Multiplying by 75 looks hard. Most students have no strategy and use column multiplication. But 75 has a beautiful structure: 75 = 100 − 25 = 3 × 25. Two different tricks, both fast, both exact.

Method 1: multiply by 100 then subtract a quarter. Method 2: triple the number then apply the ×25 trick. Both get you to the same answer in under three seconds. You can choose whichever feels more natural depending on the number.

Why 75 = 100 − 25 Is the Key Insight

75 is three quarters of 100. So multiplying by 75 is the same as multiplying by 100 and then taking away one quarter. The quarter of 100n is found by halving 100n twice — two halvings replace an entire division operation.

💡 Core insight: 75 = 100 − 25. So n × 75 = 100n − 25n = 100n − (100n ÷ 4). Multiply by 100, halve twice to find the quarter, subtract. Three steps. Under 3 seconds.

This connects to the ×25 trick from How to Multiply Any Number by 25 Mentally (Post 107). If you already know ×25, you know the hardest part of ×75 — finding the quarter.

Method 1: x100 Minus Quarter — The Primary Method

Three steps: (1) Multiply by 100. (2) Divide that by 4 (halve twice) to get the ×25 part. (3) Subtract step 2 from step 1.

⚡ Method 1: x100 Minus Quarter
Rule: n × 75 = (n × 100) − (n × 100 ÷ 4)
48 × 75: 4800 − 1200 = 3600 ✓ // 4800÷4=1200
36 × 75: 3600 − 900 = 2700 ✓ // 3600÷4=900
24 × 75: 2400 − 600 = 1800 ✓ // 2400÷4=600
40 × 75: 4000 − 1000 = 3000 ✓ // 4000÷4=1000
52 × 75: 5200 − 1300 = 3900 ✓ // 5200÷4=1300
n × 75
→
n × 100
→
= 100n
→
100n ÷ 4
→
= 25n
→
100n − 25n
→
Answer ✓
Multiply any number by 75 — times 100, find the quarter, subtract

Method 2: x3 Then x25 — The Alternative Method

Since 75 = 3 × 25, you can also multiply by 3 first and then apply the ×25 trick (halve twice then add two zeros).

⚡ Method 2: x3 Then x25 (halve twice, add 00)
48 × 75: 48×3=144 → 144÷2=72 → 72÷2=36 → 36×100 = 3600 ✓
36 × 75: 36×3=108 → 108÷2=54 → 54÷2=27 → 27×100 = 2700 ✓
24 × 75: 24×3=72 → 72÷2=36 → 36÷2=18 → 18×100 = 1800 ✓
16 × 75: 16×3=48 → 48÷2=24 → 24÷2=12 → 12×100 = 1200 ✓
⚡ Method 1: Best For
Numbers divisible by 4. The quarter comes out clean.

48×75: 4800−1200 = 3600
40×75: 4000−1000 = 3000
100×75: 10000−2500 = 7500
📈 Method 2: Best For
Small numbers whose triple you know instantly.

