Arithmetic

Guide Note

Arithmetic is the most basic form of mathematics. It concerns counting and working with numbers and fractions based on the four operations: addition, subtraction, multiplication and division.¹

Fast Facts

1. The word "Arithmetic" from Greek "arithmos," meaning "number"¹
2. Elementary arithmetic is taught in primary school¹
3. "Higher arithmetic" refers to number theory¹

• When multiplying any two digit number by eleven, separate the two digits and place the sum of the two in between them. For example:
• 35 x 11
• Separate the digits: 3 and 5
• Find the sum: 3 + 5 = 8
• Place the sum in the center: 385
• Thus: 11 x 35= 385

• This can also be done when the central sum is not a single digit. To account for the extra digit take the tens digit and add it to the higher digit of the multiplicand. For example:
• 76 x 11
• Separate the digits: 7 and 6
• Find the sum: 7 + 6 = 13
• Add the 7 and the 1 from the 13: 7 + 1 = 8
• Place the sum in the center: 836
• Thus: 11 x 76= 836

• When multiplying by 5, take the other multiplicand and divide it in half. If it is an odd number subtract one and then divide it in half. Then add a zero as the last digit if the multiplicand was even or a five if it was odd. For example:
• 44 x 5
• Divide 44 by 2: 44 / 2 = 22
• Place on a zero at the end: 220
• For an odd number: 33 x 5
• Subtract 1 from 33: 33 - 1 = 32
• Divide 32 in half: 32 / 2 = 16
• Place five at the end: 165

• When dividing by 9, for any number less then or equal to ten, count on your fingers and drop the finger that represents the multiplicand. Then, simply count how many fingers are on each side of the dropped finger. The first set of fingers represents the tens digit while the second represents the ones. For example:
• 9 x 7
• Count to the 7th finger and fold it down
• Count the number of fingers before it: 6
• Count the number after: 3
• Thus: 9 x 7 = 63