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To multiply \(237\) by \(4\) without using a calculator, you can set it out like this:

1. Start with \(4\times7\), which is \(28\), so write the \(8\) and carry the \(2\) to the tens column.
2. \(4 \times 3 = 12\), but remember to add the carried \(2\) to get \(14\). Write the \(4\) and carry the \(1\) to the hundreds column.
3. \(4 \times 2 = 8\), and we add the carried \(1\) to get \(9\).

Therefore \(237 \times 4 = 948\)

To multiply \(237\) by \(24\) without using a calculator, you can set it out like this:

1. The first line of the calculation is the same procedure as multiplying with a single digit number.
2. In the second line we are multiplying by \(20\) (two tens). As we are multiplying by tens the unit's digit will always be a zero.
3. In a similar procedure to above:- \(2 \times 7 = 14\). Put the \(4\) in the tens column and carry the \(1\) to the hundreds column.
4. \(2 \times 3 = 6\) - add the carried \(1\) to get \(7\) and put this in the hundreds column.
5. \(2 \times 2 = 4\), nothing has been carried so put the \(4\) in the thousands column.
6. Add \(948\) and \(4740\).

Therefore \(237 \times 24 = 5668\)