Proportional adjustment: 5x38 = (5x2)*(38/2) = 10x19 = 190 Doubling and Halving.

- Factors & Multiples. 2 is a factor of 38 and 10 is a multiple of 5.

Place value partitioning: 5x38 = 5x30 + 5x8 = 150 + 40 = 190 Split the number.

Rounding and compensation: 5x38 = 5x40 - 5x2 = 200 - 10 = 190 Tidy numbers.

Proportional adjustment: 184/8 instead of diving by 8, divide by 2, three times.

- The prime factors of 8 are 2x2x2. Sometimes call factorisation.

Place value partitioning: 184/8 = 160/8 + 24/8 = 20 + 3 = 23 Split the number.

Rounding and compensation: 184/8 = 200/8 - 16/8 = 25 - 2 = 23 Tidy numbers.

25 x 200 = (25/5) x (200x5) = 5 x 1000 = 5000 (Proportional Adjustment = P.A.)

25 x 200 = (20 + 5)x200 = 20x200 + 5x200 = 4000 + 1000 = 5000 (Place Value Partition = P.V.P.)

27 x 3 = (27/3) x (3x3) = 9 x 9 = 81 (Proportional Adjustment)

27 x 3 = (30-3)x3 = 30x3 - 3x3 = 90 -9 = 81 (Rounding and Compensating - Tidy numbers = R.A.C.)

33 x 18 = (33/3) x (18x3) = 11 x 6x3x3 = 11 x 54 = 10x54 + 1x54 = 540 + 54 = 594 (P.A.)

33 x 18 = 33 x (20 - 2) = 33x20 - 33x2 = 660 - 66 = 594 (R.A.C.)

44 x 25 = (44/4) x (25x4) = 11 x 100 = 1100 (P.A.)

24 x 125 = (24/8) x (125x8) = 3 x 1000 = 3000 (P.A.)

24 x 125 = 3 x 2 x 2 x 2 x 25 x 5 = (25 x 2 x 2) x (3 x 2 x 5) = 100 x 30 = 3000 (P.A.)

125 x 24 = 125 x 2 x 2 x 2 x 3 = 250 x 2 x 2 x 3 = 500 x 2 x 3 = 1000 x 3 = 3000 (P.A.)