Subtract correctly every time, even across zeros, then do it faster: count up like a cashier, take from 9 and 10, round and adjust, and shift both numbers. Always check by adding back.
25 min read · Professional and Sub-Professional
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What it is
Subtraction finds what is left, or how far apart two amounts are. In 7,003 − 2,468 = 4,535, the first number is the minuend, the number taken away is the subtrahend, and the answer is the difference. Subtraction is the opposite of addition: 4,535 + 2,468 = 7,003.
Why it matters on the exam
"How much is left", "how many more", "change from ₱1,000", "how much did it increase" — all of these are subtraction, and they are everywhere in word problems, percent change and data tables. Borrowing across zeros is where most people slip, and the exam choices are built from those slips.
How to recognize it
Look for a − sign or the words left, remain, change, difference, how many more, how much less, decreased by, fewer, older than, farther than.
What to look for
Zeros in the top number (7,003, 40,005): borrowing across zeros.
A bill or round total (₱500, ₱1,000, 10,000): count up or "all from 9, last from 10".
A number just below a round one (398, 1,995): round and adjust.
Which number is bigger: in "how many more", always big − small.
Words to know
Minuend − subtrahend = difference.
Borrow (regroup): take 1 from the next column on the left; it is worth 10 in this column.
Inverse: subtraction undoes addition, so you can always check by adding.
Same change: moving both numbers by the same amount keeps their difference.
Method 1 of 7
Column subtraction with borrowing (even across zeros)
Line up the ones digits. Subtract each column from right to left. When the top digit is smaller than the bottom digit, borrow 1 from the column on its left: that column goes down by 1 and this column goes up by 10. If the column to the left is 0, keep going left to the first non-zero digit; every 0 you pass becomes 9.
How to use it
Line up the ones.
If the top digit is smaller, borrow from the left (across zeros, the zeros become 9).
Subtract the column.
Move one column left and repeat.
Example
Subtract 7,003 − 2,468.
Ones: 3 < 8, and the tens and hundreds are 0. Borrow from the 7: it becomes 6, the two 0s become 9, the 3 becomes 13.
Ones: 13 − 8 = 5.
Tens: 9 − 6 = 3.
Hundreds: 9 − 4 = 5.
Thousands: 6 − 2 = 4.
7,003 − 2,468 on paper, one column at a time
699137003−24684535
Step 1BORROWOnes: 3 is less than 8, so borrow 1 from the thousands (7 → 6); each 0 on the way becomes 9SUBOnes: 13 − 8 = 5
Step 2SUBTens: 9 − 6 = 3
Step 3SUBHundreds: 9 − 4 = 5
Step 4SUBThousands: 6 − 2 = 4
Answer4,535
Check: 4,535 + 2,468 = 7,003 ✓
Answer:4,535
Check: Add back: 4,535 + 2,468 = 7,003 ✓
Tandaan: Top too small? Borrow. Zeros on the way become 9s.
Watch out: Taking the smaller digit from the bigger one in each column (8 − 3 = 5 in the ones), which gives 5,465. Forgetting that the 7 became 6 (gives 5,535).
Method 2 of 7
Count up, like a cashier giving change
Instead of taking away, start at the smaller number and count up to the bigger one in easy jumps: to the next ten, to the next hundred, to the next thousand, then the rest. The difference is the total of the jumps.
How to use it
Jump from the smaller number to the next round number.
Keep jumping by round amounts until you reach the bigger number.
Add up the jumps.
Example
A ₱637 purchase is paid with ₱1,000. What is the change?
637 → 640: jump 3.
640 → 700: jump 60.
700 → 1,000: jump 300.
3 + 60 + 300 = 363.
Count up
Difference = total of the jumps
From 637
To 1,000
1,000 − 637SETPut the numbers into the formula640 − 637 =3A/SJump to 640700 − 640 =60A/SJump to 7001,000 − 700 =300A/SJump to 1,0003 + 60 + 300 =363A/SAdd them all✓Check: 637 + 363 = 1,000 ✓CHECK
Answer₱363
Answer:₱363
Check: 637 + 363 = 1,000 ✓
Tandaan: Difference = distance: count up in round jumps.
