Elementary Algebra

# Review Exercises

Elementary AlgebraReview Exercises

### Review Exercises

##### Introduction to Whole Numbers

Use Place Value with Whole Number

In the following exercises find the place value of each digit.

913.

26,915

1
2
9
5
6

914.

359,417

9
3
4
7
1

915.

58,129,304

5
0
1
8
2

916.

9,430,286,157

6
4
9
0
5

In the following exercises, name each number.

917.

6,104

918.

493,068

919.

3,975,284

920.

85,620,435

In the following exercises, write each number as a whole number using digits.

921.

three hundred fifteen

922.

sixty-five thousand, nine hundred twelve

923.

ninety million, four hundred twenty-five thousand, sixteen

924.

one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven

In the following exercises, round to the indicated place value.

925.

Round to the nearest ten.

407 8,564

926.

Round to the nearest hundred.

25,846 25,864

In the following exercises, round each number to the nearest hundred thousand ten thousand.

927.

864,951

928.

3,972,849

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

929.

168

930.

264

931.

375

932.

750

933.

1430

934.

1080

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

935.

420

936.

115

937.

225

938.

2475

939.

1560

940.

56

941.

72

942.

168

943.

252

944.

391

In the following exercises, find the least common multiple of the following numbers using the multiples method.

945.

6,15

946.

60, 75

In the following exercises, find the least common multiple of the following numbers using the prime factors method.

947.

24, 30

948.

70, 84

##### Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

949.

$25−725−7$

950.

$5·65·6$

951.

$45÷545÷5$

952.

$x+8x+8$

953.

$42≥2742≥27$

954.

$3n=243n=24$

955.

$3≤20÷43≤20÷4$

956.

$a≠7·4a≠7·4$

In the following exercises, determine if each is an expression or an equation.

957.

$6·3+56·3+5$

958.

$y−8=32y−8=32$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

959.

$3535$

960.

$108108$

In the following exercises, simplify

961.

$6+10/2+26+10/2+2$

962.

$9+12/3+49+12/3+4$

963.

$20÷(4+6)·520÷(4+6)·5$

964.

$33÷(3+8)·233÷(3+8)·2$

965.

$42+5242+52$

966.

$(4+5)2(4+5)2$

Evaluate an Expression

In the following exercises, evaluate the following expressions.

967.

$9x+79x+7$ when $x=3x=3$

968.

$5x−45x−4$ when $x=6x=6$

969.

$x4x4$ when $x=3x=3$

970.

$3x3x$ when $x=3x=3$

971.

$x2+5x−8x2+5x−8$ when $x=6x=6$

972.

$2x+4y−52x+4y−5$ when
$x=7,y=8x=7,y=8$

Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

973.

$12n12n$

974.

$9x29x2$

In the following exercises, identify the like terms.

975.

$3n,n2,12,12p2,3,3n23n,n2,12,12p2,3,3n2$

976.

$5,18r2,9s,9r,5r2,5s5,18r2,9s,9r,5r2,5s$

In the following exercises, identify the terms in each expression.

977.

$11x2+3x+611x2+3x+6$

978.

$22y3+y+1522y3+y+15$

In the following exercises, simplify the following expressions by combining like terms.

979.

$17a+9a17a+9a$

980.

$18z+9z18z+9z$

981.

$9x+3x+89x+3x+8$

982.

$8a+5a+98a+5a+9$

983.

$7p+6+5p−47p+6+5p−4$

984.

$8x+7+4x−58x+7+4x−5$

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

985.

the sum of 8 and 12

986.

the sum of 9 and 1

987.

the difference of $xx$ and 4

988.

the difference of $xx$ and 3

989.

the product of 6 and $yy$

990.

the product of 9 and $yy$

991.

##### Visualize Fractions

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

1065.

$1414$

1066.

$1313$

1067.

$5656$

1068.

$2727$

Simplify Fractions

In the following exercises, simplify.

1069.

$721721$

1070.

$824824$

1071.

$15201520$

1072.

$12181218$

1073.

$−168192−168192$

1074.

$−140224−140224$

1075.

$11x11y11x11y$

1076.

$15a15b15a15b$

Multiply Fractions

In the following exercises, multiply.

1077.

$25·1325·13$

1078.

$12·3812·38$

1079.

$712(−821)712(−821)$

1080.

$512(−815)512(−815)$

1081.

