Maths Tricks and Shortcuts , Two Numbers that Differ by an Odd Number: a < b and c = [1 + (b – a)]/2

Mental Math with Tricks and Shortcuts

Two Numbers that Differ by an Odd Number: a < c =" [1">

Examples

a x b = (a + c)2 – [b + (c –1)2] , 79 x 92 = 862 – (92 + 36) = 7396 – 128 = 7268

Other Multiplying Techniques

Multiplying by 11

a x 11 = a + 10a , 76 x 11 = 76 + 760 = 836

a x 11 = If a > 9 insert a 0 between digits and

add sum of digits x 10 76 x 11 = 706 + 130 = 836

Multiplying by Other Two Digit Numbers Ending in 1 (X = 1 to 9)

a x X1 = a + X0a , 63 x 41 = 63 + (40 x 63) = 63 + 2520 = 2583

Multiplying with Numbers Ending in 5 (X = 1 to 9)

a x X5 = a/2 x 2(X5), 83 x 45 = 41.5 x 90 = 415 x 9 = 3735

Multiplying by 15

a x 15 = (a + a/2) x 10 , 77 x 15 = (77 + 38.5) x 10 = 1155

Multiplying by 45

a x 45 = 50a – 50a/10, 59 x 45 = 2950 – 295 = 2655

Multiplying by 55

a x 55 = 50a + 50a/10, 67 x 55 = 3350 + 335 = 3685

Multiplying by Two Digit Numbers that End in 9 (X = 1 to 9)

a x X9 = (X9 + 1)a – a , 47 x 29 = (30 x 47) – 47 = 1410 – 47 = 1363

Multiplying by Multiples of 9 (b = multiple of 9 up to 9 x 9)

a x b = round b up to next highest 0 29 x 54 = 29 x 60 – (29 x 60)/10

multiply then subtract 1/10 of result = 1740 – 174 = 1566

Multiplying by Multiples of 99 (b = multiple of 99 up to 99 x 10)

a x b = round up to next highest 0 38 x 396 = 38 x 400 – (38 x 400)/100