Subtraction and Division – Mental Math or Algorithm Examples
    Division:
    •
    Subtracting groups of the divisor
    159 ÷ 13
    159
    29 OR Use the Big 7 method of recording
    10 x 13 = 130 -130
    -26
    2 x 13 = 26
    29
    3
    12 r3
    •
    Breaking the problem into parts
    150 ÷ 48 = (50 ÷ 48) + (50 ÷ 48) + (50 ÷ 48) = 3 r 6
    (There is one 48 with 2 left over in each 50)
    OR
    159/13
    Break into 130 + 29, 130 divided by 13 is 10; 29 divided by 13 is 2 with 3 remaining
    •
    Transferring the problem into an equivalent problem that is easier to solve.
    1400 ÷ 35 = 200 ÷ 5 (divide both numbers by 7)
    928/16 = 464/8 = 232/4 = 116/2 = 58
    •
    Solving and easier related problem, then compensating
    247 ÷ 13
    Solve 260 ÷ 13 (There are 20 thirteens in 260, but 247 is 13 less than 260. So there are only 19 thirteens in
    247)
    •
    Dealing out into groups
    159/13
    Give 10 to each group; that uses up 130; 29 is left
    Give 1 more to each group; that uses up 13; 16 is left
    Give 1 more to each group; 3 is left.
    The result is 12 in each group, remainder 3
    Subtraction: 465 – 129
    •
    Subtract one number in parts from the other.
    465 – 100 = 365 OR
    465 – 125 = 340
    365 – 20 = 345
    340 – 4 = 336
    345 – 5 = 340
    340 – 4 = 336
    •
    Change one number, then compensate for the change.
    465 – 130 = 335
    OR
    460 – 129 = 331
    335 + 1 = 336
    331 + 5 = 336
    •
    Add up from the number being subtracted.
    129 + 1 = 130
    OR
    129 + 130 = 429
    130 + 300 = 430
    429 + 1 = 430
    430 + 35 = 465
    430 + 35 = 465
    1 + 300 + 35 = 336
    300 + 1 + 35 = 336
    •
    Transform the entire problem to an equivalent problem that is easier to solve.
    465 – 129 = 466 – 130
    466 – 130 = 336
    •
    Subtract each column and record each difference, whether it is positive or negative.
    400 – 100 = 300
    60 – 20 = 40
    5 – 9 = -4
    300 + 40 – 4 = 336

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