8.6: Exercise Supplement

Estimation by Rounding

For problems 1-70, estimate each value using the method of rounding. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise \(\PageIndex{1}\)

\(286 + 312\)

Answer

600 (598)

Exercise \(\PageIndex{2}\)

\(419 + 582\)

Exercise \(\PageIndex{3}\)

\(689 + 511\)

Answer

(1,200)

Exercise \(\PageIndex{4}\)

\(926 + 1,105\)

Exercise \(\PageIndex{5}\)

\(1,927 + 3,017\)

Answer

4,900 (4,944)

Exercise \(\PageIndex{6}\)

\(5,026 + 2,814\)

Exercise \(\PageIndex{7}\)

\(1,408 + 2,352\)

Answer

3,800 (3,760)

Exercise \(\PageIndex{8}\)

\(1,186 + 4,228\)

Exercise \(\PageIndex{9}\)

\(5,771 + 246\)

Answer

6,050 (6,017)

Exercise \(\PageIndex{10}\)

\(8,305 + 484\)

Exercise \(\PageIndex{11}\)

\(3,812 + 2,906\)

Answer

6,700 (6,718)

Exercise \(\PageIndex{12}\)

\(5,293 + 8,007\)

Exercise \(\PageIndex{13}\)

\(28,481 + 32,856\)

Answer

61,400 (61,337)

Exercise \(\PageIndex{14}\)

\(92,512 + 26,071\)

Exercise \(\PageIndex{15}\)

\(87,612 + 2,106\)

Answer

89,700 (89,718)

Exercise \(\PageIndex{16}\)

\(42,612 + 4,861\)

Exercise \(\PageIndex{17}\)

\(212,413 + 609\)

Answer

213,000 (213,022)

Exercise \(\PageIndex{18}\)

\(487,235 + 494\)

Exercise \(\PageIndex{19}\)

\(2,409 + 1,526\)

Answer

3,900 (3,935)

Exercise \(\PageIndex{20}\)

\(3,704 + 4,704\)

Exercise \(\PageIndex{21}\)

\(41 \cdot 63\)

Answer

2,400 (2,583)

Exercise \(\PageIndex{22}\)

\(38 \cdot 81\)

Exercise \(\PageIndex{23}\)

\(18 \cdot 28\)

Answer

600 (504)

Exercise \(\PageIndex{24}\)

\(52 \cdot 21\)

Exercise \(\PageIndex{25}\)

\(307 \cdot 489\)

Answer

150,123 147,000 (150,123)

Exercise \(\PageIndex{26}\)

\(412 \cdot 807\)

Exercise \(\PageIndex{27}\)

\(77 \cdot 614\)

Answer

47,278 48,000 (47,278)

Exercise \(\PageIndex{28}\)

\(62 \cdot 596\)

Exercise \(\PageIndex{29}\)

\(27 \cdot 473\)

Answer

12,771 14,100 (12,711)

Exercise \(\PageIndex{30}\)

\(92 \cdot 336\)

Exercise \(\PageIndex{31}\)

\(12 \cdot 814\)

Answer

8,100 (9,768)

Exercise \(\PageIndex{32}\)

\(8 \cdot 2,106\)

Exercise \(\PageIndex{33}\)

\(192 \cdot 452\)

Answer

90,000 (86,784)

Exercise \(\PageIndex{34}\)

\(374 \cdot 816\)

Exercise \(\PageIndex{35}\)

\(88 \cdot 4,392\)

Answer

396,000 (386,496)

Exercise \(\PageIndex{36}\)

\(126 \cdot 2,834\)

Exercise \(\PageIndex{37}\)

\(3,896 \cdot 413\)

Answer

1,609,048 1,560,000 (1,609,048)

Exercise \(\PageIndex{38}\)

\(5,794 \cdot 837\)

Exercise \(\PageIndex{39}\)

\(6,311 \cdot 3,512\)

Answer

22,050,000 (22,164,232)

Exercise \(\PageIndex{40}\)

\(7,471 \cdot 5,782\)

Exercise \(\PageIndex{41}\)

\(180 \div 12\)

Answer

18 (15)

Exercise \(\PageIndex{42}\)

\(309 \div 16\)

Exercise \(\PageIndex{43}\)

\(286 \div 22\)

Answer

14\(\dfrac{1}{2}\) (13)

Exercise \(\PageIndex{44}\)

\(527 \div 17\)

Exercise \(\PageIndex{45}\)

\(1,007 \div 19\)

Answer

50 (53)

Exercise \(\PageIndex{46}\)

\(1,728 \div 36\)

Exercise \(\PageIndex{47}\)

\(2,703 \div 53\)

Answer

54 (51)

Exercise \(\PageIndex{48}\)

\(2,562 \div 61\)

Exercise \(\PageIndex{49}\)

\(1.260 \div 12\)

Answer

130 (105)

Exercise \(\PageIndex{50}\)

\(3,618 \div 18\)

Exercise \(\PageIndex{51}\)

\(3,344 \div 76\)

Answer

41.25 (44)

Exercise \(\PageIndex{52}\)

