Math · Stage 6

Multiply two 2-digit numbers with tens summing to ten and equal units

A lightning mental-maths trick for a special family of products — like 23 × 83 or 47 × 67. Multiply the tens and add the shared unit for the hundreds, then stick the unit-squared on the end. No column method needed.

✦ Math📘 Stage 6 · S6⏱ ~12 min🧒 Ages 10–12★ Free to start

I can multiply two 2-digit numbers whose tens digits sum to ten and share the same units digit.

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Kavi's Lightning Ledger ⚡

A shopkeeper asks Kavi for 23 × 83. Before anyone reaches for a pencil, Kavi hoots the answer: "1909!" The secret? The tens 2 + 8 = 10 and both numbers end in 3. Kavi does 2 × 8 + 3 = 19 for the hundreds, then 3² = 09 on the end — 1909. Same trick cracks 47 × 67, 52 × 52 and a whole family more.

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What your child will learn

1When does the lightning trick work?This trick only fits a special pair: the two tens digits add to 10 AND both numbers share the same units digit. Spot the family first — tap a row to see a pair that fits.

2Hundreds part, then the last two digitsMultiply the two tens digits and add the shared unit — that is how many hundreds. Then square the units digit and write it as the last two digits. Tap a row.

3The algebra behind the magicWrite the numbers as (10a + c) and (10b + c) with a + b = 10. Multiply out and the middle terms collect to 10c(a+b) = 100c. Tap a row to see the pieces line up.

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A peek inside

Use the trick for 26 × 86.

tens 2+8 = 10, units both 6. Hundreds: 2×8+6 = 22. End: 6² = 36.

Try this at home: Warm-up (tens × tens + unit = hundreds): 23 × 83 = __ · 47 × 67 = __

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.