Multiplying by Place Value
Multiplying by Place Value is a Grade 5 math skill from Illustrative Mathematics Chapter 4 (Wrapping Up Multiplication and Division with Multi-Digit Numbers) that teaches students to use the full place value of each digit — not just its face value — when computing partial products. For example, the digit 4 in the tens place of 245 has a value of 40, so multiplying it by a digit in the tens place of the other factor produces a product in the thousands.
Key Concepts
To find a partial product, multiply the place value of the digit from the first factor by the place value of the digit from the second factor. For a number like $abc$, the values of the digits are $a \times 100$, $b \times 10$, and $c \times 1$.
Common Questions
Why is it important to use place value when multiplying?
Using place value ensures each partial product reflects the true value of the digits being multiplied. For example, 40 × 30 = 1200, not 4 × 3 = 12. Ignoring place value when computing partial products leads to incorrect final answers.
How do you find partial products using place value?
Identify the value of each digit based on its position. Multiply the full values, not just the digits. For the 8 in 418 (tens place) and the 6 in 62 (tens place): the values are 80 and 60, so the partial product is 80 × 60 = 4800.
What chapter covers multiplying by place value in Illustrative Mathematics Grade 5?
Multiplying by place value is covered in Chapter 4 of Illustrative Mathematics Grade 5, titled Wrapping Up Multiplication and Division with Multi-Digit Numbers.
What is a common error when computing partial products?
A common error is using just the digit (face value) instead of the full place value. For example, seeing 4 in the tens position and multiplying 4 × something instead of 40 × something, giving answers 10 times too small.
What is an example of multiplying by place value?
For 245 × 35: the 4 in 245 is worth 40 (tens place). The 3 in 35 is worth 30 (tens place). The partial product for these two digits is 40 × 30 = 1200, not 4 × 3 = 12.