\(7,476 \div 356\)

Exercise \(\PageIndex{53}\)

\(20,984 \div 488\)

Answer

42 (43)

Exercise \(\PageIndex{54}\)

\(43,776 \div 608\)

Exercise \(\PageIndex{55}\)

\(7,196 \div 514\)

Answer

14.4 (14)

Exercise \(\PageIndex{56}\)

\(51,492 \div 514\)

Exercise \(\PageIndex{57}\)

\(26,962 \div 442\)

Answer

60 (61)

Exercise \(\PageIndex{58}\)

\(33,712 \div 112\)

Exercise \(\PageIndex{59}\)

\(105,152 \div 106\)

Answer

1,000 (992)

Exercise \(\PageIndex{60}\)

\(176,978 \div 214\)

Exercise \(\PageIndex{61}\)

\(48.06 + 23.11\)

Answer

71.1 (71.17)

Exercise \(\PageIndex{62}\)

\(73.73 + 72.9\)

Exercise \(\PageIndex{63}\)

\(62.91 + 56.4\)

Answer

119.4 (119.31)

Exercise \(\PageIndex{64}\)

\(87.865 + 46.772\)

Exercise \(\PageIndex{65}\)

\(174.6 + 97.2\)

Answer

272 (271.8)

Exercise \(\PageIndex{66}\)

\((48.3)(29.6)\)

Exercise \(\PageIndex{67}\)

\((87.11)(23.2)\)

Answer

2,001 (2,020.952)

Exercise \(\PageIndex{68}\)

\((107.02)(48.7)\)

Exercise \(\PageIndex{69}\)

\((0.76)(5.21)\)

Answer

2,001 (2,020.952)

Exercise \(\PageIndex{70}\)

\((1.07)(13.89)\)

Estimation by Clustering

For problems 71-90, estimate each value using the method of clustering. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise \(\PageIndex{71}\)

\(38 + 51 + 41 + 48\)

Answer

\(2(40) + 2(50) = 180\) (178)

Exercise \(\PageIndex{72}\)

\(19 + 73 + 23 + 71\)

Exercise \(\PageIndex{73}\)

\(27 + 62 + 59 + 31\)

Answer

\(2(30) + 2(60) = 180\) (179)

Exercise \(\PageIndex{74}\)

\(18 + 73 + 69 + 19\)

Exercise \(\PageIndex{75}\)

\(83 + 49 + 79 + 52\)

Answer

\(2(80) + 2(50) = 260\) (263)

Exercise \(\PageIndex{76}\)

\(67 + 71 + 84 + 81\)

Exercise \(\PageIndex{77}\)

\(16 + 13 + 24 + 26\)

Answer

\(3(20) + 1(10) = 70\) (79)

Exercise \(\PageIndex{78}\)

\(34 + 56 + 36 + 55\)

Exercise \(\PageIndex{79}\)

\(14 + 17 + 83 + 87\)

Answer

\(2(15) + 2(80) = 190\) (201)

Exercise \(\PageIndex{80}\)

\(93 + 108 + 96 + 111\)

Exercise \(\PageIndex{81}\)

\(18 + 20 + 31 + 29 + 24 + 38\)

Answer

\(3(20) + 2(30) + 40 = 160\) (160)

Exercise \(\PageIndex{82}\)

\(32 + 27 + 48 + 51 + 72 + 69\)

Exercise \(\PageIndex{83}\)

\(64 + 17 + 27 + 59 + 31 + 21\)

Answer

\(2(60) + 2(20) + 2(30) = 220\) (219)

Exercise \(\PageIndex{84}\)

\(81 + 41 + 92 + 38 + 88 + 80\)

Exercise \(\PageIndex{85}\)

\(87 + 22 + 91\)

Answer

\(2(90) + 20 = 200\) (200)

Exercise \(\PageIndex{86}\)

\(44 + 38 + 87\)

Exercise \(\PageIndex{87}\)

\(19 + 18 + 39 + 22 + 42\)

Answer

\(3(20) + 2(40) = 140\) (140)

Exercise \(\PageIndex{88}\)

\(31 + 28 + 49 + 29\)

Exercise \(\PageIndex{89}\)

\(88 + 86 + 27 + 91 + 29\)

Answer

\(3(90) + 2(30) = 330\) (321)

Exercise \(\PageIndex{90}\)

\(57 + 62 + 18 + 23 + 61 + 21\)

Mental Arithmetic- Using the Distributive Property

For problems 91-110, compute each product using the distributive property.

