Question

To start dividing 126 by 23, Miranda used the estimate 120÷20 = 6. How could you tell six is too high?

Answer 1

the product of 6 and 23 is more than 126

Explanation:

You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.

Trial dividend

When the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.

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Additional comment

Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.