Question

create 1 smaller friendly equations to solve 3347 / 7 using multiples of 7 and a number less than 106

Answer 1

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.

1. We know that \(7 \times 400 = 2800\) (which is a friendly number).
2. Now, we can find how much more we need to reach 3347:
\[
3347 - 2800 = 547
\]
3. 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:
\[
3347 \div 7 = 478 \quad (\text{with a remainder of } 1)
\]