Pamela Leutwyler
Examine the familiar base 10 algorithm. Multiplication in other bases works the same way.
26 x34
hundreds tens ones 26 x34
hundreds tens ones 26 x34 ones times ones = ones 6x4 = 24
hundreds tens ones 26 x34 ones times ones = ones 6x4 = 24 Each set of 10 “ones” is replaced by 1 “ten”
hundreds tens ones 26 x34 4 ones times ones = ones 6x4 = 24 Each set of 10 “ones” is replaced by 1 “ten” 2 Put down 4 and carry 2
hundreds tens ones 26 x34 4 2
hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 2
hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 2 plus the 2 carried from the last step puts ten pebbles In the tens pile
hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2
hundreds tens ones 26 x34 4 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2
hundreds tens ones 26 x34 04 ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2 Put down 0 and carry one 1
hundreds tens ones 26 x ones times tens = tens 4x2 = 8 Each set of 10 “tens” is replaced by 1 “hundred” 2 Put down 0 and carry one 1
hundreds tens ones 26 x34 104
hundreds tens ones 26 x34 104
hundreds tens ones 26 x tens times ones = tens 3x6 = 18
hundreds tens ones 26 x tens times ones = tens 3x6 = 18 Each set of 10 “tens” is replaced by 1 “hundred”
hundreds tens ones 26 x tens times ones = tens 3x6 = 18 Each set of 10 “tens” is replaced by 1 “hundred” Put down 8 and carry one 1
hundreds tens ones 26 x
hundreds tens ones 26 x tens times tens = hundreds 3x2 = 6
hundreds tens ones 26 x tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step
hundreds tens ones 26 x tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step Put down 7
hundreds tens ones 26 x tens times tens = hundreds 3x2 = 6 plus the 1 carried from the last step Put down 7
hundreds tens ones 26 x
hundreds tens ones 26 x Add
24 5 x13 5
twenty fives fives ones 24 5 x13 5
twenty fives fives ones 24 5 x x 4
twenty fives fives ones 24 5 x x 4 Base 10 Base 5 3x4= 122 2
twenty fives fives ones 24 5 x x 4 Base 10 Base 5 3x4= Put down 2 and carry 2
twenty fives fives ones 24 5 x Base 10 Base 5 3x4=
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= x 2
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= x 2
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) x 2
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2)
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) Put down 3 and carry 1
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2)
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2)
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2)
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) x 4
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) x 2 fives times fives = twenty fives
fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) Add in the base 5
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2)
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) = 7
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) =
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) = 712 1
twenty fives fives ones 24 5 x Base 10 Base 5 3x4= 1222 (3x2) = 712 1
another example This time we will not bother with the pebble board. As you work the familiar algorithm, it helps if you think in the base ten and then switch to the base 5.
fives ones 43 5 x32 5 Base 10 Base 5
fives ones x Base 10 Base 5 2x3= 61 1
fives ones 43 5 x Base 10 Base 5 2x3= 61 (2x4)
fives ones 43 5 x Base 10 Base 5 2x3= 611 (2x4)
fives ones 43 5 x Base 10 Base 5 2x3= 611 (2x4)
fives ones 43 5 x Base 10 Base 5 2x3= 611 (2x4)
fives ones x Base 10 Base 5 2x3= 611 2x x33x
fives ones 43 5 x Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4)
fives ones 43 5 x Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4)
fives ones 43 5 x Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) = Add in the base 5 1
fives ones 43 5 x Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) = = Add in the base 5 1 1
fives ones 43 5 x Base 10 Base 5 2x3= 611 2x4= 813 3x3= 914 (3x4) = =