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

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

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

Scoring: 1 point for each correct quotient.

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

\(26\times4=104\).

\(50+4=54\).

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.

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

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

Answer: 81 R 9

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

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

\(60+3=63\).

Answer: 63

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

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.

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.

(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.

(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.