How this calculator works
The partial products method splits each factor into its place values. For 34 × 26 the split is (30 + 4) × (20 + 6). Every term of the first bracket multiplies every term of the second, giving four small products instead of one large one. Adding the four products gives the full answer. The same grid appears in the area model, where each cell holds one partial product.
Formula
a × b = Σ (aᵢ × bⱼ), where aᵢ and bⱼ are the nonzero place-value parts of a and b. In expanded form, 34 × 26 = 30 × 20 + 30 × 6 + 4 × 20 + 4 × 6.
Worked example
34 × 26: the partial products are 30 × 20 = 600, 30 × 6 = 180, 4 × 20 = 80 and 4 × 6 = 24. Their sum is 600 + 180 + 80 + 24 = 884.
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Frequently asked questions
Is partial products the same as long multiplication?
They rest on the same place-value idea but write the work differently. Long multiplication records one row per digit of the lower factor and carries between columns; partial products writes each place-value pair openly and adds at the end.
What happens with a zero digit?
A zero place value contributes zero to every product, so this calculator leaves it out of the list. The total is unchanged. If either factor is zero the whole product is zero.
Can I multiply decimals?
Not here. This tool is limited to whole numbers so the place values stay visible. For decimal multiplication, multiply the digit strings and place the decimal point afterwards.