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