8 junio, 2024

Solved 2-digit divisions

The divisions of two digits are carried out in a similar way to the divisions of one digit. With the help of the following examples the method is illustrated.

1. 36 will be divided by 12

– Both digits of 36 are chosen, since 36 ≥ 12.

– Find a number that, when multiplied by 12, the result is close to 36. You can make a short list: 12*1=12, 12*2=24, 12*3=36, 12*4=48. By choosing 4, the result exceeded 36, therefore, 3 is chosen.

– Subtracting 36-12*3 gives 0.

– All digits of the dividend have already been used.

The result of the division 36÷12 is 3.

2. Divide 96 by 24

– Both digits of 96 must be chosen.

– After investigating it can be seen that 4 should be chosen, since 4*24=96 and 5*24=120.

– By subtracting 96-96 you get 0.

– All 96 digits have already been used.

The result of 96÷24 is 4.

3. Divide 120 by 10

– The first two digits of 120 are chosen; that is, 12, since 12 ≥ 10.

– You must take 1, since 10*1=10 and 10*2=20.

– By subtracting 12-10*1 you get 2.

– Now the previous result is joined with the third figure of 120, that is, 2 with 0. Therefore, the number 20 is formed.

– A number is chosen that when multiplied by 10 is close to 20. This number must be 2.

– Subtracting 20-10*2 gives 0.

– All the figures of 120 have already been used.

The result is 120÷10=12.

4. Divide 465 by 15

– 46 is chosen.

– After making the list, it can be concluded that 3 must be chosen, since 3*15=45.

– Subtract 46-45 and get 1.

– By joining 1 with 5 (third digit of 465), you get 45.

– Choose 1, since 1*45=45.

– Subtract 45-45 and get 0.

– All the figures of 465 have already been used.

The result is 465÷15=31.

5. Divide 828 by 36

– Choose 82 (only the first two digits).

– 2 is taken, since 36*2=72 and 36*3=108.

– Subtract 82 minus 2*36=72 and get 10.

– By joining 10 with 8 (third digit of 828) the number 108 is formed.

– Thanks to step two, it can be known that 36*3=108, therefore, 3 is chosen.

– Subtracting 108 from 108 gives you 0.

– All the figures of 828 have already been used.

The result is 828÷36=23.

Observation

In the previous divisions the final subtraction always resulted in 0, but this is not always the case. This happened because the divisions raised were exact.

When the division is not exact, decimal numbers appear, which must be learned in detail.

If the dividend has more than 3 digits, the division process is the same.

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