$−28p(−14)−28p(−14)$

1082.

$−51q(−13)−51q(−13)$

1083.

$145(−15)145(−15)$

1084.

$−1(−38)−1(−38)$

Divide Fractions

In the following exercises, divide.

1085.

$12÷1412÷14$

1086.

$12÷1812÷18$

1087.

$−45÷47−45÷47$

1088.

$−34÷35−34÷35$

1089.

$58÷a1058÷a10$

1090.

$56÷c1556÷c15$

1091.

$7p12÷21p87p12÷21p8$

1092.

$5q12÷15q85q12÷15q8$

1093.

$25÷(−10)25÷(−10)$

1094.

$−18÷−(92)−18÷−(92)$

In the following exercises, simplify.

1095.

$23892389$

1096.

$4581545815$

1097.

$−9103−9103$

1098.

$258258$

1099.

$r5s3r5s3$

1100.

$−x6−89−x6−89$

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

1101.

$4+1184+118$

1102.

$9+379+37$

1103.

$307−12307−12$

1104.

$154−9154−9$

1105.

$22−1419−1322−1419−13$

1106.

$15+918+1215+918+12$

1107.

$5·8−105·8−10$

1108.

$3·4−243·4−24$

1109.

$15·5−522·1015·5−522·10$

1110.

$12·9−323·1812·9−323·18$

1111.

$2+4(3)−3−222+4(3)−3−22$

1112.

$7+3(5)−2−327+3(5)−2−32$

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

1113.

the quotient of c and the sum of d and 9.

1114.

the quotient of the difference of h and k, and $−5−5$.

Add and Subtract Fractions with a Common Denominator

1115.

$49+1949+19$

1116.

$29+5929+59$

1117.

$y3+23y3+23$

1118.

$7p+9p7p+9p$

1119.

$−18+(−38)−18+(−38)$

1120.

$−18+(−58)−18+(−58)$

In the following exercises, subtract.

1121.

$45−1545−15$

1122.

$45−3545−35$

1123.

$y17−917y17−917$

1124.

$x19−819x19−819$

1125.

$−8d−3d−8d−3d$

1126.

$−7c−7c−7c−7c$

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

1127.

$13+1513+15$

1128.

$14+1514+15$

1129.

$15−(−110)15−(−110)$

1130.

$12−(−16)12−(−16)$

1131.

$23+3423+34$

1132.

$34+2534+25$

1133.

$1112−381112−38$

1134.

$58−71258−712$

1135.

$−916−(−45)−916−(−45)$

1136.

$−720−(−58)−720−(−58)$

1137.

$1+561+56$

1138.

$1−591−59$

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

1139.

$(15)22+32(15)22+32$

1140.

$(13)25+22(13)25+22$

1141.

$23+1234−2323+1234−23$

1142.

$34+1256−2334+1256−23$

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

1143.

$x+12x+12$ when
$x=−18x=−18$
$x=−12x=−12$

1144.

$x+23x+23$ when
$x=−16x=−16$
$x=−53x=−53$

1145.

$4p2q4p2q$ when $p=−12p=−12$ and $q=59q=59$

1146.

$5m2n5m2n$ when $m=−25m=−25$ and $n=13n=13$

1147.

$u+vwu+vw$ when
$u=−4,v=−8,w=2u=−4,v=−8,w=2$

1148.

$m+npm+np$ when
$m=−6,n=−2,p=4m=−6,n=−2,p=4$

##### Decimals

Name and Write Decimals

In the following exercises, write as a decimal.

1149.

Eight and three hundredths

1150.

Nine and seven hundredths

1151.

One thousandth

1152.

Nine thousandths

In the following exercises, name each decimal.

1153.

7.8

1154.

5.01

1155.

0.005

1156.

0.381

Round Decimals

In the following exercises, round each number to the nearest hundredth tenth whole number.

1157.

5.7932

1158.

3.6284

1159.

12.4768

1160.

25.8449

In the following exercises, add or subtract.

1161.

$18.37+9.3618.37+9.36$

1162.

$256.37−85.49256.37−85.49$

1163.

$15.35−20.8815.35−20.88$

1164.

$37.5+12.2337.5+12.23$

1165.

$−4.2+(−9.3)−4.2+(−9.3)$

1166.

$−8.6+(−8.6)−8.6+(−8.6)$

1167.

