Lesson 7: Practice Multiplying Multi-Digit Numbers

Property

To estimate the product of two numbers, round each factor to a nearby, easy-to-multiply number (like its greatest place value). The calculated product should be close to this estimate. If $A \approx A_{est}$ and $B \approx B_{est}$, then the exact product $A \times B$ should be reasonably close to the estimated product $A_{est} \times B_{est}$.

Examples

Property

To multiply multi-digit numbers, multiply the top number by each digit of the bottom number, one at a time, from right to left. These intermediate results are called partial products. The final product is the sum of the partial products.

Examples

• To calculate $86 \times 42$:

$$

\begin{array}{r r r r}
& & & 8 & 6 \\
\times & & & 2 & 4 \\
\hline
&& 3 & 4& 4 \\

• & 1 & 7 & 2 &0 \\

\hline
& 2 & 0 & 6& 4 \\
\end{array}

\begin{array}{r r r r r}
& & & 5 & 2 & 7 \\
\times & & && 3 & 5 \\
\hline
&& 2 & 6 & 3& 5 \\

• & 1 & 5 & 8 & 1& 0\\

\hline
& 1 & 8 & 4 & 4& 5 \\
\end{array}