Multiply a 2-digit number by a 2-digit number

Multiplying two whole numbers from 10 through 99 involves decomposing each factor by place value and combining partial products according to the distributive property, such as $(20+3)(10+4)$ , while interpreting each product’s value and positioning digits correctly. The standard algorithm organizes these same place-value relationships; the understanding excludes decimals, factors with more than two digits, and generalized algebraic or symbolic extensions beyond this whole-number case.

Detailed Explanation: Multiply a 2-digit number by a 2-digit number

To multiply two 2-digit numbers, break them into tens and ones. Then multiply each part and add the partial products.

Example: Find $23 \times 14$ .

Break apart the numbers:

23=20+3 \qquad \text{and} \qquad 14=10+4

Multiply each part:

\begin{aligned} 23\times14 &=(20+3)(10+4)\\ &=(20\times10)+(20\times4)+(3\times10)+(3\times4)\\ &=200+80+30+12\\ &=322 \end{aligned}

So,

23\times14=\boxed{322}

The standard algorithm shows the same place-value thinking:

   23
×  14
-----
   92   ← 23 × 4
  230   ← 23 × 10
-----
  322

The $3$ in $14$ means $3$ ones, so $23\times3=69$ —but in this example, using $14\times23$ , the rows shown calculate $23\times4=92$ and $23\times10=230$ . Add the two partial products to get the final answer, $322$ .

Learn by doing: Multiply a 2-digit number by a 2-digit number

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Multiplication - Whole Number 2 x 2 - Columns

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Multiply a 2-digit number by a 2-digit number

Detailed Explanation: Multiply a 2-digit number by a 2-digit number

Learn by doing: Multiply a 2-digit number by a 2-digit number

Practice with unlimited practice problems

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Multiplication - Whole Number 2 x 2 - Columns