SME
Grade 5 Math · Number & Base Ten
Divide whole numbers by two-digit divisors
Use this for “Divide 1,987 by 23. What are the quotient and the remainder?”
Diagram
1,840 + 138 + 9 left over = 1,987.
1,987 ÷ 23 = 86, remainder 9: 80 + 6.
Quotient: 86
This is an example. Type your own values to start a new problem.
Dividend
÷
Divisor
=
Quotient
remainder
Remainder
Used in the groups
worked out (not typed)
Formulas
86 × 23 = 1,978
Quotient × divisor = used in the groups
1,978 + 9 = 1,987
Used in the groups + remainder = dividend
1,987 ÷ 23 → 86 whole groups
Dividend ÷ divisor → quotient whole groups
Assumptions
•
Make groups the size of the divisor. The number of groups is the quotient.
•
Estimate each digit with the divisor rounded to tens, then check: multiply, take away, bring down.
•
What is left is the remainder. It is always less than the divisor.
•
Dividends to 99,999, divisors from 10 to 99.
Step-by-step
WE KNOW
Dividend: 1,987
Divisor: 23
FIND
quotient, used in the groups, remainder
Step 1 · Find quotient
1,987 ÷ 23 → ? whole groups
Dividend ÷ divisor → quotient whole groups
Estimate each digit with the divisor rounded to tens. Too big? Try one less.
23 is about 20
198 ÷ 20 is about 9
Try 9: 9 × 23 = 207
207 is more than 198: use 8
147 ÷ 20 is about 7
Try 7: 7 × 23 = 161
161 is more than 147: use 6
8
6
23
)
1
9
8
7
−
1
8
4
1
4
7
−
1
3
8
9
Quotient = 86
Step 2 · Find used in the groups
86 × 23 = ?
Quotient × divisor = used in the groups
The groups times the divisor: what is used in the groups.
1
1
8
6
×
2
3
2
5
8
+
1
7
2
0
1
9
7
8
Used in the groups = 1,978
Step 3 · Find remainder
1,978 + ? = 1,987
Used in the groups + remainder = dividend
The remainder is what is left after making the groups.
Remainder = 1,987 − 1,978
Remainder = 9
Check
Put the numbers back in. Both sides should match.
86 × 23 = 1,978 ✓
1,978 + 9 = 1,987 ✓
1,987 ÷ 23 = 86 remainder 9 ✓
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Add, subtract, multiply and divide decimals
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