Multiplying two numbers with the same tens digit (e.g. 43×47)

Some two-digit multiplications are much faster than they look — you just need to notice the pattern first. When both numbers share the same tens digit, like 43 and 47, or 62 and 68, there's a shortcut that turns the whole thing into one small multiplication and one addition.

The pattern to spot

The trick applies whenever two numbers have the same tens digit. Write them as:

where a is the shared tens digit, and b, c are the units digits. For 43 × 47, that's a = 4, b = 3, c = 7.

The formula

Expanding (10a + b)(10a + c) gives:

Which breaks into three easy mental steps:

• Multiply the tens digit by one more than itself, then by 100: a × (a + 1) × 100
• Add the tens digit times the sum of the units digits, times 10: a × (b + c) × 10
• Add the product of the units digits: b × c

Worked example: 43 × 47

Here a = 4, b = 3, c = 7.

• a × (a + 1) × 100 = 4 × 5 × 100 = 2000
• a × (b + c) × 10 = 4 × 10 × 10 = 400
• b × c = 3 × 7 = 21

Worked example: 62 × 68

Here a = 6, b = 2, c = 8.

• a × (a + 1) × 100 = 6 × 7 × 100 = 4200
• a × (b + c) × 10 = 6 × 10 × 10 = 600
• b × c = 2 × 8 = 16

A shortcut inside the shortcut

Notice that a × (a + 1) × 100 only depends on the tens digit, so it's worth pre-computing these nine values once (for a = 1 through 9) until they're automatic — 1×2, 2×3, 3×4, and so on, all ×100. That leaves just one small addition and one small multiplication to do live.

Also notice: if b + c happens to equal 10, the middle term becomes a clean multiple of 100, which makes the whole calculation even quicker. For example, 44 × 46 (b=4, c=6, b+c=10) becomes 4×5×100 + 4×10×10 + 24 = 2000 + 400 + 24 = 2024 — but since b+c=10 here, this is actually the same base-100-style pattern as squaring a number ending in 5, just shifted.

Where this actually helps

This shows up constantly in bank exam quant sections — simplification questions, approximation-based DI, and any place two nearby two-digit numbers need to be multiplied quickly. Since it avoids the full four-step cross-multiplication of standard long multiplication, it's one of the fastest wins for exam speed once it's automatic.