8.7: Proficiency Exam

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Proficiency Exam

For problems 1 - 16, estimate each value. After you have made an estimate, find the exact value. Results may vary.

Exercise \(\PageIndex{1}\)

\(3,716 + 6,789\)

Answer: 10,500 (10,505)

Exercise \(\PageIndex{2}\)

\(8,821 + 9,217\)

Answer: 18,000 (18,038)

Exercise \(\PageIndex{3}\)

\(7,316 - 2,305\)

Answer: 5,000 (5,011)

Exercise \(\PageIndex{4}\)

\(110,812 - 83,406\)

Answer: 28,000 (27,406)

Exercise \(\PageIndex{5}\)

\(82 \cdot 38\)

Answer: 3,200 (3,116)

Exercise \(\PageIndex{6}\)

\(51 \cdot 92\)

Answer: 4,500 (4,692)

Exercise \(\PageIndex{7}\)

\(48 \cdot 6,012\)

Answer: 300,000 (288,576)

Exercise \(\PageIndex{8}\)

\(238 \div 17\)

Answer: 12 (14)

Exercise \(\PageIndex{9}\)

\(2,660 \div 28\)

Answer: 90 (95)

Exercise \(\PageIndex{10}\)

\(43.06 + 37.94\)

Answer: 81 (81.00)

Exercise \(\PageIndex{11}\)

\(307.006 + 198.0005\)

Answer: 505 (505.0065)

Exercise \(\PageIndex{12}\)

\((47.2)(92.8)\)

Answer: 4,371 (4,380.16)

Exercise \(\PageIndex{13}\)

\(58 + 91 + 61 + 88\)

Answer: \(2(60) + 2(90) = 300\) (298)

Exercise \(\PageIndex{14}\)

\(43 + 39 + 89 + 92\)

Answer: \(2(40) + 2(90) = 260\) (263)

Exercise \(\PageIndex{15}\)

\(81 + 78 + 27 + 79\)

Answer: \(30 + 3(80) = 270\) (265)

Exercise \(\PageIndex{16}\)

\(804 + 612 + 801 + 795 + 606\)

Answer: \(3(800) + 2(600) = 3,600\) (3,618)

For problems 17-21, use the distributive property to obtain the exact result.

Exercise \(\PageIndex{17}\)

\(25 \cdot 14\)

Answer: \(25 (10 + 4) = 250 + 100 = 350\)

Exercise \(\PageIndex{18}\)

\(15 \cdot 83\)

Answer: \(15 (80 + 3) = 1,200 + 45 = 1,245\)

Exercise \(\PageIndex{19}\)

\(65 \cdot 98\)

Answer: \(65 (100 - 2) = 6,500 - 130 = 6,370\)

Exercise \(\PageIndex{20}\)

\(80 \cdot 107\)

Answer: \(80 (100 + 7) = 8,000 + 560 = 8,560\)

Exercise \(\PageIndex{21}\)

\(400 \cdot 215\)

Answer: \(400 (200 + 15) = 80,000 + 6,000 = 86,000\)

For problems 22-25, estimate each value. After you have made an estimate, find the exact value. Results may vary.

Exercise \(\PageIndex{22}\)

\(\dfrac{15}{16} + \dfrac{5}{8}\)

Answer: \(1 + \dfrac{1}{2} = 1 \dfrac{1}{2}\) (\(1 \dfrac{9}{16}\))

Exercise \(\PageIndex{23}\)

\(\dfrac{1}{25} + \dfrac{11}{20} + \dfrac{17}{30}\)

Answer: \(0 + \dfrac{1}{2} + \dfrac{1}{2} = 1\) (\(1 \dfrac{47}{300}\))

Exercise \(\PageIndex{24}\)

\(8 \dfrac{9}{16} + 14 \dfrac{1}{12}\)

Answer: \(8 \dfrac{1}{2} + 14 = 22 \dfrac{1}{2}\) (\(22 \dfrac{31}{48}\))

Exercise \(\PageIndex{25}\)

\(5 \dfrac{4}{9} + 1 \dfrac{17}{36} + 6 \dfrac{5}{12}\)

Answer: \(5 \dfrac{1}{2} + 1 \dfrac{1}{2} + 6 \dfrac{1}{2} = 13 \dfrac{1}{2}\) (\(13 \dfrac{1}{3}\))