5th Grade Dividing by Two-Digit Divisors Test Solutions and Scoring (PDF)

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

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This divide whole test answers for 5th Grade covers dividing by two-digit divisors (Common Core 5.NBT.B.6), with a free PDF to print.

Use this answer key to grade the division test. It shows partial quotients, checks and a scoring guide for each question. The total is 20 points. Accept any correct strategy, such as partial quotients, an area model or the standard long-division algorithm.

Grade 5 · Common Core State Standards: 5.NBT.B.6

Divide whole test answers: worked solutions

Question 1 – Short quotients [2 pts]

(a) \(12\times14=168\). 14

(b) \(540\div9=60\). 60

Scoring: 1 point for each correct quotient.

Question 2 – Divide 1,404 [3 pts]

\(26\times50=1{,}300\), \(1404-1300=104\).

\(26\times4=104\).

\(50+4=54\).

Answer: 54

Scoring: 1 point for each correct partial quotient (50 and 4), 1 point for the correct sum. Accept other correct partial quotients such as 40 + 10 + 4.

Question 3 – Division with a remainder [3 pts]

\(47\times80=3{,}760\), \(3816-3760=56\). \(47\times1=47\), \(56-47=9\).

Check: \(47\times81+9=3{,}807+9=3{,}816\).

Answer: 81 R 9

Solution layout.

Scoring: 1 point for the partial quotients, 1 point for the quotient 81, 1 point for the remainder 9.

Question 4 – Area model [2 pts]

\(1{,}920\div32=60\) and \(96\div32=3\).

\(60+3=63\).

Answer: 63

Solution.

Scoring: 1 point for the widths 60 and 3, 1 point for the quotient.

Question 5 – Estimate and solve [2 pts]

Estimate: \(2{,}800\div40=70\) (or \(3{,}000\div40=75\)).

Exact: \(42\times70=2{,}940\), \(2982-2940=42\), \(42\times1=42\).

\(70+1=71\).

Answer: 71

Scoring: 1 point for an estimate from 70 to 75, 1 point for 71.

Question 6 – Diego's work [2 pts]

Diego ignored the zero in 1,260. \(18\times7=126\) is only 126, not 1,260. He needs 7 tens: \(18\times70=1{,}260\).

Answer: 70

Scoring: 1 point for the explanation, 1 point for 70.

Question 7 – Field trip vans [3 pts]

(a) \(15\times25=375\), \(389-375=14\). 25 R 14

(b) 14 students are left over and need another van: 26 vans.

Scoring: (a) 1 point for the quotient 25, 1 point for the remainder 14. (b) 1 point.

Question 8 – Pencil boxes [3 pts]

(a) \(36\times40=1{,}440\), so \(1{,}440\div36=40\). 40 pencils

(b) \(40\div8=5\). 5 pencils

Scoring: (a) 2 points; 1 point for a correct partial quotient method with an arithmetic slip. (b) 1 point.

Total score

Total

20 points

Key facts behind this divide whole test answers

Key facts

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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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