$100−64.2100−64.2$

1168.

$100−65.83100−65.83$

1169.

$2.51+402.51+40$

1170.

$9.38+609.38+60$

Multiply and Divide Decimals

In the following exercises, multiply.

1171.

$(0.3)(0.4)(0.3)(0.4)$

1172.

$(0.6)(0.7)(0.6)(0.7)$

1173.

$(8.52)(3.14)(8.52)(3.14)$

1174.

$(5.32)(4.86)(5.32)(4.86)$

1175.

$(0.09)(24.78)(0.09)(24.78)$

1176.

$(0.04)(36.89)(0.04)(36.89)$

In the following exercises, divide.

1177.

$0.15÷50.15÷5$

1178.

$0.27÷30.27÷3$

1179.

$8.49÷128.49÷12$

1180.

$16.99÷916.99÷9$

1181.

$12÷0.0812÷0.08$

1182.

$5÷0.045÷0.04$

Convert Decimals, Fractions, and Percents

In the following exercises, write each decimal as a fraction.

1183.

0.08

1184.

0.17

1185.

0.425

1186.

0.184

1187.

1.75

1188.

0.035

In the following exercises, convert each fraction to a decimal.

1189.

$2525$

1190.

$4545$

1191.

$−38−38$

1192.

$−58−58$

1193.

$5959$

1194.

$2929$

1195.

$12+6.512+6.5$

1196.

$14+10.7514+10.75$

In the following exercises, convert each percent to a decimal.

1197.

5%

1198.

9%

1199.

40%

1200.

50%

1201.

115%

1202.

125%

In the following exercises, convert each decimal to a percent.

1203.

0.18

1204.

0.15

1205.

0.009

1206.

0.008

1207.

1.5

1208.

2.2

##### The Real Numbers

Simplify Expressions with Square Roots

In the following exercises, simplify.

1209.

$6464$

1210.

$144144$

1211.

$−25−25$

1212.

$−81−81$

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

1213.

9 8.47

1214.

$−15−15$ 3.591

In the following exercises, list the rational numbers, irrational numbers.

1215.

$0.84,0.79132…,1.3–0.84,0.79132…,1.3–$

1216.

$2.38–,0.572,4.93814…2.38–,0.572,4.93814…$

In the following exercises, identify whether each number is rational or irrational.

1217.

$121121$ $4848$

1218.

$5656$ $1616$

In the following exercises, identify whether each number is a real number or not a real number.

1219.

$−9−9$ $−169−169$

1220.

$−64−64$ $−81−81$

In the following exercises, list the whole numbers, integers, rational numbers, irrational numbers, real numbers for each set of numbers.

1221.

$−4,0,56,16,18,5.2537…−4,0,56,16,18,5.2537…$

1222.

$−4,0.36—,133,6.9152…,48,1012−4,0.36—,133,6.9152…,48,1012$

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

1223.

$23,54,12523,54,125$

1224.

$13,74,13513,74,135$

1225.

$213,−213213,−213$

1226.

$135,−135135,−135$

In the following exercises, order each of the following pairs of numbers, using < or >.

1227.

$−1___−18−1___−18$

1228.

$−314___−4−314___−4$

1229.

$−79___−49−79___−49$

1230.

$−2___−198−2___−198$

Locate Decimals on the Number Line

In the following exercises, locate on the number line.

1231.

$0.30.3$

1232.

$−0.2−0.2$

1233.

$−2.5−2.5$

1234.

2.7

In the following exercises, order each of the following pairs of numbers, using < or >.

1235.

$0.9___0.60.9___0.6$

1236.

$0.7___0.80.7___0.8$

1237.

$−0.6___−0.59−0.6___−0.59$

1238.

$−0.27___−0.3−0.27___−0.3$

##### Properties of Real Numbers

Use the Commutative and Associative Properties

In the following exercises, use the Associative Property to simplify.

1239.

$−12(4m)−12(4m)$

1240.

$30(56q)30(56q)$

1241.

$(a+16)+31(a+16)+31$

1242.

$(c+0.2)+0.7(c+0.2)+0.7$

In the following exercises, simplify.

1243.

$6y+37+(−6y)6y+37+(−6y)$

1244.

$14+1115+(−14)14+1115+(−14)$

1245.

$1411·359·14111411·359·1411$

1246.

$−18·15·29−18·15·29$

1247.

