Revision of multiplication and Division

You can probably already multiply two numbers together and divide one number by another. However, if you need a revision then the following worked problems should be helpful. 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 2 in the units (U) column and ‘carry’ the 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. Confidence with handling numbers will be greatly 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 2 in the units column and carry 3 into the tens column.
2. 8 × 6 = 48; 48 + 3 (carried) = 51. Place the 1 in the tens column and carry the 5 into the hundreds column.
3. 8 × 7 = 56; 56 + 5 (carried) = 61. Place 1 in the hundreds column and 6 in the thousands column.
4. Place 0 in the units column under the 2.
5. 3 × 4 = 12. Place the 2 in the tens column and carry 1 into the hundreds column.
6. 3 × 6 = 18; 18 + 1 (carried) = 19. Place the 9 in the hundreds column and carry the 1 into the thousands column.
7. 3 × 7 = 21; 21 + 1 (carried) = 22. Place 2 in the thousands column and  2 in the ten thousand columns.
8. 6112 + 22920 = 29032

Hence, 764 × 38 = 29032

Again, knowing multiplication tables is rather important when multiplying such numbers.

It is appreciated, of course, that such a multiplication can, and probably will be performed using a calculator.
However, there are times when a calculator may not be available and it is then useful 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 3 of 1834 and carry the 1 remainder to the next digit on the right, making it 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 57 goes 4; place 4 above the 7 of 5796.
2. 4 × 12 = 48; place the 48 below the 57 of 5796.
3. 57 − 48 = 9.
4. Bring down the 9 of 5796 to give 99.
5. 12 into 99 goes 8; place 8 above the 9 of 5796.
6. 8 × 12 = 96; place 96 below the 99.
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