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# Calculator Trouble

Alignments to Content Standards: 5.NF.B.5

Luke had a calculator that will only display numbers less than or equal to 999,999,999. Which of the following products will his calculator display? Explain.

1. $792 \times 999,999,999$
2. $\frac12 \times 999,999,999$
3. $\frac{15}{4} \times 999,999,999$
4. $0.67 \times 999,999,999$

## IM Commentary

Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

## Solution

Since multiplying a positive number by a factor greater than 1 always results in a larger number, the first and third products will be too large to display.

Since multiplying a positive number by a factor less than 1 (but greater than zero) always results in a smaller number, the second and fourth products will be displayed on his calculator.