Revision of multiplication and Division

You can most likely already multiply 2 numbers together and divide one number by another. However, if you wish a revision then the subsequently worked issues should be useful. MULTIPLICATION AND DIVISION

BASIC ARITHMETIC – MATHEMATICS

Problem 1.   Determine 86 × 7

    H T U

       8 6

×       7

6  0  2

4

1. 7 × 6 = 42. Place the two (2) in the units (U) column and ‘carry’ the four (4) into the tens (T) column.
2. 7 × 8 = 56; 56 + 4 (carried) = 60. Place the 0 in the tens column and the 6  in the hundreds (H) column.

Hence, 86 × 7 = 602

A good grasp of multiplication tables is needed when multiplying such numbers; a reminder of the multiplication table up to 12 × 12 is shown above. Sureness with handling numbers will be really improved if this table is memorized. (MULTIPLICATION AND DIVISION)

HCF AND LCM

Problem 2. Determine 764 × 38

764

     ×   3 8

       6112

    22 920

    2 9032

1. 8 × 4 = 32. Place the two (2) in the units column and carry three (3) into the tens column.
2. 8 × 6 = 48; 48 + 3 (carried) = 51. Place the one (1) in the tens column and carry the five (5) into the hundreds (100) column.
3. 8 × 7 = 56; 56 + 5 (carried) = 61. Place one (1) in the hundreds column and six (6) in the thousands column.
4. Place 0 in the unit’s column under the 2.
5. 3 × 4 = 12. Place the two (2) in the tens column and carry one (1) into the hundreds column.
6. 3 × 6 = 18; 18 + 1 (carried) = 19. Place the nine (9) in the hundreds column and carry the one (1) into the thousands column.
7. 3 × 7 = 21; 21 + 1 (carried) = 22. Place two (2) in the thousands column and two (2) in the ten thousand columns.
8. 6112 + 22920 = 29032

Hence, 764 × 38 = 29032

Again, knowing multiplication tables is very necessary once multiplying such numbers.

It is appreciated, of course, that such a multiplication can, and doubtless will be performed employing a calculator. Though there are times once a calculator might not be out there and it’s then helpful to be able to calculate the ‘long way’. (MULTIPLICATION AND DIVISION)

Problem 3.   Multiply 178 by −46

When the numbers have different signs, the result will be negative. (With this in mind, the problem can now be solved by multiplying 178 by  46). Following the procedure of Problem 2 gives.

       178

   ×    46

      1068

       7120

       8188

Thus, 178 × 46 = 8188 and 178 × (−46) = −8188

Problem 4.   Determine 1834 ÷ 7

1834/7

1. 7 into 18 goes 2, remainder 4. Place the 2 above the 8 of 1834 and carry the 4 remainders to the next digit on the right, making it 43.
2. 7 into 43 goes 6, remainder 1. Place the 6 above the three (3) of 1834 and carry the one (1) remainder to the following digit on the correct, making it fourteen (14).
3. 7 into 14 goes 2, remainder 0. Place 2 above 4 of 1834.

Hence, 1834 ÷ 7 = 1834/7 = 262.

The method shown is called short division.

Problem 5.   Determine 5796 ÷ 12

        483

12^{)‾‾‾‾‾‾‾‾}

      5796

     48

       99

       96

         36

         36

         00

1. 12 into 5 won’t go. 12 into fifty-seven (57) goes four (4); place four (4) above the seven of 5796.
2. 4 × 12 = 48; place the forty eight (48) below fifty seven (57) of 5796.
3. 57 − 48 = 9.
4. Bring down the nine (9) of 5796 to provide ninety-nine (99).
5. Twelve (12) into ninety nine (99) goes eight (8); place 8 above the nine (9) of 5796.
6. 8 × 12 = 96; place ninety six (96) below the ninety nine (96).
7. 99 − 96 = 3.
8. Bring down the 6 of 5796 to give 36.
9. 12 into 36 goes 3 exactly.
10. Place the 3 above the final 6.
11. Place the 36 below the 36.
12. 36 − 36 = 0.

Hence, 5796 ÷ 12 = 5796/12 = 483.

The method shown is called long division.

This post contains the content of the book Basic Engineering Mathematics below is a link of the complete book Basic Engineering Mathematics