Dividing a 2-digit number by 1 1/7

STEPS

1. Select a 2-digit number.
2. Multiply it by 7.
3. Divide the product by 8.

Example:

1. The number chosen to divide by 1 1/7 is 26.
2. Multiply by 7: 7 × 26 = 140 + 42 = 182
3. Divide by 8: 182/8 = 22 3/4
4. So 26 divided by 1 1/7 = 22 3/4.

See the pattern?

1. The number chosen to divide by 1 1/7 is 61.
2. Multiply by 7: 7 × 61 = 427
3. Divide by 8: 427/8 = 53 3/8
4. So 61 divided by 1 1/7 = 53 3/8

Dividing a 2-digit number by 1 1/8

STEPS

1. Select a 2-digit number.
2. Multiply by 8.
3. Divide the result by 9.

Example:

1. The 2-digit number chosen to divide by 1 1/8 is 42.
2. Multiply by 8: 8 × 42 = 320 + 16 = 336
3. Divide by 9: 336/9 = 37 1/3
4. So 42 divided by 1 1/8 = 37 1/3.

See the pattern?

1. The 2-digit number chosen to divide by 1 1/8 is 71.
2. Multiply by 8: 8 × 71 = 568
3. Divide by 9: 568/9 = 63 1/9
4. So 71 divided by 1 1/8 = 63 1/9.

Dividing a number by 0.125

steps

1. Select a number.
2. Multiply it by 8.

Example:

1. The number chosen to divide by 0.125 is 21.
2. Multiply it by 8: 8 × 21 = 168.
3. So 21 divided by 0.125 = 168.

See the pattern?

1. The 2-digit number chosen to divide by 1/8 is 68.
2. Multiply it by 8: 8 × 68 = 480 + 64 = 544.
3. So 68 divided by 0.125 = 544.

Dividing a 2-digit number by 1 1/9

steps

1. Select a 2-digit number.
2. Multiply by 9.
3. Move the decimal point one place to the left.

Example:

1. The 2-digit number chosen to divide by 1 1/9 is 24.
2. Multiply by 9: 9 × 24 = 180 + 36 = 216
3. Move the decimal point one place to the left: 21.6
4. So 24 divided by 1 1/9 = 21.6.

See the pattern?

1. The 2-digit number chosen to divide by 1 1/9 is 91.
2. Multiply by 9: 9 × 91 = 819
3. Move the decimal point one place to the left: 81.9
4. So 91 divided by 1 1/9 = 81.9.

Multiplying two selected 3-digit numbers

steps

1. Select a 3-digit number with a middle digit of 0.
2. Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
3. The first digit(s) will be the square of the first digit:
   X _ _ _ _ or X X _ _ _ _.
4. The next digit will be the first digit of the numbers:
   _ X _ _ _ or _ _ X _ _ _.
5. The next digit is zero: _ _ 0 _ _ or _ _ _ 0 _ _.
6. The last two digits will be the product of the third digits:
   _ _ _ X X or _ _ _ _ X X.

Example:

1. If the first number is 407, choose 403 as the second number (same first digits, second digits add to 10).
2. 4 × 4 = 16 (square the first digit): 1 6 _ _ _ _.
3. The next digit will be the first digit of the numbers:
   _ _ 4 _ _ .
4. The next digit is zero: _ _ 0 _ _ .
5. 7 × 3 = 21 (the last two digits will be the product of the third digits: _ _ _ 2 1.
6. So 407 × 403 = 164021.

See the pattern?

1. If the first number is 201, choose 209 as the second number (same first digits, second digits add to 10).
2. 2 × 2 = 4 (square the first digit): 4 _ _ _ _.
3. The next digit will be the first digit of the numbers:
   _ 2 _ _ _ .
4. The next digit is zero: _ _ 0 _ _ .
5. 1 × 9 = 09 (the last two digits will be the product of the third digits: _ _ _ 0 9.
6. So 201 × 209 = 42009.

Multiplying two 2-digit numbers

steps

1. Both numbers should have the same second digit.
2. Choose first digits whose sum is 10.
3. Multiply the first digits and add one second: X X _ _.
4. Multiply the second digits together: _ _ X X.

Example:

1. If the first number is 67, choose 47 as the second number (same second digit, first digits add to 10).
2. Multiply the 1st digits, add one 2nd.
   6x4 = 24, 24+7 = 31. 3 1 _ _
3. Multiply the 2nd digits. 7x7 = 49 _ _ 4 9
4. So 67 × 47 = 3149.

See the pattern?

1. If the first number is 93, choose 13 as the second number (same second digit, first digits add to 10).
2. Multiply the 1st digits, add one 2nd. 9x1 = 9, 9+3 = 12.
   1 2 _ _
3. Multiply the 2nd digits. 3x3 = 9 _ _ 0 9
4. So 93 × 13 = 1209.

Multiplying two 2-digit numbers

steps

1. Select two 2-digit numbers with the same first digit.
2. Multiply their second digits (keep the carry). _ _ _ X
3. Multiply the sum of the second digits by the first digit,
   add the carry (keep the carry). _ _ X _
4. Multiply the first digits (add the carry). X X _ _

Example:

1. If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).
2. Multiply the last digits: 2 × 5 = 10 (keep carry)
   _ _ _ 0
3. Multiply the sum of the 2nd digits by the first:
   5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)
   _ _ 9 _
4. Multiply the first digits (add the carry)
   4 × 4 = 16; 16 + 2 = 18
   1 8 _ _
   
   
5. So 42 × 45 = 1890.

See the pattern?

1. If the first number is 62, choose 67 as the second number
   (any 2-digit number with first digit 6).
2. Multiply the last digits: 2 × 7 = 14 (keep carry)
   _ _ _ 4
3. Multiply the sum of the 2nd digits by the first (add carry):
   2 + 7 = 9; 6 × 9 = 54; 54 + 1 = 55 (keep carry)
   _ _ 5 _
4. Multiply the first digits (add the carry)
   6 × 6 = 36; 36 + 5 = 41
   4 1 _ _
   
   
5. So 62 × 67 = 4154.

Multiplying two 2-digit numbers

steps

1. Both numbers should have the same first digit।
2. Choose second digits whose sum is 10.
3. Multiply the first digit by one number greater than itself; this number will be the first part of the answer:
   X X _ _.
4. Multiply the two second digits together; the product
   will be the last part of the answer: _ _ X X.

Note: If the two second digits are 1 and 9 (or, more generally, have a product that is less than ten), insert a 0 (zero) for the first X in step 4.

(Thanks to Michael Richardson, age 10, for this note.)

Example:

1. If the first number is 47, choose 43 as the second number (same first digit, second digits add to 10).
2. 4 × 5 = 20 (multiply the first digit by one number greater than itself): the first part of the answer is
   2 0 _ _.
3. 7 × 3 = 21 (multiply the two second digits together); the last part of the answer is _ _ 2 1.
4. So 47 × 43 = 2021.

See the pattern?

1. If the first number is 62, choose 68 as the second number (same first digit, second digits add to 10).
2. 6 × 7 = 42 (multiply the first digit by one greater), the first part of the answer is 4 2 _ _.
3. 2 × 8 = 16 (multiply the two second digits together); the last part of the answer is _ _ 1 6.
4. So 62 × 68 = 4216.