Year 6 Arithmetic (SATs): Multiplying by a two-digit number
Part of the Year 6 Arithmetic (SATs) multiplication and division chapter. Chapter overview · whole chapter on one page
Multiplying by a two-digit number
Rule
In long multiplication, multiply by the ones digit, then by the tens digit (which is worth ten times as much). Write each answer as a partial product, then add the partial products.
Commutativity: 24 × 4836 gives the same answer as 4836 × 24, so you can choose the easier order.
Key ideas
- Multiply by the ones digit, then by the tens digit.
- Each partial product for the tens digit ends in a zero.
- Add the partial products to get the answer.
- Estimate first: round each number to see whether the answer is about right.
Method. Work out two partial products and add them.
- Multiply by the ones digit of 24, which is 4 (4). Write the partial product, and put a zero in each empty column below it.4,836 × 4 = 19,344
- Multiply by the tens digit of 24, which is 2 (20). Write the partial product, and put a zero in each empty column below it.4,836 × 20 = 96,720
- Add the partial products. Line up the place values and add.19,344 + 96,720 = 116,064
- Write the answer. 116,064
Check. About 5,000 × 24 = 120,000, close to 116,064. ✓
Watch out. The tens partial product is ten times bigger, so it has a zero in the ones column.
Method. Multiply by the ones digit, then the tens digit, then add.
- Multiply by the ones digit of 36, which is 6 (6). Write the partial product, and put a zero in each empty column below it.307 × 6 = 1,842
- Multiply by the tens digit of 36, which is 3 (30). Write the partial product, and put a zero in each empty column below it.307 × 30 = 9,210
- Add the partial products. Line up the place values and add.1,842 + 9,210 = 11,052
- Write the answer. 11,052
Check. About 300 × 36 = 10,800, close to 11,052. ✓
Watch out. Do not forget the empty tens column: the zero in 307 must be multiplied too.
Method. Multiply by 8, then by 10, then add the two partial products.
- Multiply by the ones digit of 18, which is 8 (8). Write the partial product, and put a zero in each empty column below it.2,015 × 8 = 16,120
- Multiply by the tens digit of 18, which is 1 (10). Write the partial product, and put a zero in each empty column below it.2,015 × 10 = 20,150
- Add the partial products. Line up the place values and add.16,120 + 20,150 = 36,270
- Write the answer. 36,270
Check. 36,270 ÷ 18 = 2,015. ✓
Exercise 2B Practice: multiplying by a two-digit number
Non-calculatorMethod. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 14, which is 4 (4). Write the partial product, and put a zero in each empty column below it.58 × 4 = 232
- Multiply by the tens digit of 14, which is 1 (10). Write the partial product, and put a zero in each empty column below it.58 × 10 = 580
- Add the partial products. Line up the place values and add.232 + 580 = 812
- Write the answer. 812
Check. Estimate: 100 × 10 is about 1,000, close to 812. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 26, which is 6 (6). Write the partial product, and put a zero in each empty column below it.73 × 6 = 438
- Multiply by the tens digit of 26, which is 2 (20). Write the partial product, and put a zero in each empty column below it.73 × 20 = 1,460
- Add the partial products. Line up the place values and add.438 + 1,460 = 1,898
- Write the answer. 1,898
Check. Estimate: 100 × 30 is about 3,000, close to 1,898. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 35, which is 5 (5). Write the partial product, and put a zero in each empty column below it.406 × 5 = 2,030
- Multiply by the tens digit of 35, which is 3 (30). Write the partial product, and put a zero in each empty column below it.406 × 30 = 12,180
- Add the partial products. Line up the place values and add.2,030 + 12,180 = 14,210
- Write the answer. 14,210
Check. Estimate: 400 × 40 is about 16,000, close to 14,210. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 48, which is 8 (8). Write the partial product, and put a zero in each empty column below it.912 × 8 = 7,296
- Multiply by the tens digit of 48, which is 4 (40). Write the partial product, and put a zero in each empty column below it.912 × 40 = 36,480
- Add the partial products. Line up the place values and add.7,296 + 36,480 = 43,776
