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Multiply a 4-digit number by a 1-digit number

Multiplying a four-digit whole number by a one-digit whole number involves decomposing the factor by place value and applying the distributive property to find and combine partial products. Regrouping ten ones, tens, or hundreds into the next place explains the standard algorithm, including products with internal zeros; estimation and place-value reasoning help verify that the result is reasonable. This scope excludes multiplication by multi-digit factors and more generalized algorithms.

Detailed Explanation: Multiply a 4-digit number by a 1-digit number

To multiply a 4-digit number by a 1-digit number, multiply from right to left, working with the ones, tens, hundreds, and thousands. If a product is 10 or more, regroup by carrying to the next place value.

Example: Find 2,406×72{,}406 \times 7.

  1. Multiply the ones.
    6×7=426 \times 7 = 42
    Write 22 in the ones place and regroup 44 tens.

  2. Multiply the tens.
    There are 00 tens:
    0×7=00 \times 7 = 0
    Add the 44 regrouped tens: 0+4=40+4=4.
    Write 44 in the tens place.

  3. Multiply the hundreds.
    4×7=284 \times 7 = 28
    Write 88 in the hundreds place and regroup 22 thousands.

  4. Multiply the thousands.
    2×7=142 \times 7 = 14
    Add the 22 regrouped thousands: 14+2=1614+2=16.
    Write 1616 in the thousands and ten-thousands places.

Therefore,

2,406×  716,842\begin{array}{r} 2{,}406\\ \times\ \ 7\\ \hline 16{,}842 \end{array}

So, 2,406×7=16,8422{,}406 \times 7=\boxed{16{,}842}.

To check that the answer is reasonable, round 2,4062{,}406 to 2,4002{,}400:

2,400×7=16,8002{,}400 \times 7=16{,}800

Since 16,84216{,}842 is close to 16,80016{,}800, the answer makes sense.

Learn by doing: Multiply a 4-digit number by a 1-digit number

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    Multiplication - Whole Number 4 x 1 - Columns

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