الأسبوع 7 · الطريقة المعتادة لضرب الأعداد متعددة الأرقام · 3 دروس
2
Four digits times two digits
Discover Mathematics P5: Term 1, Unit 3, Lessons 5–7
GoalMultiply a four-digit number by a two-digit number and check the answer with an estimate.
New words
estimate · a quick answer found with rounded numberscompatible numbers · rounded numbers that are easy to multiply, like 4,000 and 50
Explanation
The standard algorithm works with any size of number: more digits only mean more carrying and a bigger answer. To multiply 2,483 × 36, multiply by the 6 ones, 2,483 × 6 = 14,898, then by the 3 tens, 2,483 × 30 = 74,490, and add: 14,898 + 74,490 = 89,388. Keep every digit in its column, and write small carries above the next place. Always estimate first with compatible numbers: 2,483 is close to 2,500 and 36 is close to 40, so the answer should be near 2,500 × 40 = 100,000. The exact answer 89,388 is a bit smaller because we rounded both numbers up.
Multiply 4,075 × 28. 4,075 × 8 = 32,600 and 4,075 × 20 = 81,500. Add: 32,600 + 81,500 = 114,100. A farm with 4,075 date palms, each giving 28 kg of dates, collects 114,100 kg.
Check 3,918 × 47 with an estimate. 4,000 × 50 = 200,000. The exact answer: 3,918 × 7 = 27,426 and 3,918 × 40 = 156,720, so 27,426 + 156,720 = 184,146. It is a little under 200,000, as expected.
Class activity
Big product hunt. Write a four-digit number and a two-digit number on cards. Estimate the product first and write it down. Then multiply exactly. The estimate should be within 10 percent of the answer. Try three different pairs and keep a score of how close your estimates are.
