5th Grade Dividing by Two-Digit Divisors Worksheet Solutions (PDF)
This divide whole answers for 5th Grade covers dividing by two-digit divisors (Common Core 5.NBT.B.6), with a free PDF to print.
This answer key shows partial quotients and checks for all 20 division problems. If your steps are different, that is fine as long as the quotient is right. You can always check by multiplying the quotient by the divisor and adding the remainder.
Grade 5 · Common Core State Standards: 5.NBT.B.6
Divide whole answers: exercises 1 to 10
Exercise 1 – Basic facts
\(12\times8=96\).
Answer: 8
Exercise 2 – Division fact
\(14\times6=84\).
Answer: 6
Exercise 3 – Multiples of ten
Divide 640 tens by 8 tens: \(640\div8=80\). Check: \(80\times80=6{,}400\).
Answer: 80
Exercise 4 – Two digits by two digits
\(21\times10=210\), \(252-210=42\), \(21\times2=42\).
\(10+2=12\).
Answer: 12
Exercise 5 – Partial quotients, 345
\(15\times20=300\), \(345-300=45\), \(15\times3=45\).
\(20+3=23\).
Answer: 23
Exercise 6 – Partial quotients, 972
\(36\times20=720\), \(972-720=252\). \(36\times7=252\), so \(252-252=0\).
\(20+7=27\).
Answer: 27
Exercise 7 – Area model division
\(1{,}080\div18=60\) and \(72\div18=4\).
Quotient: \(60+4=64\).
Answer: 64
Exercise 8 – Four-digit dividend
\(28\times70=1{,}960\), \(2184-1960=224\). \(28\times8=224\).
\(70+8=78\).
Answer: 78
Exercise 9 – Larger divisor
\(54\times80=4{,}320\), \(4536-4320=216\). \(54\times4=216\).
\(80+4=84\).
Answer: 84
Exercise 10 – Three-digit quotient
\(48\times100=4{,}800\), \(7296-4800=2496\). \(48\times50=2{,}400\), \(2496-2400=96\). \(48\times2=96\).
\(100+50+2=152\).
Answer: 152
Exercises 11 and up
Exercise 11 – Compatible numbers
Estimate: 29 is about 30, and 2,262 is about 2,400. \(2{,}400\div30=80\).
Exact: \(29\times70=2{,}030\), \(2262-2030=232\), \(29\times8=232\). \(70+8=78\).
Answer: estimate 80, exact 78
Exercise 12 – A remainder
\(22\times20=440\), \(475-440=35\). \(22\times1=22\), \(35-22=13\).
13 is less than 22, so stop.
Check: \(22\times21+13=462+13=475\).
Answer: 21 R 13
Exercise 13 – Dividing 1,000
\(32\times30=960\), \(1000-960=40\). \(32\times1=32\), \(40-32=8\).
Check: \(32\times31+8=992+8=1{,}000\).
Answer: 31 R 8
Exercise 14 – A bigger remainder
\(41\times90=3{,}690\), \(3805-3690=115\). \(41\times2=82\), \(115-82=33\).
Check: \(41\times92+33=3{,}772+33=3{,}805\).
Answer: 92 R 33
Exercise 15 – Baseball boxes
\(432\div24\): \(24\times10=240\), \(432-240=192\), \(24\times8=192\).
\(10+8=18\).
The league fills 18 boxes.
Exercise 16 – Cupcake trays
\(648\div36\): \(36\times10=360\), \(648-360=288\). \(36\times8=288\).
\(10+8=18\).
She needs 18 trays.
Exercise 17 – Miles per hour
\(1{,}368\div24\): \(24\times50=1{,}200\), \(1368-1200=168\). \(24\times7=168\).
\(50+7=57\).
They drive 57 miles per hour.
Exercise 18 – Field trip buses
\(250\div48=5\text{ R }10\) because \(48\times5=240\) and \(250-240=10\).
The 10 students left over still need a ride, so the school needs one more bus.
Answer: 6 buses
Exercise 19 – Sticker pages
\(35\times10=350\), \(500-350=150\). \(35\times4=140\), \(150-140=10\).
\(10+4=14\) full pages, remainder 10.
Check: \(35\times14+10=490+10=500\).
Answer: 14 full pages and 10 stickers left over
Exercise 20 – Pencils for classes
Pencils: \(18\times45=810\) (\(18\times40=720\) and \(18\times5=90\)).
Classes: \(810\div27\): \(27\times30=810\).
Answer: 30 classes
Key facts behind this divide whole answers
- The dividend is divided by the divisor to give the quotient.
- Partial quotients break the answer into easy pieces that add up to the quotient.
- An area model shows the dividend as an area with the divisor as one side.
- A remainder is always smaller than the divisor.
- Check by multiplying the quotient by the divisor and adding the remainder.
How to use this divide whole answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
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