Egypt Primary 4 Mathematics, Week 4: Taking away across the zeros

Subtraction with regrouping and story problems

Week 4 · Subtraction with regrouping and story problems · 3 lessons

Taking away across the zeros

Discover Mathematics P4: Term 1, Unit 2, Lessons 5–7

GoalSubtract big numbers with regrouping, even when there are zeros, and check by adding.

New words

regroup · to trade 1 of a place for 10 of the place to its rightminuend · the number we take away fromsubtrahend · the number we take awayinverse operation · addition undoes subtraction, so we use it to check

Explanation

In a column subtraction, if a digit on top is smaller than the digit below it, we regroup from the place to its left. When the next place is a zero, we go further left to the first digit that is not zero and take 1 from it. Look at 5,000 − 2,346. There is nothing in the hundreds, tens or ones places, so take 1 thousand from the 5. Now 5,000 is 4 thousands, 9 hundreds, 9 tens and 10 ones. Subtract place by place: 10 − 6 = 4, 9 − 4 = 5, 9 − 3 = 6, 4 − 2 = 2. The difference is 2,654. Always check with the inverse operation: 2,654 + 2,346 = 5,000.

Place	Th	H	T	O
Before	5	0	0	0
Regrouped	4	9	9	10
Take away	2	3	4	6
Difference	2	6	5	4

Worked examples

Find 5,000 − 2,346. After regrouping the top row is 4, 9, 9 and 10. The ones: 10 − 6 = 4. The tens: 9 − 4 = 5. The hundreds: 9 − 3 = 6. The thousands: 4 − 2 = 2. The difference is 2,654, and 2,654 + 2,346 = 5,000.

A farm had 40,300 eggs and sent 18,675 to the market. How many are left? Regroup across the zero in the tens place: 40,300 − 18,675 = 21,625. Check: 21,625 + 18,675 = 40,300.

Step	Work
1	4,008 − 1,500 = 2,508
2	2,508 − 39 = 2,469
Check	2,469 + 1,539 = 4,008

Find 4,008 − 1,539. Long regrouping is slow here, so subtract in steps: 4,008 − 1,500 = 2,508, and 2,508 − 39 = 2,469. Check by adding: 2,469 + 1,539 = 4,008.

Class activity

Zero challenge. Make up three subtractions that start with a number with zeros, such as 6,000, 20,000 and 100,000. Subtract any number from each. Ask someone to check each answer by adding the difference to the number you took away.

Practice

Find 6,000 − 3,478.

Find 30,005 − 12,987.

Find 8,200 − 4,365.

Find 100,000 − 45,672.

Sherif says 7,000 − 2,314 = 5,314. Use addition to show he is wrong and find the right answer.