Exercise \(\PageIndex{91}\)

\(15 \cdot 33\)

Answer

\(15(30 + 3) = 450 + 45 = 495\)

Exercise \(\PageIndex{92}\)

\(15 \cdot 42\)

Exercise \(\PageIndex{93}\)

\(35 \cdot 36\)

Answer

\(35(40 - 4) = 1400 - 140 = 1,260\)

Exercise \(\PageIndex{94}\)

\(35 \cdot 28\)

Exercise \(\PageIndex{95}\)

\(85 \cdot 23\)

Answer

\(85(20 + 3) = 1,700 + 225 = 1,955\)

Exercise \(\PageIndex{96}\)

\(95 \cdot 11\)

Exercise \(\PageIndex{97}\)

\(30 \cdot 14\)

Answer

\(30(10 + 4) = 300 + 120 = 420\)

Exercise \(\PageIndex{98}\)

\(60 \cdot 18\)

Exercise \(\PageIndex{99}\)

\(75 \cdot 23\)

Answer

\(75(20 + 3) = 1,500 + 225 = 1,725\)

Exercise \(\PageIndex{100}\)

\(65 \cdot 31\)

Exercise \(\PageIndex{101}\)

\(17 \cdot 15\)

Answer

\(15(20 - 3) = 300 - 45 = 255\)

Exercise \(\PageIndex{102}\)

\(38 \cdot 25\)

Exercise \(\PageIndex{103}\)

\(14 \cdot 65\)

Answer

\(65(10 + 4) = 650 + 260 = 910\)

Exercise \(\PageIndex{104}\)

\(19 \cdot 85\)

Exercise \(\PageIndex{105}\)

\(42 \cdot 60\)

Answer

\(60(40 + 2) = 2,400 + 120 = 2,520\)

Exercise \(\PageIndex{106}\)

\(81 \cdot 40\)

Exercise \(\PageIndex{107}\)

\(15 \cdot 105\)

Answer

\(15(100 + 5) = 1,500 + 75 = 1,575\)

Exercise \(\PageIndex{108}\)

\(35 \cdot 202\)

Exercise \(\PageIndex{109}\)

\(45 \cdot 306\)

Answer

\(45(300 + 6) = 13,500 + 270 = 13,770\)

Exercise \(\PageIndex{110}\)

\(85 \cdot 97\)

Estimation by Rounding Fractions

For problems 111-125, estimate each sum using the method of rounding fractions. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise \(\PageIndex{111}\)

\(\dfrac{3}{8} + \dfrac{5}{6}\)

Answer

\(\dfrac{1}{2} + 1 = 1 \dfrac{1}{2}\) (\(1 \dfrac{5}{24}\))

Exercise \(\PageIndex{112}\)

\(\dfrac{7}{16} + \dfrac{1}{24}\)

Exercise \(\PageIndex{113}\)

\(\dfrac{7}{15} + \dfrac{13}{30}\)

Answer

\(\dfrac{1}{2} + \dfrac{1}{2} = 1\) (\(\dfrac{27}{30}\) or \(\dfrac{9}{10}\))

Exercise \(\PageIndex{114}\)

\(\dfrac{14}{15} + \dfrac{19}{20}\)

Exercise \(\PageIndex{115}\)

\(\dfrac{13}{25} + \dfrac{7}{30}\)

Answer

\(\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4}\) (\(\dfrac{113}{150}\))

Exercise \(\PageIndex{116}\)

\(\dfrac{11}{12} + \dfrac{7}{8}\)

Exercise \(\PageIndex{117}\)

\(\dfrac{9}{32} + \dfrac{15}{16}\)

Answer

\(\dfrac{1}{4} + 1 = 1\dfrac{1}{4}\) (\(\dfrac{39}{32}\) or 1 \(\dfrac{7}{32}\))

Exercise \(\PageIndex{118}\)

\(\dfrac{5}{8} + \dfrac{1}{32}\)

Exercise \(\PageIndex{119}\)

\(2 \dfrac{3}{4} + 6 \dfrac{3}{5}\)

Answer

\(2 \dfrac{3}{4} + 6 \dfrac{1}{2} = 9 \dfrac{1}{4}\) (\(9 \dfrac{7}{20}\))

Exercise \(\PageIndex{120}\)

\(4 \dfrac{5}{9} + 8 \dfrac{1}{27}\)

Exercise \(\PageIndex{121}\)

\(11 \dfrac{5}{18} + 7 \dfrac{22}{45}\)

Answer

\(11 dfrac{1}{4} + 7 \dfrac{1}{2} = 18 \dfrac{3}{4}\) (\(18 \dfrac{23}{30}\))

Exercise \(\PageIndex{122}\)

\(14 \dfrac{19}{36} + 2\dfrac{7}{18}\)

Exercise \(\PageIndex{123}\)

\(6 \dfrac{1}{20} + 2 \dfrac{1}{10} + 8 \dfrac{13}{60}\)

Answer

\(6 + 2 + 8 \dfrac{1}{4} = 16 \dfrac{1}{4}\) (\(16 \dfrac{11}{30}\))

Exercise \(\PageIndex{124}\)

\(5 \dfrac{7}{8} + 1 \dfrac{1}{4} + 12 \dfrac{5}{12}\)

Exercise \(\PageIndex{125}\)

\(10 \dfrac{1}{2} + 6 \dfrac{15}{16} + 8 \dfrac{19}{80}\)

Answer

\(10 \dfrac{1}{2} + 7 + 8 \dfrac{1}{4} = 25 \dfrac{3}{4}\) (\(25 \dfrac{3}{4}\))