Sequences: Consecutive Integers - Counting Consecutive Multiples within a Range
How many multiples of 7 are there between 700 and 1000, inclusive?
Incorrect.
[[snippet]]
Correct.
Remember the 3-step method for counting the number of multiples of $$x$$ within a range. In this case, $$x=7$$.
1. Find the relevant *extremes*—the nearest *multiples* of $$x$$ within the specified range. Clearly, 700 is the **smallest multiple** of 7 in the range.
>To find the largest multiple, start adding or subtracting multiples of 7. For example, you know that 280 is a multiple of 7. So that means $$700+280=980$$ is a multiple of 7. From there, it should be clear that $$980+14 = 994$$ is the **largest multiple** of 7 in the range.
2. Subtract the *relevant extremes* and divide by $$x$$:
>>$$\displaystyle \frac{994-700}{7} = \frac{294}{7} = 42$$.
3. *Add one*:
>>$$42+1=43$$.
43
42
22
21
20
