ReviewTayoSign inCreate account
Numerical Ability lesson

Multiplication: Methods and Mental Shortcuts

Multiply correctly with partial products, then cut the work: break numbers apart, use the shortcuts for 5, 25, 50, 125, 9, 99 and 11, halve and double, and the special products (squares ending in 5, numbers near 100). Check with the last digit and the digit sum.

30 min read · Professional and Sub-Professional

Learn

What it is

Multiplication is repeated addition: 4 × 25 means four 25s, which is 100. The numbers multiplied are the factors; the answer is the product. You can multiply in any order (4 × 25 = 25 × 4) and split a factor into parts (4 × 27 = 4 × 20 + 4 × 7).

Why it matters on the exam

Prices × quantity, area, percent, rates, unit conversion, averages turned back into totals: multiplication is in almost every word problem. A few shortcuts turn a 30-second column into a 5-second mental step, which matters in a timed exam.

How to recognize it

Look for ×, "of" (34 of), each, per, times, twice, triple, every, for every, rate, and "how much for n items".

What to look for

  • A factor like 5, 25, 50, 125, 9, 99 or 11: use the shortcut.
  • A factor just below a round number (49, 98, 199): break apart and subtract.
  • Zeros at the end: multiply the rest, attach the zeros.
  • Two numbers the same distance from a round number (47 and 53).
  • Choices with the same size but different last digits: check the last digit.

Words to know

  • Factor × factor = product.
  • Partial product: the result of multiplying by one digit of the other factor.
  • Distributive property: a × (b + c) = a × b + a × c.
  • Square: a number times itself (65² = 65 × 65).
Method 1 of 8

Long multiplication with partial products

Multiply the top number by the ones digit of the bottom number, then by the tens digit (shifted one place left, so the row ends in 0), then by the hundreds digit (two places left). Add the partial products.

How to use it

  1. Multiply by the ones digit (carry as you go).
  2. Multiply by the tens digit; write a 0 first.
  3. Repeat for each digit.
  4. Add the rows.
Example
Multiply 347 × 26.
  1. 347 × 6 = 2,082.
  2. 347 × 20 = 6,940.
  3. 2,082 + 6,940 = 9,022.
347 × 26 on paper, one row at a time
347×262082+69409022
  1. Step 1MUL7 × 6 = 42 → write 2, carry 4MUL4 × 6 + 4 = 28 → write 8, carry 2MUL3 × 6 + 2 = 20 → write 20ROW347 × 6 = 2,082
  2. Step 2SHIFTTens digit 2 (it means 20): write a 0 firstMUL7 × 2 = 14 → write 4, carry 1MUL4 × 2 + 1 = 9 → write 9MUL3 × 2 = 6 → write 6ROW347 × 20 = 6,940
  3. Step 3ADDAdd the rows: 2,082 + 6,940 = 9,022TIPAdd column by column from the right, carrying as usual
Answer9,022

Check: Estimate: 347 × 26 ≈ 9022

Answer: 9,022

Check: Estimate: 350 × 25 = 8,750, close ✓. Last digit: 7 × 6 = 42 → 2 ✓

Tandaan: One row per digit; shift each row one place left.

Watch out: Forgetting the 0 in the tens row (gives 347 × 6 + 347 × 2 = 2,776). Adding the carry before multiplying instead of after.

Method 2 of 8

Break apart (tens and ones, or round minus a little)

Split a factor into parts that are easy to multiply, multiply each part, then add. If a factor is just below a round number, multiply by the round number and subtract the extra.
The rulea × (b ± c) = a × b ± a × c

How to use it

  1. Split one factor: 36 = 30 + 6, or 49 = 50 − 1.
  2. Multiply the other factor by each part.
  3. Add (or subtract) the results.
Example
A box of bond paper costs ₱249. How much do 12 boxes cost?
  1. 249 = 250 − 1.
  2. 250 × 12 = 3,000.
  3. 1 × 12 = 12.
  4. 3,000 − 12 = 2,988.
Break apart
a × (b − c) = a × b − a × c
Price ₱249 = 250 − 1
Boxes 12
250 × 12− 1 × 12M/DMultiply 250 by 12=3,000 −1 × 12M/DMultiply 1 by 12=3,000 − 12A/SSubtract 12 from 3,000=2,988✓Check: 2,988 ÷ 12 = 249 ✓CHECK
Answer₱2,988

Answer: ₱2,988

Check: Column: 249 × 12 = 2,988 ✓

Tandaan: Split, multiply each part, combine.

