Place-value explanation
Why does the second partial product shift left?
The second row shifts because it represents multiplication by tens. In 34 × 26, the 2 means 20, not 2. The zero is a result of place value, not an extra step added to the calculation.
Grades 4–5 · worked example · 3 practice checks
01
Recognize the problem first
- Read 26 as 20 + 6.
- The first row records 34 × 6.
- The second row records 34 × 20, so every digit has ten times the value of 34 × 2.
02
Work through one complete example
Question
Explain the two rows in 34 × 26.
- Decompose 26 into 20 + 6.
- Calculate 34 × 6 = 204.
- Calculate 34 × 20 = 680, then combine 204 + 680.
AnswerThe shifted row is 680 because it represents 34 groups of 20, or 34 × 20.
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03
Common mistakes to catch
- Saying “just add a zero” without connecting the zero to the tens place.
- Writing 68 as the second partial product and adding it as though it were 680.
- Starting the tens row in the ones column.
0401 02 03
Try three quick checks
In 42 × 31, what does the 3 represent?
Show answer
30What is the tens partial product in 27 × 43?
Show answer
27 × 40 = 1,080Complete: 56 × 24 = 56 × ___ + 56 × 4.