$(712+45)+15(712+45)+15$

1248.

$(3.98d+0.75d)+1.25d(3.98d+0.75d)+1.25d$

1249.

$11x+8y+16x+15y11x+8y+16x+15y$

1250.

$52m+(−20n)+(−18m)+(−5n)52m+(−20n)+(−18m)+(−5n)$

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number.

1251.

$1313$
$5.15.1$
$−14−14$
$−85−85$

1252.

$−78−78$
$−0.03−0.03$
$1717$
$125125$

In the following exercises, find the multiplicative inverse of each number.

1253.

10 $−49−49$ 0.6

1254.

$−92−92$ $−7−7$ 2.1

Use the Properties of Zero

In the following exercises, simplify.

1255.

$83·083·0$

1256.

$0909$

1257.

$5050$

1258.

$0÷230÷23$

In the following exercises, simplify.

1259.

$43+39+(−43)43+39+(−43)$

1260.

$(n+6.75)+0.25(n+6.75)+0.25$

1261.

$513·57·135513·57·135$

1262.

$16·17·1216·17·12$

1263.

$23·28·3723·28·37$

1264.

$9(6x−11)+159(6x−11)+15$

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

1265.

$7(x+9)7(x+9)$

1266.

$9(u−4)9(u−4)$

1267.

$−3(6m−1)−3(6m−1)$

1268.

$−8(−7a−12)−8(−7a−12)$

1269.

$13(15n−6)13(15n−6)$

1270.

$(y+10)·p(y+10)·p$

1271.

$(a−4)−(6a+9)(a−4)−(6a+9)$

1272.

$4(x+3)−8(x−7)4(x+3)−8(x−7)$

##### Systems of Measurement

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

1273.

A floral arbor is 7 feet tall. Convert the height to inches.

1274.

A picture frame is 42 inches wide. Convert the width to feet.

1275.

Kelly is 5 feet 4 inches tall. Convert her height to inches.

1276.

A playground is 45 feet wide. Convert the width to yards.

1277.

The height of Mount Shasta is 14,179 feet. Convert the height to miles.

1278.

Shamu weights 4.5 tons. Convert the weight to pounds.

1279.

The play lasted $134134$ hours. Convert the time to minutes.

1280.

How many tablespoons are in a quart?

1281.

Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.

1282.

Trinh needs 30 cups of paint for her class art project. Convert the volume to gallons.

Use Mixed Units of Measurement in the U.S. System.

In the following exercises, solve.

1283.

John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?

1284.

Every day last week Pedro recorded the number of minutes he spent reading. The number of minutes were 50, 25, 83, 45, 32, 60, 135. How many hours did Pedro spend reading?

1285.

Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?

1286.

Dalila wants to make throw pillow covers. Each cover takes 30 inches of fabric. How many yards of fabric does she need for 4 covers?

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

1287.

Donna is 1.7 meters tall. Convert her height to centimeters.

1288.

Mount Everest is 8,850 meters tall. Convert the height to kilometers.

1289.

One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.

1290.

One cup of yogurt contains 13 grams of protein. Convert this to milligrams.

1291.

Sergio weighed 2.9 kilograms at birth. Convert this to grams.

1292.

A bottle of water contained 650 milliliters. Convert this to liters.

Use Mixed Units of Measurement in the Metric System

In the following exerices, solve.

1293.

Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?

1294.

Selma had a 1 liter bottle of water. If she drank 145 milliliters, how much water was left in the bottle?

1295.

One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?

1296.

One ounce of tofu provided 2 grams of protein. How many milligrams of protein are provided by 5 ounces of tofu?

Convert between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

1297.

Majid is 69 inches tall. Convert his height to centimeters.

1298.

A college basketball court is 84 feet long. Convert this length to meters.

1299.

Caroline walked 2.5 kilometers. Convert this length to miles.

1300.

Lucas weighs 78 kilograms. Convert his weight to pounds.

1301.

Steve’s car holds 55 liters of gas. Convert this to gallons.

1302.

A box of books weighs 25 pounds. Convert the weight to kilograms.

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

1303.

95° Fahrenheit

1304.

23° Fahrenheit

1305.

20° Fahrenheit

1306.

64° Fahrenheit

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

1307.

30° Celsius

1308.

–5° Celsius

1309.

–12° Celsius

1310.

24° Celsius

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