Watch out: Subtracting 1 instead of 1 × 12.

Method 3 of 8

Multiply by 5, 25, 50 and 125 with zeros

5 is 10 ÷ 2, 25 is 100 ÷ 4, 50 is 100 ÷ 2 and 125 is 1,000 ÷ 8. So attach the zeros and divide.

How to use it

  1. Attach 1, 2 or 3 zeros (for 550, 25, 125: one, two, three zeros; 50 uses two).
  2. Divide by 2 (for 5 and 50), 4 (for 25) or 8 (for 125).
Example
36 × 25
  1. 36 × 100 = 3,600.
  2. 3,600 ÷ 4 = 900.
Multiply by…Do thisExample
5× 10, then ÷ 248 × 5 = 480 ÷ 2 = 240
25× 100, then ÷ 436 × 25 = 3,600 ÷ 4 = 900
50× 100, then ÷ 286 × 50 = 8,600 ÷ 2 = 4,300
125× 1,000, then ÷ 824 × 125 = 24,000 ÷ 8 = 3,000
9× 10, then − the number47 × 9 = 470 − 47 = 423
99× 100, then − the number36 × 99 = 3,600 − 36 = 3,564
11digits apart, their sum in the middle72 × 11 = 7|9|2 = 792
Shortcut table

Answer: 900

Check: 4 × 25 = 100, and 36 = 9 × 4, so 36 × 25 = 9 × 100 = 900 ✓

Tandaan: × 25 = × 100 ÷ 4.

Watch out: Dividing by 2 for × 25.

Method 4 of 8

Multiply by 9, 99 and 11

× 9 is × 10 minus the number; × 99 is × 100 minus the number. For a two-digit number × 11, write its two digits apart and put their sum in between (if the sum is 10 or more, carry 1 to the first digit).

How to use it

  1. × 9: × 10, then subtract the number.
  2. × 11: first digit | sum of digits | last digit; carry if the sum ≥ 10.
Example
86 × 11
  1. Digits 8 and 6.
  2. Sum: 8 + 6 = 14 → write 4, carry 1.
  3. First digit 8 + 1 = 9.
  4. Answer: 9 | 4 | 6.

Answer: 946

Check: 860 + 86 = 946 ✓

Tandaan: 11: apart, sum in the middle, carry.

Watch out: 86 × 11 = 8146: the carry was not added to the 8.

Method 5 of 8

Zeros first; halve and double

Ignore the end zeros, multiply what is left, then attach all the zeros from both factors. When one factor is even, you may halve it and double the other: the product does not change.
The rulea × b = (a ÷ 2) × (b × 2)

How to use it

  1. Count and set aside the end zeros.
  2. Halve the even factor and double the other until it is easy.
  3. Multiply and attach the zeros.
Example
16 × 35
  1. Halve 16, double 35: 8 × 70.
  2. Again: 4 × 140.
  3. Again: 2 × 280 = 560.

Answer: 560

Check: 16 × 35 = 16 × 30 + 16 × 5 = 480 + 80 = 560 ✓

Tandaan: Zeros aside; halve one, double the other.

Watch out: Counting the zeros wrongly in 400 × 2,500 (the 4 × 25 already makes 100).

Method 6 of 8

Special products

Squares ending in 5: n5 × n5 = n × (n + 1), then write 25. Both numbers just below 100: first part = one number minus the other number's gap from 100; last two digits = the two gaps multiplied. Same distance from a round number: (a − b)(a + b) = a² − b².

How to use it

  1. Ends in 5: tens digit × next number, then 25.
  2. Near 100: gaps x and y; write (100 − x − y) and then x × y as two digits.
  3. a − b and a + b: a² − b².
Example
97 × 96
  1. Gaps from 100: 3 and 4.
  2. First part: 97 − 4 = 93.
  3. Last two digits: 3 × 4 = 12.
  4. Answer: 9,312.

Answer: 9,312

Check: 97 × 96 = 97 × 100 − 97 × 4 = 9,700 − 388 = 9,312 ✓

Tandaan: 5-squares: n(n + 1)|25. Near 100: 100 − gaps | gaps multiplied.

Watch out: 98 × 97: 2 × 3 = 6 must be written 06 → 9,506, not 956.

Method 7 of 8

Check a product fast

The last digit of a product comes from the last digits of the factors. The digit sum (casting out nines) of the product must equal the digit sum of the two digit sums multiplied. Estimate the size by rounding.

