explain how you can tell without multiplying that 700 * 60,000 and
7,000 * 6,000 have the same value.
count the zeros in both problems.
Count the number of zeros in each problem and then multiply 6 * 7
To determine whether the values of 700 * 60,000 and 7,000 * 6,000 are the same without actually multiplying them, we can apply a property of multiplication called the commutative property.
The commutative property of multiplication states that the order of the factors does not affect the product. In other words, when multiplying two numbers, you can switch their positions without changing the result.
To apply this property, we can rewrite the given multiplication expressions by swapping the positions of the factors:
700 * 60,000 = 60,000 * 700
7,000 * 6,000 = 6,000 * 7,000
Now, we can observe that these two expressions are essentially the same. The first factor in each multiplication expression is the same (7 or 60) and the second factor in each expression is also the same (6,000 or 60,000), albeit in a different order.
Since the commutative property tells us that switching the order of the factors doesn't change the product, we can conclude that 700 * 60,000 and 7,000 * 6,000 have the same value without actually multiplying them.