Missing factors, step by step

A missing factor turns a times-table fact into a division question without ever printing a division sign.

The question

4 × ? = 32

4×?=32
4×?=32
32÷4=8
4×8=32
  1. The gap is not at the end this time — the ANSWER is already there. What is missing is one of the two numbers going in, so the sum cannot just be worked left to right.
  2. Counting in 4s would take too long here, so undo the multiplying instead: 4 of something makes 32, so the something is 32 shared into 4.
  3. Put it back in to be sure: 4 × 8 = 32. It holds, so the missing number is 8.

How it works.

  1. 01

    The gap is not at the end this time — the ANSWER is already there. What is missing is one of the two numbers going in, so the sum cannot just be worked left to right.

  2. 02

    Counting in 4s would take too long here, so undo the multiplying instead: 4 of something makes 32, so the something is 32 shared into 4.

  3. 03

    Put it back in to be sure: 4 × 8 = 32. It holds, so the missing number is 8.