5th Grade Dividing by Two-Digit Divisors Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Dividing by Two-Digit Divisors – Maths PDF

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

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

The widths are 60 and 4.

Exercise 8 – Four-digit dividend

\(28\times70=1{,}960\), \(2184-1960=224\). \(28\times8=224\).

\(70+8=78\).

Answer: 78

Partial quotients.

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

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

Division with a remainder.

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

All Grade 5 chapters: Grade 5 math.

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