Week 9 · Commutative property and multiplying by tens · 3 lessons
2
Zero patterns when multiplying by tens
Discover Mathematics P4: Term 1, Unit 5, Lessons 4–8
GoalMultiply a number by 10, 100 and 1,000 and by multiples of ten using the zero pattern.
New words
place value · each place is 10 times the place to its rightmultiple of ten · a number like 20, 300 or 4,000 that ends in zerosbasic fact · a multiplication fact such as 6 × 7 = 42
Explanation
When we multiply by 10, every digit moves one place to the left, so the number is 10 times as big and a zero is written at the end: 7 × 10 = 70. For 100 we write two zeros: 7 × 100 = 700. For 1,000 we write three zeros: 7 × 1,000 = 7,000. To multiply by a multiple of ten, first use the basic fact and then count the zeros in both factors. For 30 × 200: the basic fact is 3 × 2 = 6, and there are 1 + 2 = 3 zeros, so 30 × 200 = 6,000. Be careful when the basic fact already ends in zero: 50 × 40 uses 5 × 4 = 20, and then 2 more zeros, so 2,000.
Multiply
× 1
× 10
× 100
× 1,000
7
7
70
700
7,000
12
12
120
1,200
12,000
Worked examples
Factor
1
10
100
1,000
6 ×
6
60
600
6,000
Fill in the pattern: 6 × 1 = 6, 6 × 10 = 60, 6 × 100 = 600, 6 × 1,000 = 6,000. Each step has one more zero, and each product is 10 times as big as the one before.
Product
Basic fact
Zeros
Answer
40 × 5
4 × 5 = 20
1
200
30 × 200
3 × 2 = 6
3
6,000
Find 40 × 5. The basic fact is 4 × 5 = 20. 40 is 4 tens, so 40 × 5 = 20 tens = 200. Find 30 × 200: 3 × 2 = 6, and there are three zeros in all, so 6,000.
Step
Work
1
5 × 4 = 20
2
add 2 zeros
3
50 × 40 = 2,000
Careful when the basic fact ends in zero. For 50 × 40, 5 × 4 = 20, and there are 2 more zeros from 50 and 40. So 50 × 40 = 2,000, not 200.
Class activity
Zero patterns with a calculator or paper. Pick any number from 2 to 9. Multiply it by 10, then by 100, then by 1,000. Write all the products in a column and describe what happens to the digits and the zeros. Try 25 as well.
Practice
1
Find 9 × 100 and 9 × 1,000.
900 and 9,000.
2
Find 60 × 7.
6 × 7 = 42, so 60 × 7 = 420.
3
Find 80 × 300.
8 × 3 = 24 and three zeros: 24,000.
4
Find 50 × 60.
5 × 6 = 30 and two more zeros: 3,000.
5
Marwan says 40 × 20 = 80 because 4 × 2 = 8. What did he forget?
