To solve \(3347 \div 7\) using smaller, friendly equations with multiples of 7, we can break it down. First, we can find the closest multiple of 7 that is less than 3347, while making a smaller addition to reach the full number.
- We know that \(7 \times 400 = 2800\) (which is a friendly number).
- Now, we can find how much more we need to reach 3347: \[ 3347 - 2800 = 547 \]
- We can break down \(547\) using smaller multiples of \(7\): \[ 7 \times 78 = 546 \] (because \(546\) is the largest multiple of \(7\) under \(547\).)
Now we add these two equations: \[ 3347 = 2800 + 546 + 1 \] Which can be expressed in terms of \(7\): \[ 3347 = (7 \times 400) + (7 \times 78) + 1 \]
To convert this back to the division:
- Calculate \(400 + 78\) gives \(478\),
- And we know we have that extra \(1\).
So, we have: \[ 3347 \div 7 = 478 + \left(\frac{1}{7}\right) \]
The friendly equations illustrate that you can work with smaller parts leading to the solution, hence showing: \[ 3347 \div 7 = 478 \quad (\text{with a remainder of } 1) \]