Multiplication Basics

Single-Digit Multiplication With a Carry

Multiply 7 × 8 = 56. The product has two digits: the ones digit (6) stays in the ones place, and the tens digit (5) becomes a carry that moves to the next column — the same carry used in long multiplication.

single-digit-carry When two single digits multiply to give a two-digit product, the tens digit "carries" to the next column. This is the building block of every multi-digit multiplication algorithm.

Example

Multiply 7 by 8 and place the carry. When a single-digit product is ten or more, it will not fit in one place-value column, so the tens part is carried into the next column to the left. Carrying is just regrouping: recording the ones digit where it belongs and passing the overflow to the higher place to be added there.

highlighted = computed this step

Step 1 — Set up

Start with the multiplication fact.

7×8=□7\times 8=\square
Set up 7 x 8multiply7 x 8--split the productproduct splits into tens and onestensones------write place valuesproduct

Step 2 — Multiply

7 x 8 = 56: write 6, carry 5.

7×8=567\times 8=56
7 x 8 = 56: write 6, carry 5multiply7 x 856split the product56 = 5 tens + 6 onestensones--6--write place valuesproduct6 ones5 tens carried

Step 3 — Place digits

Product 56: ones digit 6, carry 5 to tens.

56=10⋅5+656=10\cdot \hl{5}+\hl{6}
Place 5 tens and 6 onesmultiply7 x 856split the product56 = 5 tens + 6 onestensones56--write place valuesproduct6 ones5 tens carried

Step 4 — Result

So 7 x 8 = 56.

7×8=567\times 8=56
7 x 8 = 56multiply7 x 856split the product56 = 5 tens + 6 onestensones5656write place valuesproduct6 ones5 tens carried