Dividing by two-digit numbers
Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
What a learner can do afterwards
- Use short division to compute 3,648 ÷ 16 efficiently
- Explain when short division is more appropriate than long division
- Interpret a remainder as a decimal or fraction in a measurement context
1 · Read
You already know how to divide with remainders, and you can picture multiplication with arrays. Short division (the bus-stop method) uses both those skills. So far the divisor has been a single digit. Now you will divide by a two-digit number instead, using the exact same steps to share things among a whole class.
Work out 2,548 ÷ 14. The first digit, 2, is too small to divide by 14, so take the first two digits together: 25. 25 ÷ 14 = 1 remainder 11. Carry the remainder to make 114. 114 ÷ 14 = 8 remainder 2. Carry the remainder to make 28. 28 ÷ 14 = 2 remainder 0. Read the answer across the top: 182.
Short division is fastest when you know the multiples of the divisor well, like 11, 12, or 15. When the divisor is an unfamiliar number, such as 47 or 89, long division can help because you write out each multiplication step instead of holding it in your head.
A remainder does not always mean 'stop'. A tailor has 2,090 cm of fabric and cuts pieces that are 12 cm long. Short division gives 174 remainder 2, so that's 174 whole pieces with 2 cm left over. As a fraction of one piece, that leftover is 2/12, which simplifies to 1/6.
A leftover can also wear a decimal name. A shopkeeper splits 15 kg of flour into 4 bags. Short division gives 3 remainder 3. To keep dividing, write a decimal point and carry the 3 as 30 tenths: 30 ÷ 4 = 7 remainder 2. Carry the 2 as 20 hundredths: 20 ÷ 4 = 5. Each bag holds 3.75 kg.
Short division works one digit at a time even with a two-digit divisor, and a remainder can turn into a fraction or decimal once you know what it is measuring.
The rewritten readings were written for this dataset.
More to read
Division with fewer written calculations
Short division follows the long-division method but leaves more calculations in your head. Small remainder notes replace written subtraction lines. Try 3,648 / 16. First, 36 contains two 16s, leaving 4. Write 2 and combine that remainder with the next digit to get 44. Next, 44 contains two 16s, leaving 12. Write another 2; carrying 12 beside the final 8 makes 128. This contains eight 16s exactly, giving 228. Use short division when the divisor's multiples are familiar. Larger divisors often make written long division easier.
Keeping track with long division
Long division records the multiplication and subtraction calculations, helping you track larger divisors. Put the number being divided inside the division bracket and the number dividing it outside. Begin on the left. Divide the current amount, multiply to check, subtract, then lower the next digit. Repeat this cycle for 7,182 / 42. You can leave a remainder as a whole number, express it as a fraction or continue into decimals. For example, 10 / 4 gives 2 with remainder 2, or 2.5. Choose the shorter method for familiar divisors and the written method when mental remainders become hard to manage.
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