الأسبوع 7 · الطريقة المعتادة لضرب الأعداد متعددة الأرقام · 3 دروس
1
The standard algorithm for multiplying
Discover Mathematics P5: Term 1, Unit 3, Lessons 5–7
GoalMultiply by a two-digit number with the standard algorithm, writing two rows and adding them.
New words
algorithm · a set of steps that always works for a type of calculationcarry · a digit written above the next place when a column is 10 or moreplace holder zero · the 0 written in the ones place of the second row
Explanation
The standard algorithm is the partial-products method written in a short, tidy way. To work out 346 × 27, write 27 under 346 with ones under ones. First multiply 346 by the 7 ones: 346 × 7 = 2,422, carrying when a product is 10 or more. Then multiply 346 by the 2 tens. Because this digit is worth 20, begin the row with a 0 in the ones place, then write 346 × 2 = 692 to its left: 6,920. The zero is a place holder; it keeps the digits in their right places. Finally add the two rows: 2,422 + 6,920 = 9,342. Before you start, estimate: 346 × 27 is close to 350 × 30 = 10,500.
Ten thousands
Thousands
Hundreds
Tens
Ones
346
3
4
6
× 27
2
7
346 × 7
2
4
2
2
346 × 20
6
9
2
0
Sum
9
3
4
2
Worked examples
Thousands
Hundreds
Tens
Ones
58
5
8
× 36
3
6
58 × 6
3
4
8
58 × 30
1
7
4
0
Sum
2
0
8
8
Multiply 58 × 36. Row 1: 58 × 6 = 348. Row 2: 58 × 30 = 1,740 (58 × 3 = 174, then a 0). Add: 348 + 1,740 = 2,088. Estimate: 60 × 40 = 2,400, so the answer is reasonable.
A zero inside a number needs care. 306 × 24: Row 1: 306 × 4 = 1,224. Row 2: 306 × 20 = 6,120. Add: 1,224 + 6,120 = 7,344. The 0 in 306 gives 0 × 4 = 0 in the tens place, plus any carry.
Class activity
Algorithm race. Two players choose a three-digit and a two-digit number with number cards and each multiplies with the standard algorithm on squared paper, one digit in each square. The faster correct answer scores a point. Check by an estimate first.
Practice
1
Multiply 45 × 23.
45 × 3 = 135 and 45 × 20 = 900. Sum: 1,035.
2
Multiply 128 × 14.
128 × 4 = 512 and 128 × 10 = 1,280. Sum: 1,792.
3
Multiply 560 × 32.
56 × 32 = 1,792, then one zero: 17,920.
4
Multiply 304 × 25.
304 × 5 = 1,520 and 304 × 20 = 6,080. Sum: 7,600.
5
In 72 × 35 the second row is 2,160. Why does it end in 0, and what is the whole product?
The second row is 72 × 30, the tens digit is worth 30, so the row ends in 0. The first row is 72 × 5 = 360. Product: 360 + 2,160 = 2,520.
