Before this page: know the multiplication tables to 12 × 12, be able to add in columns, and know what each digit is worth in integers and decimals.
347 × 26 is built from table facts such as 6 × 7, 6 × 4 and 2 × 3.
Multiplying by 26 is multiplying by 20 and by 6 and adding the results, and 347 splits the same way, into 300, 40 and 7.
Each of 300, 40 and 7 is multiplied by each of 20 and 6: six small multiplications.
A rectangle gives each of the six products a box of its own. 300, 40 and 7 run along the top, 20 and 6 down the side, and each box holds the product of its row and its column.
347 × 26
347 is 300 + 40 + 7. Each digit is written as the amount it stands for, so nothing about the number has changed.
The six boxes are independent and can be calculated in any order.
347 × 26
Each of the six products becomes a line in columns, its digits under the places they are worth.
The expanded calculation has six lines. The products from multiplying by 6 are 42, 240 and 1,800. The products from multiplying by 20 are 140, 800 and 6,000. We can combine each set into one row.
Every line can be checked against its box.
347 × 26
The three lines from the 6 can be added on their own, and so can the three from the 20.
Gathering the lines leaves one row for each digit of 26, and the six products are added in two stages instead of one.
The three lines that came from the 20 are 140, 800 and 6,000. Every one of them ends in a zero, because every one of them is 20 times something. Their total, 6,940, is a sum of multiples of 10, so it ends in a zero too.
347 × 2 = 694: the 4 in the ones is from 2 × 7 = 14.
Ten times as much, so the same three digits sit one place further left and a zero holds the ones.
A third digit in the multiplier is a hundreds digit, so all of its lines end in two zeros and so does its row. The pattern continues for as many digits as the multiplier has: one more zero for each place.
The short form produces those two rows without ever writing the lines that make them. Instead of 42, 240 and 1,800 written as lines, 6 × 7, 6 × 4 and 6 × 3 are written straight into one row, digit by digit. Anything too large for one column is carried into the next.
The rows are 347 × 6 and 347 × 20, and 6 + 20 = 26, so together they are 347 × 26.
Align equal place values, longer number on top.
Hold the row's place with zeros before writing in it.
Multiply every upper digit by that one lower digit.
Add the finished rows in columns.
347 × 26
26 is 2 tens and 6 ones: one row of working for each.
The six products, the two rows and the answer are unchanged. Instead of six separate lines, the carried amounts keep track of how the smaller products combine.
248 × 135 has three digits in the multiplier, so three rows, and the third starts two places further left because the 1 is worth 100. Three parts against three parts is nine products, gathered into three rows.
248 × 135
135 is 1 hundred, 3 tens and 5 ones: one row of working for each.
A fixed price for every seat makes equal groups; a length repeated across a width makes a rectangle. Both structures lead to multiplication even when the operation is not named.
A coach company charges £24 a seat and 37 seats are booked. The cost is 24 × 37 = £888.
Anything counted in equal amounts has this shape: boxes of the same size, wages for the same hourly rate, identical parts on an order.
A worktop is 246 cm long and 84 cm deep. Both measurements are in the same unit, so its area is in that unit squared: 246 cm × 84 cm = 20,664 cm².
The equal-group or rectangular structure—not one keyword—makes multiplication appropriate. The context also supplies the answer's unit, which the columns alone cannot give.
38 is 3 tens and 8 ones: one row of working for each.