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E.3 Divide numbers ending in zeros: word problems

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What does it mean to divide numbers ending in zeros?

Dividing numbers ending in zeros is a method for simplifying division problems when both the dividend (the number being divided) and the divisor (the number you are dividing by) end in one or more zeros. You can cancel an equal number of zeros from the end of both numbers to make the calculation easier.

Examples:
  • 2,400 ÷ 60 = 240 ÷ 6
  • 35,000 ÷ 700 = 350 ÷ 7
  • 180,000 ÷ 3,000 = 180 ÷ 3
Note

This strategy works because you are essentially dividing both numbers by 10, 100, or 1,000, which does not change the answer.

How do you simplify the division?

To simplify, count the number of zeros at the end of both the dividend and the divisor. Cancel the same number of zeros from the end of both numbers before dividing.

Steps:
  • Look at the problem: 4,500 ÷ 90
  • Identify the zeros: The dividend has two zeros, the divisor has one.
  • Cancel one zero from both: 4,500 becomes 450, 90 becomes 9.
  • Solve the simpler problem: 450 ÷ 9 = 50
Note

You can only cancel zeros when both numbers end in them. Always cancel an equal number from both.

Applying the skill to word problems

In word problems, you first need to identify the numbers involved and set up the division equation. Then, you can apply the zero-canceling strategy to find the solution efficiently.

Example problem:
  • "A factory produced 32,000 toys and packaged them into boxes of 800. How many boxes were used?"
  • Set up the equation: 32,000 ÷ 800
  • Cancel two zeros from both numbers: 32,000 ÷ 800 becomes 320 ÷ 8
  • Solve: 320 ÷ 8 = 40 boxes
Note

Always read the word problem carefully to ensure you are dividing the correct numbers in the correct order.

Why is this a useful strategy?

This strategy makes mental math and long division much faster and less prone to error by working with smaller, more manageable numbers.

Comparing methods:
  • Without simplifying: 5,600 ÷ 80 (This requires long division).
  • With simplifying: Cancel one zero: 560 ÷ 8 = 70 (This is a basic fact).
Note

This is not a trick; it is a valid mathematical property based on place value. The quotient (answer) remains the same.