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Written division – short method
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Foundational skills
Setting up short division
\[ \text{Example: } 847 \div 7 \rightarrow \begin{array}[b]{r} 7 \end{array} \; \begin{array}[b]{c} \begin{array}{c@{\hspace{1em}}c@{\hspace{1em}}c} \phantom{0} & \phantom{0} & \phantom{0} \end{array} \\ \hline \begin{array}{|c@{\hspace{1em}}c@{\hspace{1em}}c} 8 & 4 & 7 \end{array} \end{array} \]
Set up a division in the correct bus stop format ready to calculate.
2-digit รท 1-digit
Exact with no exchanging
\[ \text{Example: } 48 \div 4 = 12 \]
Divide a 2-digit number by a single digit with no exchanging and no remainder.
Exact with exchanging
\[ \text{Example: } 72 \div 3 = 24 \]
Divide a 2-digit number by a single digit with exchanging but no remainder.
With remainder no exchanging
\[ \text{Example: } 47 \div 4 = 11 \text{ r } 3 \]
Divide a 2-digit number by a single digit with no exchanging but with a final remainder.
With remainder and exchanging
\[ \text{Example: } 58 \div 4 = 14 \text{ r } 2 \]
Divide a 2-digit number by a single digit with both exchanging and a final remainder.
3-digit รท 1-digit
Exact with no exchanging
\[ \text{Example: } 648 \div 2 = 324 \]
Divide a 3-digit number by a single digit with no exchanging and no remainder.
Exact with exchanging
\[ \text{Example: } 534 \div 3 = 178 \]
Divide a 3-digit number by a single digit with exchanging but no remainder.
Exact with first digit smaller than divisor
\[ \text{Example: } 245 \div 5 = 49 \]
Divide a 3-digit number by a single digit where the hundreds digit is smaller than the divisor.
With remainder
\[ \text{Example: } 527 \div 3 = 175 \text{ r } 2 \]
Divide a 3-digit number by a single digit where there is a remainder.
With remainder and first digit smaller than divisor
\[ \text{Example: } 258 \div 4 = 64 \text{ r } 2 \]
Divide a 3-digit number by a single digit where the hundreds digit is smaller than the divisor and there is a remainder.
4-digit รท 1-digit
Exact division
\[ \text{Example: } 3{,}648 \div 4 = 912 \]
Divide a 4-digit number by a single digit with no remainder.
Exact with leading digit(s) smaller than divisor
\[ \text{Example: } 2{,}156 \div 7 = 308 \]
Divide a 4-digit number by a single digit where the thousands digit is smaller than the divisor.
With remainder
\[ \text{Example: } 5{,}347 \div 6 = 891 \text{ r } 1 \]
Divide a 4-digit number by a single digit where there is a remainder.
Zeros in quotient
Zero in middle of quotient
\[ \text{Example: } 612 \div 6 = 102 \]
Divide where the quotient has a zero in the middle.
Zero at end of quotient
\[ \text{Example: } 450 \div 9 = 50 \]
Divide where the quotient ends in zero.
Multiple zeros in quotient
\[ \text{Example: } 4{,}004 \div 4 = 1{,}001 \]
Divide where the quotient contains two or more zeros.
Special cases
Missing digit in dividend
\[ \text{Find } \Box: 5\Box2 \div 4 = 138 \]
Find a missing digit in the dividend of a division.
Missing digit in quotient
\[ \text{Find } \Box: 738 \div 6 = 1\Box3 \]
Find a missing digit in the quotient of a division.
Missing divisor
\[ \text{Find } \Box: 846 \div \Box = 141 \]
Find the single-digit divisor in a division.
Timer (Optional)
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