8×75: 24×25 = 600
12×75: 36×25 = 900
16×75: 48×25 = 1200
📋 Step-by-Step: How to Multiply Any Number by 75 Mentally
1
Choose your method — x100 minus quarter OR x3 then x25
If the number is divisible by 4, Method 1 gives the cleanest quarter. If the number is small and easy to triple, Method 2 is often faster. Both always give the exact same answer.
48 (div by 4) → Method 1 | 8 (easy to triple) → Method 2
2
Method 1: Multiply by 100, then halve twice
Add two zeros (times 100), then halve that result twice to get one quarter. This is your 25n value. Every halving is a simple mental operation.
48×100=4800 4800÷2=2400 2400÷2=1200 (this is 48×25)
3
Method 1: Subtract the quarter from the x100 result
100n minus 25n = 75n. Subtract the Step 2 result from the Step 1 result. Work left to right for speed. Verify: answer must end in 00, 25, 50, or 75.
4800 − 1200 = 3600 ✓ (ends in 00, original was div by 4)
4
Verify with the last-two-digits rule
Multiples of 4 × 75 end in 00. Numbers giving remainder 2 mod 4 end in 50. Odd numbers end in 25 or 75. This check is instant and catches most errors.
48 (mod 4=0) × 75 → ends in 00 ✓ | 37 (odd) × 75 → ends in 75
💡 Expert Tip
A
Ashwani SharmaMental Math, Abacus & Vedic Math Trainer and Expert
Why I Always Teach ×75 Last in the Quarter Family
In my classes, I introduce ×25 first, then ×50, then ×75. By the time students reach ×75, they already know how to halve twice (for the quarter) and how to halve once (for the half). The subtraction in ×75 is the only new element. I find that students who try to learn ×75 without first mastering ×25 always struggle with the halve-twice step. But students who reach ×75 after ×25 and ×50 treat it as trivial — the quarter is nothing new. The correct sequence matters enormously in mental math education. Build each trick on the previous one and the difficulty stays manageable.
— Ashwani Sharma, MentalMathChampions.com

Answer Patterns When Multiplying by 75

Every product of n × 75 ends in one of four two-digit combinations: 00, 25, 50, or 75. The pattern depends on n mod 4:

⚡ Last-Two-Digit Patterns for x75
n mod 4 = 0 (e.g. 4,8,12,48,100) → answer ends in 00
n mod 4 = 1 (e.g. 1,5,9,37,101) → answer ends in 75
n mod 4 = 2 (e.g. 2,6,10,38,102) → answer ends in 50
n mod 4 = 3 (e.g. 3,7,11,39,103) → answer ends in 25
Check: 37×75 = 3700−925 = 2775 ✓ ends in 75 (37 mod 4 = 1)
Check: 38×75 = 3800−950 = 2850 ✓ ends in 50 (38 mod 4 = 2)

Multiplying Large Numbers by 75 Mentally

⚡ Large Numbers × 75 — Method 1
348 × 75: 34800 − 8700 = 26100 ✓ // 34800÷4=8700
124 × 75: 12400 − 3100 = 9300 ✓ // 12400÷4=3100
200 × 75: 20000 − 5000 = 15000 ✓ // 20000÷4=5000
1000 × 75: 100000 − 25000 = 75000 ✓ // trivially 75×1000

The 25, 50, 75, 100 Family — The Quarter System

Multiply byAs fraction of 100MethodExample (n=48)
×251 quarterHalve twice, add 0048×25 = 1200
×501 halfHalve once, add 0048×50 = 2400
×753 quartersx100 minus quarter48×75 = 3600
×1004 quartersAdd two zeros48×100 = 4800

Notice the pattern: 25, 50, 75, 100 are the four quarter points of 100. Knowing all four tricks means you can multiply any number by any quarter of 100 instantly. That is a powerful set of tools for everyday calculation.

Real-World Uses of Multiplying by 75

Multiplying by 75 appears in: 75% marks on an exam (what score out of 480?), 75 paisa per item pricing, 75-minute sessions in scheduling, 75 km/h speed calculations, 75% battery charge questions. The x100-minus-quarter trick handles all of these in seconds.

Practice System — Master Both Methods

Days 1–2: Method 1 with multiples of 4

Start with numbers divisible by 4 where the quarter is always clean (4, 8, 12, 16, 20, 24, 48, 100). Target: 15 problems in 90 seconds.

Days 3–4: Method 1 with all even numbers

Add even non-multiples of 4. The quarter will end in 50 but the subtraction is still manageable. Target: 2-digit answers in under 3 seconds.

Day 5: Odd numbers and method switching

Odd numbers give quarters ending in 25 or 75. Practice choosing between Method 1 and Method 2 based on the number. Target: any 2-digit × 75 in under 4 seconds.