- Write the answer. 43,776
Check. Estimate: 900 × 50 is about 45,000, close to 43,776. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 18, which is 8 (8). Write the partial product, and put a zero in each empty column below it.2,015 × 8 = 16,120
- Multiply by the tens digit of 18, which is 1 (10). Write the partial product, and put a zero in each empty column below it.2,015 × 10 = 20,150
- Add the partial products. Line up the place values and add.16,120 + 20,150 = 36,270
- Write the answer. 36,270
Check. Estimate: 2,000 × 20 is about 40,000, close to 36,270. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 27, which is 7 (7). Write the partial product, and put a zero in each empty column below it.1,384 × 7 = 9,688
- Multiply by the tens digit of 27, which is 2 (20). Write the partial product, and put a zero in each empty column below it.1,384 × 20 = 27,680
- Add the partial products. Line up the place values and add.9,688 + 27,680 = 37,368
- Write the answer. 37,368
Check. Estimate: 1,400 × 30 is about 42,000, close to 37,368. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 63, which is 3 (3). Write the partial product, and put a zero in each empty column below it.562 × 3 = 1,686
- Multiply by the tens digit of 63, which is 6 (60). Write the partial product, and put a zero in each empty column below it.562 × 60 = 33,720
- Add the partial products. Line up the place values and add.1,686 + 33,720 = 35,406
- Write the answer. 35,406
Check. Estimate: 600 × 60 is about 36,000, close to 35,406. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 41, which is 1 (1). Write the partial product, and put a zero in each empty column below it.3,207 × 1 = 3,207
- Multiply by the tens digit of 41, which is 4 (40). Write the partial product, and put a zero in each empty column below it.3,207 × 40 = 128,280
- Add the partial products. Line up the place values and add.3,207 + 128,280 = 131,487
- Write the answer. 131,487
Check. Estimate: 3,200 × 40 is about 128,000, close to 131,487. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 12, which is 2 (2). Write the partial product, and put a zero in each empty column below it.4,096 × 2 = 8,192
- Multiply by the tens digit of 12, which is 1 (10). Write the partial product, and put a zero in each empty column below it.4,096 × 10 = 40,960
- Add the partial products. Line up the place values and add.8,192 + 40,960 = 49,152
- Write the answer. 49,152
Check. Estimate: 4,100 × 10 is about 41,000, close to 49,152. ✓
Method. Use partial products, one for each digit of the two-digit number.
- Multiply by the ones digit of 85, which is 5 (5). Write the partial product, and put a zero in each empty column below it.719 × 5 = 3,595
- Multiply by the tens digit of 85, which is 8 (80). Write the partial product, and put a zero in each empty column below it.719 × 80 = 57,520
- Add the partial products. Line up the place values and add.3,595 + 57,520 = 61,115
- Write the answer. 61,115
Check. Estimate: 700 × 80 is about 56,000, close to 61,115. ✓
Method. Multiply the rows by the seats in each row.
- Multiply by the ones digit of 24, which is 4 (4). Write the partial product, and put a zero in each empty column below it.35 × 4 = 140
- Multiply by the tens digit of 24, which is 2 (20). Write the partial product, and put a zero in each empty column below it.35 × 20 = 700
- Add the partial products. Line up the place values and add.140 + 700 = 840
- Write the answer. 840
Check. 840 ÷ 24 = 35. ✓
Method. Multiply the pencils in one box by the number of boxes.
- Multiply by the ones digit of 27, which is 7 (7). Write the partial product, and put a zero in each empty column below it.36 × 7 = 252
- Multiply by the tens digit of 27, which is 2 (20). Write the partial product, and put a zero in each empty column below it.36 × 20 = 720
- Add the partial products. Line up the place values and add.252 + 720 = 972
- Write the answer. 972
Check. Estimate: 40 × 30 = 1,200, close to 972. ✓
Method. Find the correct answer by long multiplication.
- Multiply by 2. 45 × 2 = 90.45 × 2 = 90
- Multiply by 10. 45 × 10 = 450.45 × 10 = 450
- Add the partial products. Sam left out the 45 × 2 part.450 + 90 = 540
- Write the answer. 540
Check. Sam is wrong: the answer is 540. ✓
Watch out. A two-digit multiplier needs two partial products.