How to use it

  1. Estimate: round and multiply.
  2. Last digit: multiply the last digits; keep the last digit.
  3. Digit sums: reduce each factor to one digit, multiply, reduce; compare.
Example
Is 347 × 26 = 9,032?
  1. Last digit: 7 × 6 = 42 → 2. 9,032 ends in 2, so it passes this test.
  2. Digit sums: 347 → 14 → 5; 26 → 8; 5 × 8 = 40 → 4.
  3. 9,032 → 14 → 5 ≠ 4, so it is wrong. 9,022 → 13 → 4 ✓

Answer: No; 9,022 is right.

Check: Estimate 350 × 26 ≈ 9,100: both are close, which is why the digit sum is needed.

Tandaan: Size, last digit, digit sum.

Watch out: Stopping after the last-digit test.

Method 8 of 8

Multiplying decimals: count the places

Do NOT line up the points. Multiply the numbers as if they were whole numbers, then count the decimal places in both factors together and put that many places in the answer, counting from the right.

How to use it

  1. Ignore the points and multiply.
  2. Count the decimal places in both factors and add them.
  3. Count that many places from the right of the product; add zeros in front if needed.
Example
3.4 × 2.6
  1. 34 × 26 = 884.
  2. 3.4 has 1 place and 2.6 has 1: 2 places.
  3. 884 → 8.84.
3.4 × 2.6 on paper
3.4×2.6204+68088.8844
  1. Step 1POINTMultiply as if there were no points: 34 × 26MUL4 × 6 = 24 → write 4, carry 2MUL3 × 6 + 2 = 20 → write 20ROW34 × 6 = 204
  2. Step 2SHIFTTens digit 2 (it means 20): write a 0 firstMUL4 × 2 = 8 → write 8MUL3 × 2 = 6 → write 6ROW34 × 20 = 680
  3. Step 3ADDAdd the rows: 204 + 680 = 884TIPAdd column by column from the right, carrying as usual
  4. Step 4POINTCount the decimal places: 1 in 3.4 + 1 in 2.6 = 2POINTCount 2 places from the right of 884: 8.84
Answer8.84

Check: Estimate: 3 × 3 ≈ 9

Answer: 8.84

Check: Estimate: 3 × 3 = 9 ✓

Tandaan: Places in = places out.

Watch out: Putting 1 decimal place because each factor has 1 (they add: 2). Lining up the points as in addition.

Which multiplication tool do I use?

You see…UseExample
Two big numbers, exact answerLong multiplication (T1)347 × 26
A factor near a round numberBreak apart (T2)49 × 32 = 50 × 32 − 32
× 5, 25, 50, 125Zeros, then divide (T3)36 × 25
× 9, 99, 11T472 × 11
Zeros, or an even × a5-ending numberZeros / halve and double (T5)16 × 35 = 8 × 70
Squares ending in 5; both near 100; a − b and a + bSpecial products (T6)65², 97 × 96, 47 × 53
Close choicesLast digit, digit sum (T7)9,022 vs 9,032
Which multiplication tool?

Multiplication table (1 to 10)

×12345678910
112345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
66121824303642485460
77142128354249566370
88162432404856647280
99182736455463728190
10102030405060708090100
Multiplication table: row × column; the squares are on the diagonal. Also know 11 × n (the × 11 trick) and 12 × 12 = 144.
Worked example 1 of 4Easy: × 25 with zeros
What is 44 × 25?
  1. 1,100
  2. 1,000
  3. 880
  4. 2,200
Step 1 · Use the shortcut× 25 = × 100 ÷ 4.
Step 2 · Attach zeros44 × 100 = 4,400.
Step 3 · Divide by 44,400 ÷ 4 = 1,100.
Step 4 · Check44 = 11 × 4 and 4 × 25 = 100, so 11 × 100 = 1,100 ✓

Answer: A. 1,100

Why not the others:

  • 1,000 is 40 × 25: the 4 was dropped.
  • 880 multiplies by 20.
  • 2,200 divides by 2 instead of 4.
Worked example 2 of 4Medium: price × quantity by breaking apart
An office ordered 18 chairs at ₱1,995 each. What is the total cost?
  1. ₱35,910
  2. ₱36,000
  3. ₱35,900
  4. ₱35,990
Step 1 · Round the price1,995 = 2,000 − 5.
Step 2 · Multiply the parts2,000 × 18 = 36,000 and 5 × 18 = 90.
Step 3 · Subtract36,000 − 90 = 35,910.
Step 4 · CheckLast digits: 5 × 8 = 40 → ends in 0 ✓; size about ₱36,000 ✓

