99 groups are one fewer than 100
To multiply a number by 99, multiply it by 100 and subtract the original number. You have made 100 equal groups, then removed one whole group.
For 36 × 99, start with 36 × 100 = 3,600. Take away one group of 36: 3,600 − 36 = 3,564. It is the same grouping idea used when multiplying by nine.
Why subtract 36 instead of 1?
The 1 in 100 − 1 counts a group. Each group contains 36, so losing one group removes 36 items. Subtracting only 1 would leave 3,599, which is much too close to the full 100 groups.
Written as one line, 36 × (100 − 1) = 36 × 100 − 36 × 1. This is an example of the distributive property explained by OpenStax: multiplication applies to both parts inside the brackets.
Two more numbers, the same idea
For 7 × 99, work out 700 − 7 = 693. For 75 × 99, use 7,500 − 75 = 7,425.
You can split the last subtraction if it helps: 7,500 − 70 = 7,430, then take away 5 more. That leaves 7,425. The method changes the calculation’s shape while keeping its exact value.
Give the answer a quick size check
For a positive starting number, 99 groups must be slightly smaller than 100 groups. If your answer for 75 × 99 is larger than 7,500, stop and check the adjustment.
Once the grouping makes sense, compare it with rounding and adjusting other calculations. The useful habit is remembering exactly what you changed.