Learn on PengienVision, Mathematics, Grade 5Chapter 3: Fluently Multiply Multi-Digit Whole Numbers

Lesson 6: Multiply Whole Numbers With Zeros

In this Grade 5 lesson from enVision Mathematics Chapter 3, students learn how to apply the standard multiplication algorithm to multiply multi-digit whole numbers that contain zeros, such as 208 × 31 or 302 × 17. The lesson emphasizes that multiplying by zero always yields a product of zero and that this does not change the steps of the standard algorithm. Students also practice estimating products to check for reasonableness throughout the exercises.

Section 1

Multiplying Three-Digit by Two-Digit Numbers

Property

To multiply a 3-digit number containing a zero by a 2-digit number, use the standard algorithm.
First, find the partial product by multiplying the top number by the ones digit of the bottom number.
Then, find the second partial product by multiplying the top number by the tens digit, placing a zero in the ones place.
Finally, add the two partial products to find the final product.

Examples

  • Find the product of 309×42309 \times 42:
309×42618+1236012978\begin{array}{r r r r r} & & & 3 & 0 & 9 \\ \times & & & & 4 & 2 \\ \hline & & & 6 & 1 & 8 \\ + & 1 & 2 & 3 & 6 &0 \\ \hline & 1 & 2 & 9 & 7 &8 \\ \end{array}
  • Find the product of 704×56704 \times 56:
704×564224+3520039424\begin{array}{r r r r r} & & & 7 & 0 & 4 \\ \times & & & & 5 & 6 \\ \hline & & 4 & 2 & 2 & 4 \\ + & 3 & 5 & 2 & 0 &0 \\ \hline & 3 & 9 & 4 & 2 &4 \\ \end{array}
  • Find the product of 430×56430 \times 56:

$$

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiplying Three-Digit by Two-Digit Numbers

Property

To multiply a 3-digit number containing a zero by a 2-digit number, use the standard algorithm.
First, find the partial product by multiplying the top number by the ones digit of the bottom number.
Then, find the second partial product by multiplying the top number by the tens digit, placing a zero in the ones place.
Finally, add the two partial products to find the final product.

Examples

  • Find the product of 309×42309 \times 42:
309×42618+1236012978\begin{array}{r r r r r} & & & 3 & 0 & 9 \\ \times & & & & 4 & 2 \\ \hline & & & 6 & 1 & 8 \\ + & 1 & 2 & 3 & 6 &0 \\ \hline & 1 & 2 & 9 & 7 &8 \\ \end{array}
  • Find the product of 704×56704 \times 56:
704×564224+3520039424\begin{array}{r r r r r} & & & 7 & 0 & 4 \\ \times & & & & 5 & 6 \\ \hline & & 4 & 2 & 2 & 4 \\ + & 3 & 5 & 2 & 0 &0 \\ \hline & 3 & 9 & 4 & 2 &4 \\ \end{array}
  • Find the product of 430×56430 \times 56:

$$