Split at the ten
An array has 7 rows with 13 squares in each row. The number of squares is 13 × 7, and 13 × 7 is not a fact in the times tables. But 13 is 10 + 3, so every row can be split into 10 squares and 3 squares.
Start with the tens: 7 rows of 10 squares make 10 × 7 = 70.
The array has 7 rows of 13. The gold part is 7 rows of 10, which is 70 squares.
Then the rest, then together
The rest of each row is 3 squares, and there are 7 rows of them: 3 × 7 = 21. Add the two parts: 70 + 21 = 91. So 13 × 7 = 91.
Splitting does not change the answer. Every square in the array is in the gold part or in the rest, and no square is in both, so the two parts together count every square once.
The gold part is 70 squares and the white part is 21 squares. Together they make 91.
7 × 13 = 7 × 4 + 7 × 9 = 91: the cut moves squares from one part to the other, so the total stays
Cut the 13 columns after 10
Wherever the cut goes, the two parts add up to 91. The cut after 10 is the easy one: 7 × 10 = 70 needs no working.
Tens and ones
Any two-digit number splits into its tens and its ones. For 6 × 34, split 34 into 30 + 4. Then 6 × 30 = 180, because 6 × 3 = 18 and multiplying by 10 moves each digit one place to the left. Next, 6 × 4 = 24. Add the parts: 180 + 24 = 204.
Both parts are multiplied. Multiplying the tens and then only adding the ones gives 180 + 4 = 184, which counts one 4 when there are six of them.
46 × 10 = 460: the anchor alone, a shift of one place with no correction strip
Drag M to 12 and read the two strips added on top
The gold block is 10 rows of 46, which is 460. Drag the top edge up to 12 rows: the strip added on top is 2 rows of 46, so 46 × 12 = 460 + 92 = 552.
Worked example: Rows of Seats Split into Tens and Ones
Question A hall has 6 rows of seats with 34 seats in each row. In every row the first 30 seats are blue and the last 4 seats are red. (a) How many blue seats are there? (b) How many seats are there altogether?
1.Split 34 into 30 and 4. Each row has 30 blue seats and 4 red seats.
Each row of 34 seats is 30 blue seats and 4 red seats. 2.(a) 6 × 3 = 18, so 6 × 30 = 180. There are 180 blue seats.
(a) 6 × 30 = 180 blue seats. 3.Multiply the other part: there are 6 × 4 = 24 red seats.
The red part is 6 × 4 = 24 seats. 4.(b) Add the two parts: 180 + 24 = 204. There are 204 seats altogether.
(b) 180 + 24 = 204 seats altogether.
Answer: (a) 180 blue seats; (b) 204 seats
Common mistakes
- Multiplying only the tens and giving 180 as the total. The 4 red seats in each row must be multiplied by 6 as well.
- Working out 6 × 3 = 18 and 6 × 4 = 24, then adding them to get 42. The 3 in 34 stands for 3 tens, so that part is 6 × 30 = 180.
More multiplying and dividing in your head problems, worked step by step →
Just below a round number
A number just below a ten can be split the other way. 29 is 30 − 1, so seven 29s are seven 30s with 1 taken off each of them. 7 × 30 = 210, and 7 × 1 = 7 comes off: 7 × 29 = 210 − 7 = 203. In the drawing above, dragging the top edge below 10 rows takes a strip off instead of adding one.
Worked example: A Price That Is One Dollar Less Than a Round Number
Question A T-shirt costs $29. A coach buys 7 T-shirts for her team. (a) How much would 7 T-shirts cost if each one cost $30? (b) How much does the coach really pay?
1.$29 is $1 less than $30. Work with $30 first, because 30 is easy to multiply.
$29 is $1 less than $30. 2.(a) 7 × 3 = 21, so 7 × 30 = 210. At $30 each, the T-shirts would cost $210.
(a) At $30 each, 7 T-shirts would cost 7 × 30 = $210. 3.Each T-shirt really costs $1 less. So $210 is 7 × $1 = $7 too much.
Each T-shirt costs $1 less, so $210 is $7 too much. 4.(b) Take off the extra: 210 − 7 = $203. Check: 7 × 20 = 140 and 7 × 9 = 63, and 140 + 63 = 203.
(b) The coach pays 210 − 7 = $203.
Answer: (a) $210; (b) $203
Common mistakes
- Taking off only $1 and writing $209. The price was rounded up by $1 for each of the 7 T-shirts, so $7 must come off.
- Adding $7 and writing $217. The rounded price of $30 is more than the real price, so the real total is less than $210.
More multiplying and dividing in your head problems, worked step by step →