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The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Two-digit divisor in long division
Free lesson plan from HomeschoolMath.net

When the divisor has two digits, the procedure works the same way but instead of using facts from multiplication tables when dividing, we might have to use pencil and paper to perform helping multiplications on the side, so to speak.      14    7  4  3  4  14 goes into 7 zero times, so we look at 74. To find how many times does 14 go into 74, you probably have to do several guesses. Check until you find the maximum number of times that 14 goes into 74. 2 × 14 = 28 4 × 14 = 56            5 × 14 = 70 6 × 14 = 84 From this we can see that 14 goes into 74 five times. 5 14    7  4  3  4  -  7  0 4 3 Now the question is how many times does 14 go into 43. 2 × 14 = 28  3 × 14 = 42  4 × 14 = 56, so it is three times.   5 3 1 14  7  4  3  4  - 7  0 4 3 - 4 2 1 4       At this point it is easy: how many times does 14 go into 14?  That is exactly once, so the division is exact and over.       1    531 ×  14 2124 5310 7434 The check confirms our result.

Example problems

1.  Divide using long division.  Use the extra empty space for any multiplications you need to do.  Finally check your division by multiplication.

15   8 7 6 0       ×  15

When the divisor is a multiple of ten (that is, 20, 30, 40, etc.), the division is easier because it is easier to perform the helping multiplications.        3 20    6  4  4  0    20 goes into 6 zero times, so we look at 64. We know that 3 × 20 = 60 and 4 × 20 = 80 so 20 goes into 64 three times.   3 2 20    6  4  4  0  - 6  0 4 4 Now how many times does 20 go into 44?  Again, answer is easy since 2 × 20 = 40 and 3 × 20 = 60.     3 2 2 20    6  4  4  0  - 6  0 4 4 - 4  0 4 0       Lastly we know 20 goes into 40 exactly two times.           322 ×  20 000 6440 6440 The check confirms our result.

2.  Divide using long division.  Do the divisions in your notebook, and record the results here.  Remember to check each one by multiplication!

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