Answer: A. ₱35,910

Why not the others:

  • ₱36,000 forgets to subtract 5 × 18.
  • ₱35,900 subtracts 100 instead of 90.
  • ₱35,990 subtracts only 10.
Worked example 3 of 4Hard: two numbers the same distance from 50
What is 47 × 53?
  1. 2,491
  2. 2,500
  3. 2,509
  4. 2,591
Step 1 · Spot the pattern47 = 50 − 3 and 53 = 50 + 3.
Step 2 · Use a² − b²50² − 3² = 2,500 − 9 = 2,491.
Step 3 · Check the last digit7 × 3 = 21 → ends in 1 ✓

Answer: A. 2,491

Why not the others:

  • 2,500 is just 50².
  • 2,509 adds the 9 instead of subtracting.
  • 2,591 has a slip in the hundreds.
Worked example 4 of 4Hard: both numbers near 100
What is 98 × 97?
  1. 9,506
  2. 956
  3. 9,560
  4. 9,606
Step 1 · Gaps from 10098 is 2 below, 97 is 3 below.
Step 2 · First part98 − 3 = 95 (or 97 − 2).
Step 3 · Last two digits2 × 3 = 6 → write 06.
Step 4 · Answer95 | 06 = 9,506. Check: 98 × 97 = 9,800 − 294 = 9,506 ✓

Answer: A. 9,506

Why not the others:

  • 956 forgets that the gap product takes two digits.
  • 9,560 writes 6 as 60.
  • 9,606 uses 96 as the first part.

Exam techniques

Last digit first

Multiply the last digits of the factors and eliminate choices that end differently.

When: Every multiple-choice product.

Careful: If two choices survive, use the digit sum.

Know the squares to 25 and the cubes to 10

Memorize 11² = 121 … 25² = 625 and 2³ … 10³. They show up in areas, powers and series.

When: Powers, areas, Pythagorean triples, series.

Careful: Practise them until they are instant.

Rearrange to make 10s and 100s

In a product of several numbers, pair 2 × 5, 4 × 25, 8 × 125 first.

When: Products like 4 × 17 × 25.

Careful: Order does not matter in multiplication, but it does in division.

The traps

  • Forgetting to shift the tens row in long multiplication. Write a 0 at the end of the tens row before multiplying (T1).
  • Breaking apart but multiplying only one part. Every part gets multiplied: 249 × 12 = 250 × 12 − 1 × 12 (T2).
  • × 25 by dividing by 2. × 25 = × 100 ÷ 4; × 50 = × 100 ÷ 2 (T3).
  • Dropping the carry in the × 11 trick. If the middle sum is 10 or more, add 1 to the first digit (T4).
  • Losing or adding a zero. Count the end zeros of both factors and attach them all at the end (T5).

Tandaan

  • One row per digit; shift each row left.
  • Break apart: round number ± a little.
  • × 5 = × 10 ÷ 2; × 25 = × 100 ÷ 4; × 125 = × 1,000 ÷ 8.
  • × 9 = × 10 − n; × 11: digits apart, sum in the middle.
  • n5² = n(n + 1)|25; near 100: 100 − gaps | gaps multiplied.
  • Check: size, last digit, digit sum.

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.

Open the lesson in the app Math facts sprint

Not sure where to start?Take the diagnostic test and see your strongest and weakest subjects.Start
Start learning

More Numerical Ability lessons

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.

Addition: Fast and Accurate Sums25 min · full lessonSubtraction: Borrowing, Change and Differences25 min · full lessonDivision: Long Division, Shortcuts and Remainders30 min · full lessonNumber Sense: Divisibility, Primes, GCF and LCM30 min · previewSigned Numbers and the Order of Operations25 min · previewPercent: One Template for Part, Whole and Rate25 min · previewPercent Change, Discounts and Interest35 min · previewRatio and Proportion: Direct, Inverse or Shares?30 min · previewAverages, the Missing Score, and Simple Probability30 min · previewWord Problems: The Step-by-Step Method35 min · previewWork and Motion Problems: Rates That Add30 min · previewNumber, Letter and Alphanumeric Series30 min · previewFractions and Decimals: The Operations30 min · previewBasic Algebra: Expressions and Equations30 min · previewGeometry and Measurement36 min · preview
Browse all 51 lessonsSee full access
Filing opens November 2, 2026. Add the dates to my calendar