Lesson 2: Comparing Large Numbers

What is an Unknown Factor?

When we compare two numbers, we sometimes want to know how many times bigger one number is compared to another. To do this, we set up an equation called the unknown factor equation.

We write:
smaller number × ? = bigger number

The question mark (?) is the unknown factor. To find it, we divide the bigger number by the smaller number.

Example:

Compare 9 billion and 300.
300 × ? = 9,000,000,000.
? = 9,000,000,000 ÷ 300 = 30,000,000.
So, 9 billion is 30 million times as much as 300.

Examples

1. How many times is 9,000,000,000 as much as 300?
9,000,000,000 ÷ 300 = 30,000,000. Answer: 30,000,000 times.

2. How many times is 9,000,000,000 as much as 3,000?
9,000,000,000 ÷ 3,000 = 3,000,000.

3. How many times is 9,000,000 as much as 3,000,000?
9,000,000 ÷ 3,000,000 = 3.

4. What number is 3,000 times as much as 30?
30 × 3,000 = 90,000.

5. Compare 50,800,000 and 11,400,000.
50,800,000 ÷ 11,400,000 ≈ 4.46.

6. Compare 22,460,468,000,000 and 16,100,000,000,000.
22,460,468,000,000 ÷ 16,100,000,000,000 ≈ 1.4.

7. Compare 19,542,209 and 8,398,748.
19,542,209 ÷ 8,398,748 ≈ 2.3.

8. Compare 33.1 billion and 1.629 billion.
33.1 ÷ 1.629 ≈ 20.3.

9. How many times is 600 as much as 30?
600 ÷ 30 = 20.

10. How many times is 8,000 as much as 40?
8,000 ÷ 40 = 200.

11. How many times is 120,000 as much as 600?
120,000 ÷ 600 = 200.

12. How many times is 450 as much as 15?
450 ÷ 15 = 30.

13. What number is 25 times as much as 40?
25 × 40 = 1,000.

14. What number is 120 times as much as 50?
120 × 50 = 6,000.

15. A country has 300 million people. Another has 100 million. How many times as much?
300 ÷ 100 = 3.

16. A city has 2,400 buses. A town has 600. How many times as much?
2,400 ÷ 600 = 4.

17. A jar has 48 marbles. Another has 12. How many times as much?
48 ÷ 12 = 4.

18. A school has 900 students. A class has 30. How many times as much?
900 ÷ 30 = 30.

19. The US national debt is 30 trillion dollars. A family’s debt is 60,000 dollars. How many times as much?
30,000,000,000,000 ÷ 60,000 = 500,000,000.

20. Bacteria appeared 4,000,000,000 years ago. Insects appeared 400,000,000 years ago. How many times earlier?
4,000,000,000 ÷ 400,000,000 = 10.