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The student uses the order, one and zero properties to fill blanks without computing anything.
Preview · progress not saved — Chapter 1 is free
Swap the two numbers around and the product does not change.
Look at these two equations: and . We get the exact same answer regardless of which number comes first. The same happens with and —both give .
Four order-property blanks from Worksheet 2.
We can use the order property of multiplication to solve these quickly. If 4 × 56 = 224, then 56 × 4 must also equal . Similarly, if 73 × 12 = 876, we know without calculating that 12 × 73 equals . When we see 925 × 213, it is exactly the same as 213 × . Finally, for the equation 621 × 127 = × 621, we simply check which number is missing on the left side to keep it balanced.
Multiply two of them first, then multiply that answer by the third.
In order to multiply three numbers, first we multiply two of them, and then multiply the product obtained by the third number.
Let's look at the example .
How to fill an equation with a missing number on each side.
Problem. Fill in the missing factors on both sides without doing any multiplication calculations.
Three property blanks from Worksheet 2, two with blanks on both sides.
Let's practice balancing multiplication equations. For the equation × 615 = × 713, both sides must contain the exact same factors. Next, if we know that 43 × 2 × 4 = 344, then reordering it as 2 × 43 × 4 must also equal . Finally, look at 11 × × 42 = × 42 × 56. By identifying the full set of three numbers, we can find the missing factors on each side without having to calculate the final product.
One leaves a number alone; zero flattens everything to nothing.
Notice what happens here: and .
Remember: The product of a number and 1 is the number itself.