Multiplying by 15 is one of the most common calculations students face — exam scores, time intervals, prices, recipe scaling. Yet most students still reach for a calculator or use slow column multiplication.

The mental math trick for ×15 is elegant: 15 = 10 + 5. Multiply by 10 in one step, then add half. Two fast steps and you are done. Under three seconds for any number.

Why 15 = 10 + 5 Is the Key Insight

Breaking 15 into 10 and 5 converts one awkward multiplication into two trivial ones. Multiplying by 10 is just adding a zero. Multiplying by 5 is just halving then adding a zero — and since you already have the ×10 result, halving that gives you the ×5 result instantly.

💡 Core insight: 15 = 10 + 5. So n × 15 = n × 10 + n × 5 = 10n + half of 10n. Multiply by 10, then add half of that result. One multiplication, one halving, one addition. Done.

This connects directly to the ×5 halve-and-zero trick from How to Multiply Any Number by 5 Mentally (Post 110). Once you know ×5 and ×10, you automatically know ×15 — it is just their sum.

How to Multiply Any Number by 15 — The x10 Plus Half Trick

Three steps: (1) Multiply by 10. (2) Halve that result to get the ×5 part. (3) Add both results together.

⚡ How to Multiply Any Number by 15 — x10 Plus Half
Rule: n × 15 = (n × 10) + (n × 10 ÷ 2)
48 × 15: 480 + 240 = 720 ✓
36 × 15: 360 + 180 = 540 ✓
74 × 15: 740 + 370 = 1110 ✓
37 × 15: 370 + 185 = 555 ✓ // odd → ends in 5
99 × 15: 990 + 495 = 1485 ✓ // odd → ends in 5
n × 15
→
n × 10
→
= 10n
→
10n ÷ 2
→
= 5n
→
10n + 5n
→
Answer ✓
Multiply any number by 15 mentally — times 10, halve it, add both

Even vs Odd — Two Quick Patterns

✓ Even Numbers — Clean Addition
Half of 10n is always a whole number. Both steps clean.

48×15: 480+240 = 720
76×15: 760+380 = 1140
124×15: 1240+620 = 1860
⚠ Odd Numbers — Ends in 5
Half of 10n ends in 5. Answer always ends in 5.

37×15: 370+185 = 555
53×15: 530+265 = 795
99×15: 990+495 = 1485
⚡ Odd Numbers × 15 — Always Ends in 5
23 × 15: 230 + 115 = 345 ✓
53 × 15: 530 + 265 = 795 ✓
71 × 15: 710 + 355 = 1065 ✓
89 × 15: 890 + 445 = 1335 ✓
📋 Step-by-Step: How to Multiply Any Number by 15 Mentally
1
Multiply by 10 — add a zero
Write the number with a zero appended. No calculation. This is your ×10 result and also the base for the next step. Takes zero mental effort.
48 → 480 | 37 → 370 | 348 → 3480
2
Halve the ×10 result — this is your ×5 part
Divide the Step 1 result by 2. For even originals this is always a clean whole number. For odd originals the ×10 result ends in zero so halving gives a number ending in 5.
480 ÷ 2 = 240 | 370 ÷ 2 = 185 | 3480 ÷ 2 = 1740
3
Add both parts — this is your answer
Add the ×10 result and the ×5 result. Work left to right through the digits. For even originals the sum ends in 0. For odd originals the sum always ends in 5.
480 + 240 = 720 ✓ | 370 + 185 = 555 ✓ | 3480 + 1740 = 5220 ✓
4
Verify with the last-digit rule
Every number times 15 ends in either 0 (even original) or 5 (odd original). A single glance confirms the answer is correct before you move on.
Even × 15 → ends in 0 | Odd × 15 → ends in 5
💡 Expert Tip
A
Ashwani SharmaMental Math, Abacus & Vedic Math Trainer and Expert
The Addition Shortcut I Use for the x15 Step 3 on Large Numbers
When adding 10n and 5n on large numbers, most students try to add right to left like they learned in school. I teach left to right: look at the thousands first, then hundreds, then adjust. For 348×15: 3480+1740. Thousands: 3+1=4. Hundreds: 4+7=11, carry gives 5 thousands and 1 hundred. Tens: 8+4=12, carry. Answer builds as 5220. Left-to-right addition on two similar-sized numbers is 40% faster than right-to-left once it becomes habit. This is a skill worth building separately before combining it with the ×15 trick.
— Ashwani Sharma, MentalMathChampions.com

Multiplying Large Numbers by 15 Mentally

⚡ Large Numbers × 15
348 × 15: 3480 + 1740 = 5220 ✓
126 × 15: 1260 + 630 = 1890 ✓
475 × 15: 4750 + 2375 = 7125 ✓ // odd
1200 × 15: 12000 + 6000 = 18000 ✓

Alternative Method — x3 Then x5

A second valid method: multiply by 3 first, then use the ×5 halve-and-zero trick on that result. This works because 15 = 3×5.

⚡ Alternative: x3 First, Then x5
48 × 15: 48×3=144 → 144×5: 144÷2=72, ×10 = 720 ✓
36 × 15: 36×3=108 → 108×5: 108÷2=54, ×10 = 540 ✓
37 × 15: 37×3=111 → 111×5: 110÷2=55, append 5 = 555 ✓

The ×10-plus-half method is usually faster for 2-digit numbers. The ×3-then-×5 method can be faster when the original number is easy to triple (multiples of 4, or numbers whose triple you know by heart).

Real-World Uses of Multiplying by 15

Multiplying by 15 appears constantly: 15% tip on a restaurant bill (15% of 480 = 72), 15-minute slots in scheduling (how many 15-minute blocks in 6 hours = 24), 15 runs per over in cricket scoring, 15 points per question on a 20-question test. The ×10-plus-half trick handles all of these instantly.

Extending to x150 and x1500

Same two steps with extra zeros:

  • n × 150 = (n × 100) + half of (n × 100)
  • n × 1500 = (n × 1000) + half of (n × 1000)
⚡ Extending to ×150 and ×1500
48 × 150: 4800 + 2400 = 7200 ✓
36 × 1500: 36000 + 18000 = 54000 ✓

Practice System — Master the Trick in 5 Days

Day 1–2: Even numbers only — 15 examples per day

All three steps are clean. Build the ×10-halve-add rhythm automatically. Target: 15 problems in 60 seconds by day 2.

Days 3–4: Mix in odd numbers

The half ends in 5 but addition is still simple. Target: any 2-digit ×15 in under 2.5 seconds.

Day 5: Large numbers and extensions

3-digit ×15 and ×150 problems. Target: answers in under 4 seconds.

For the complete practice framework: Build a Daily Mental Math Routine That Actually Sticks