Watch out: Losing a jump: write each jump down as you make it.
Method 3 of 7
From 1,000 or 10,000: all from 9, the last from 10
To subtract a number from 1,000, 10,000 or 100,000, take each of its digits from 9, except the last digit, which you take from 10. Write the number with as many digits as there are zeros (37 from 1,000 is 037).
How to use it
Pad the number with zeros in front to match the number of zeros.
Take every digit from 9, except the last from 10.
If the number ends in 0, use the last non-zero digit from 10 and keep the end zeros.
Example
10,000 − 3,725
3 from 9 → 6.
7 from 9 → 2.
2 from 9 → 7.
5 from 10 → 5.
Answer:6,275
Check: 6,275 + 3,725 = 10,000 ✓
Tandaan: All from 9, the last from 10.
Watch out: Taking the last digit from 9 as well (6,274, one too small).
Method 4 of 7
Round and adjust
Subtract a round number that is a little bigger, then add back the extra you took away.
The rulea − b = a − (b + k) + k
How to use it
Round the subtracted number up; note the extra.
Subtract the round number.
Add the extra back.
Example
824 − 398
398 is 2 less than 400.
824 − 400 = 424.
You took away 2 too many: 424 + 2 = 426.
Round and adjust
a − b = a − (b + k) + k
Subtracted number 398
Rounded 400 (k = 2)
824 − 400+ 2A/SSubtract 400 from 824=424 + 2A/SAdd 424 and 2=426✓Check: 426 + 398 = 824 ✓CHECK
Answer426
Answer:426
Check: 426 + 398 = 824 ✓
Tandaan: Took away too much? Give it back.
Watch out: Subtracting the extra again (424 − 2 = 422): you took away too much, so give it back.
Method 5 of 7
Same change: shift both numbers
If you add the same amount to both numbers (or take the same amount from both), the difference does not change. Shift both until the number you subtract is round.
The rulea − b = (a + k) − (b + k)
How to use it
Find k that makes the second number round.
Add k to both numbers.
Subtract.
Example
503 − 298
Add 2 to both: 505 − 300.
505 − 300 = 205.
Answer:205
Check: 205 + 298 = 503 ✓
Tandaan: Move both, keep the gap.
Watch out: Shifting only one number.
Method 6 of 7
Check by adding back
Add your answer to the number you subtracted. If you get the first number, the answer is right. For choices that are close, also check the last digit.
How to use it
Answer + subtracted number.
Compare with the first number.
For a quick filter, check only the last digits first.
Example
Is 4,545 right for 7,003 − 2,468?
4,545 + 2,468 = 7,013 ≠ 7,003.
Off by 10: a borrow in the tens was mishandled.
Correct: 4,535 + 2,468 = 7,003 ✓
Answer: No; the answer is 4,535.
Check: Last digits: 5 + 8 = 13 → ends in 3 ✓ for both, so the add-back is what decides.
Tandaan: Answer + what you took = what you had.
Watch out: Re-subtracting the same way (repeats the slip).
Method 7 of 7
Subtracting decimals: line up the points, fill with zeros
Line up the decimal points. If the top number has fewer decimal places, write zeros (₱500 = ₱500.00) so you can borrow. Subtract like whole numbers and bring the point straight down.
How to use it
Line up the points.
Write zeros so both numbers have the same decimal places.
Subtract from the right, borrowing as usual (across zeros too).
Bring the point down.
Example
20 − 7.35
20 = 20.00.
Hundredths: 0 < 5, borrow across the zeros: 10 − 5 = 5.
Tenths: 9 − 3 = 6.
Ones: 9 − 7 = 2; tens: 1 − 0 = 1.
