number above it, so you do not forget.

Forgetting to reduce the column you borrowed from is the commonest mistake here.

d) Borrowing across a zero

If the next column is a zero, you cannot borrow from it directly.

Go one more column left, borrow from there, and the zero becomes a nine.

Work slowly here. This is where most errors happen.

e) Checking by adding

Subtraction can always be checked with addition.

Add your answer to the number you took away. You should get back the number you started with.

Take 8 462 − 3 178 = 5 284. Now add 5 284 + 3 178. It gives 8 462, so the answer is right.

f) Estimating the difference

Round both numbers first, then subtract.

The estimate is 5 300 and the real answer is 5 284. They are close, so the answer looks sensible.

g) Adding and subtracting together

Some problems need both. Work from left to right, one step at a time.

Take 500 + 250 − 180. First add to get 750. Then subtract to get 570.

Do not try to do it all at once. One step at a time is faster in the end, because you make fewer mistakes.

h) Number patterns

A pattern can go down as well as up.

In 40, 34, 28, 22 the rule is "take away 6".

Find the gap between the numbers, then keep going. The next two are 16 and 10.

i) Where this is used

Working out change in a shop. Finding how much money is left. Comparing two scores. Working out how many are absent from a class.

:::checkpoint Check yourself

1. Work out 74 316 − 28 543.
2. Check your answer by adding.
3. Estimate 6 719 − 2 384 by rounding to the nearest hundred.
4. Give the next two numbers in 50, 44, 38, 32. :::

Definitions

• Minuend — the number being subtracted from.
• Subtrahend — the number being subtracted.
• Regrouping (borrowing) — taking a value of 10 from the column to the left when the current column's digit isn't big enough.
• Difference — the result of a subtraction.

Must Remember

1. Always subtract from the ones column first.
2. A borrow reduces the column you borrowed from by 1.
3. Borrowing can cascade across several columns in a row.
4. In combined operations, work strictly left to right.

Conclusion

Work column by column from the right, borrow whenever a column runs short, and use estimation to check the answer is reasonable.