How can the same decomposition method be applied to calculate 487 × 60 quickly in the head?
Executive summary
Calculating 487 × 60 quickly in the head is simplest when the multiplication is decomposed into parts: either split 487 into 400 + 80 + 7 and multiply each by 60, or multiply 487 by 6 and then by 10 — both approaches rely on breaking the problem into easier pieces and using powers of ten to simplify the arithmetic [1] [2] [3].
1. Decompose the multiplicand: break 487 into friendly chunks
The core mental trick is to rewrite 487 as 400 + 80 + 7, then use distributivity to transform 487 × 60 into (400 × 60) + (80 × 60) + (7 × 60); this “multiply-in-parts” approach is a standard mental-math strategy recommended for handling large multiplications without paper [3] [1].
2. Use powers of ten to speed each sub-product
Because 60 is 6 × 10, each sub-product becomes easy: multiply the chunk by 6, then shift the result one place to the right (i.e., append a zero) to account for the ×10 — for example 400×60 = (400×6)×10 = 2400×10 = 24,000 — using the power-of-ten shortcut is explicit advice in mental-math guides [2] [4].
3. Do the three quick multiplications and accumulate left-to-right
Compute the pieces: 400×60 = 24,000; 80×60 = 4,800; 7×60 = 420; then add them: 24,000 + 4,800 = 28,800; 28,800 + 420 = 29,220. Doing the additions left-to-right helps keep intermediate numbers manageable and lets a practitioner “call out” partial totals as they go, a technique encouraged for fluent mental calculation [5] [1].
4. An even shorter route: multiply by 6, then append a zero
An alternative decomposition that many find even quicker is to calculate 487 × 6 first and then append a zero (because multiplying by 60 = multiplying by 6 and then by 10). Compute 487×6 as (400×6) + (80×6) + (7×6) = 2,400 + 480 + 42 = 2,922, then append a zero to get 29,220; this leverages both the “multiply in parts” idea and the append-zero power-of-ten shortcut [3] [2].
5. Why practice the single-digit tables and left-to-right flow matters
Both decomposition paths depend on fast single-digit multiplication and comfortable handling of tens-place shifts; instruction sets for mental multiplication emphasize mastering basic tables and practicing left-to-right accumulation because they let learners perform partial results rapidly and avoid back-and-forth carries that slow down mental work [5] [3].
6. Quick verification and alternative mental checks
A fast sanity check is to estimate: 487 ≈ 500, so 500×60 = 30,000; the computed 29,220 is plausibly a bit below that, which matches expectation. Mental-math resources recommend checking with an approximate nearby round-number multiplication or repeating the calculation using the other decomposition method (first split then append zero versus append zero after multiplying by 6) to catch errors [2] [6].