20 − 7.35 on paper
1991020.00−7.3512.65
Step 1POINTLine up the decimal points; an empty place counts as 0BORROWHundredths: 0 is less than 5, so borrow 1 from the tens (2 → 1); each 0 on the way becomes 9SUBHundredths: 10 − 5 = 5
Step 2SUBTenths: 9 − 3 = 6POINTBring the decimal point straight down
Step 3SUBOnes: 9 − 7 = 2
Step 4SUBTens: 1 − 0 = 1
Answer12.65
Check: 12.65 + 7.35 = 20.00 ✓
Answer:12.65
Check: 12.65 + 7.35 = 20 ✓
Tandaan: Same number of decimal places on top and bottom.
Watch out: Bringing down the 35 without subtracting (20 − 7.35 ≠ 13.35).
Which subtraction tool do I use?
You see…
Use
Example
Exact answer with big numbers
Column subtraction (T1)
7,003 − 2,468
Change from a bill, "how much more"
Count up (T2)
₱1,000 − ₱637
1,00010,000 minus a number
All from 9, last from 10 (T3)
10,000 − 3,725
Subtracting a number just under a round one
Round and adjust (T4)
824 − 398
Both numbers easy to shift
Same change (T5)
503 − 298 = 505 − 300
Close choices
Add back; digit sum (T6)
4,535 vs 4,545
Which subtraction tool?
Subtraction table
−1
−2
−3
−4
−5
−6
−7
−8
−9
2 − 1 = 1
3 − 2 = 1
4 − 3 = 1
5 − 4 = 1
6 − 5 = 1
7 − 6 = 1
8 − 7 = 1
9 − 8 = 1
10 − 9 = 1
3 − 1 = 2
4 − 2 = 2
5 − 3 = 2
6 − 4 = 2
7 − 5 = 2
8 − 6 = 2
9 − 7 = 2
10 − 8 = 2
11 − 9 = 2
4 − 1 = 3
5 − 2 = 3
6 − 3 = 3
7 − 4 = 3
8 − 5 = 3
9 − 6 = 3
10 − 7 = 3
11 − 8 = 3
12 − 9 = 3
5 − 1 = 4
6 − 2 = 4
7 − 3 = 4
8 − 4 = 4
9 − 5 = 4
10 − 6 = 4
11 − 7 = 4
12 − 8 = 4
13 − 9 = 4
6 − 1 = 5
7 − 2 = 5
8 − 3 = 5
9 − 4 = 5
10 − 5 = 5
11 − 6 = 5
12 − 7 = 5
13 − 8 = 5
14 − 9 = 5
7 − 1 = 6
8 − 2 = 6
9 − 3 = 6
10 − 4 = 6
11 − 5 = 6
12 − 6 = 6
13 − 7 = 6
14 − 8 = 6
15 − 9 = 6
8 − 1 = 7
9 − 2 = 7
10 − 3 = 7
11 − 4 = 7
12 − 5 = 7
13 − 6 = 7
14 − 7 = 7
15 − 8 = 7
16 − 9 = 7
9 − 1 = 8
10 − 2 = 8
11 − 3 = 8
12 − 4 = 8
13 − 5 = 8
14 − 6 = 8
15 − 7 = 8
16 − 8 = 8
17 − 9 = 8
10 − 1 = 9
11 − 2 = 9
12 − 3 = 9
13 − 4 = 9
14 − 5 = 9
15 − 6 = 9
16 − 7 = 9
17 − 8 = 9
18 − 9 = 9
11 − 1 = 10
12 − 2 = 10
13 − 3 = 10
14 − 4 = 10
15 − 5 = 10
16 − 6 = 10
17 − 7 = 10
18 − 8 = 10
19 − 9 = 10
Subtraction facts: each column takes away the same number
Worked example 1 of 4Easy: same change in your head
What is 92 − 47?
55
45
35
139
Step 1 · Make the second number roundAdd 3 to both: 92 − 47 = 95 − 50.
Step 2 · Subtract95 − 50 = 45.
Step 3 · Check45 + 47 = 92 ✓
Answer: B. 45
Why not the others:
55 subtracts the smaller ones digit from the bigger one (7 − 2 = 5) instead of borrowing.
35 borrows one ten too many.
139 adds instead of subtracting.
Worked example 2 of 4Medium: change from a ₱5,000 bill
A clerk paid ₱3,268 for office supplies with a ₱5,000 bill. How much change did she get?
Step 3 · Or: 4,000 + (1,000 − 268)From 1,000: 0 2 6 8 → all from 9, last from 10 → 7 3 2 → 732, so 5,000 − 3,268 = 1,732.
Step 4 · Check1,732 + 3,268 = 5,000 ✓
Answer: A. ₱1,732
Why not the others:
₱2,732 forgets that one thousand was borrowed.
₱1,742 has a borrow slip in the tens.
₱1,832 drops the borrow in the hundreds.
Worked example 3 of 4Hard: borrowing across many zeros
What is 40,005 − 17,368?
22,637
23,637
22,647
37,363
Step 1 · Borrow across the zerosThe ones need a borrow, but the tens, hundreds and thousands are 0. Borrow from the 4: it becomes 3, the three 0s become 9, and the 5 becomes 15.
Step 3 · Faster with same changeSubtract 5 from both: 40,000 − 17,363. From 100,000 it would be 82,637 (all from 9, last from 10); 40,000 is 60,000 less, so 82,637 − 60,000 = 22,637.
Step 4 · Check22,637 + 17,368 = 40,005 ✓
Answer: A. 22,637
Why not the others:
23,637 forgets that the 4 became 3.
22,647 makes a borrow slip in the tens.
37,363 subtracts the smaller digit from the bigger in each column.
Worked example 4 of 4Hard: the missing digit
In 8▢2 − 357 = 465, which digit goes in the box?
1
2
3
9
Step 1 · Use the inverseIf 8▢2 − 357 = 465, then 8▢2 = 465 + 357.
Step 2 · Add465 + 357 = 822.
Step 3 · Read the box8▢2 = 822, so the box is 2.
Step 4 · Check822 − 357 = 465 ✓
Answer: B. 2
Why not the others:
1 and 3 are off by one in the tens: a lost or extra carry when adding back.
9 tries to borrow in the tens without a reason.
Exam techniques
Choose the method from the numbers
Round numbers on top → count up or all-from−9. A number just below a round one → round and adjust. Otherwise, column.
When: Before you start any subtraction.
Careful: When unsure, the column method always works.
Add back to choose
Add each close choice to the subtracted number and see which gives the first number.
When: Choices that differ by 10 or 100.
Careful: Do it on paper; it takes seconds.
Ages and dates stay apart
The difference between two ages never changes, so shift years freely (same change).
When: Age and calendar problems.
Careful: Shift both by the same amount.
The traps
Subtracting the smaller digit from the bigger one in every column. The bottom digit is always taken from the top digit; borrow when the top is smaller (T1).
Forgetting that the digit you borrowed from went down by 1. Cross it out and write the new digit above it (T1).
Borrowing across zeros: making the zeros 10 instead of 9. Only the column that needs the borrow gets +10; every zero you pass becomes 9 (T1).
Adjusting the wrong way after rounding. You took away too much, so add the extra back (T4).
Subtracting in the wrong order in "how many more". Always bigger − smaller for a difference.
Tandaan
Bottom from top; borrow when the top is smaller.
Across zeros: the zeros become 9s.
Count up like a cashier for change.
From 1,000 or 10,000: all from 9, the last from 10.
Round and adjust: took too much? Give it back.
Check: answer + subtracted number = first number.
Practice this lesson
Practice questions with step-by-step solutions, written out like on paper, and the 60-second math facts sprint are in the app.
ReviewTayo has 51 lessons that follow the official scope of the exam, each with rules, worked examples, common mistakes and practice. Open one and read the first part.
