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All Textbook Solutions for PREALGEBRA

In the following exercises, solve. 64=y4 Cookie packaging A package of 51 cookies has 3 equal rows of cookies. Find the number of cookies in each row, c, by solving the equation 3c=51.Kindergarten class Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. Find the number of children in each group, g, by solving the equation 4g=24.Is modeling the Division Property of Equality with envelopes and counters helpful to understanding how to solve the equation 3x=15? Explain why or why not.Suppose you are using envelopes and counters to model solving the equations x+4=12and 4x=12. Explain how you would solve each equation.Frida started to solve the equation 3x=36by adding 3 to both sides. Explain why Frida’s method will not solve the equation.Raoul started to solve the equation 4y=40by subtracting 4 from both sides. Explain why Raoul’s method will not solve the equation.In the following exercises, locate and label the integer on the number line.In the following exercises, locate and label the integer on the number line. -5 In the following exercises, locate and label the integer on the number line. -3 In the following exercises, locate and label the integer on the number line.In the following exercises, locate and label the integer on the number line. -8 In the following exercises, locate and label the integer on the number line. -7 In the following exercises, order each of the following pairs of numbers, using < or >. 4__8 In the following exercises, order each of the following pairs of numbers, using < or >. -6__3 In the following exercises, order each of the following pairs of numbers, using < or >. -5__-10 In the following exercises, order each of the following pairs of numbers, using < or >. -9__-4 In the following exercises, order each of the following pairs of numbers, using < or >. 2__-7 In the following exercises, order each of the following pairs of numbers, using < or >. -3__1 In the following exercises, find the opposite of each number.In the following exercises, find the opposite of each number. -2 In the following exercises, find the opposite of each number. -4 In the following exercises, find the opposite of each number. 3 In the following exercises, simplify. a. (8) b. (8)In the following exercises, simplify. a. (9) b. (9)In the following exercises, evaluate. x, when a. x=32 b. x=32 In the following exercises, evaluate. n, when a. n=20 b. n=20 In the following exercises, simplify. |21|In the following exercises, simplify. |42|In the following exercises, simplify. |36|In the following exercises, simplify. |15|In the following exercises, simplify. |0|In the following exercises, simplify. |75|In the following exercises, evaluate. |x|when x=14 In the following exercises, evaluate. |r|when r=27 In the following exercises, evaluate. |y|when y=33 In the following exercises, evaluate. |n|when n=4 In the following exercises, fill in <, >, or = for each of the following pairs of numbers. |4|__4 In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 2__ |2|In the following exercises, fill in <, >, or = for each of the following pairs of numbers. |6|__ 6 In the following exercises, fill in <, >, or = for each of the following pairs of numbers. |9|__ |9|In the following exercises, simplify. (55)and |55|In the following exercises, simplify. (48)and |48|In the following exercises, simplify. |125|In the following exercises, simplify. |9+7|In the following exercises, simplify. 6|9|In the following exercises, simplify. |148||2|In the following exercises, simplify. |93||512|In the following exercises, simplify. 5+4|153|In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. the opposite of 16 In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. the opposite of -8 In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. negative 3 In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. 19 minus negative 12 In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. a temperature of 10 below zero In the following exercises, translate each of the following phrases into expressions with positive or negative numbers. an elevation of 85 feet below sea level In the following exercises, model the following to find the sum. 3+7 In the following exercises, model the following to find the sum. 2+6 In the following exercises, model the following to find the sum. 5+(4)In the following exercises, model the following to find the sum. 3+(6)In the following exercises, simplify each expression. 14+82 In the following exercises, simplify each expression. 33+(67)In the following exercises, simplify each expression. 75+25 In the following exercises, simplify each expression. 54+(28)In the following exercises, simplify each expression. 409.11+(-15)+3 In the following exercises, simplify each expression. 19+(42)+12 In the following exercises, simplify each expression. 3+6(1+5)In the following exercises, simplify each expression. 10+4(3+7)In the following exercises, evaluate each expression. n+4when a. n=1 b. n=20 In the following exercises, evaluate each expression. x+(9)when a. x=3 b x=3 In the following exercises, evaluate each expression. (x+y)3when x=4,y=1 In the following exercises, evaluate each expression. (u+v)2when u=4,v=11 In the following exercises, translate each phrase into an algebraic expression and then simplify. the sum of -8 and 2 In the following exercises, translate each phrase into an algebraic expression and then simplify. 4 more than -12 In the following exercises, translate each phrase into an algebraic expression and then simplify. 10 more than the sum of -5 and -6 In the following exercises, translate each phrase into an algebraic expression and then simplify. 420.the sum of 3 and -5, increased by 18 In the following exercises, solve. Temperature On Monday, the high temperature in Denver was -4 degrees. Tuesday’s high temperature was 20 degrees more. What was the high temperature on Tuesday?In the following exercises, solve. Credit Frida owed $75 on her credit card. Then she charged $21 more. What was her new balance?In the following exercises, model the following. 61 In the following exercises, model the following. 4(3)In the following exercises, model the following. 2(5)In the following exercises, model the following. 14 In the following exercises, simplify each expression. 2416 In the following exercises, simplify each expression. 19(9)In the following exercises, simplify each expression. 317 In the following exercises, simplify each expression. 40(11)In the following exercises, simplify each expression. 52(17)23 In the following exercises, simplify each expression. 25(39)In the following exercises, simplify each expression. (17)(38)In the following exercises, simplify each expression. 3272 In the following exercises, evaluate each expression. x7when a. x=5 b. x=4 In the following exercises, evaluate each expression. 10ywhen a. y=15 b. y=16 In the following exercises, evaluate each expression. 2n2n+5when n=4 In the following exercises, evaluate each expression. 153u2when u=5 In the following exercises, translate each phrase into an algebraic expression and then simplify. the difference of -12 and 5 In the following exercises, translate each phrase into an algebraic expression and then simplify. subtract 23 from -50 In the following exercises, solve the given applications. Temperature One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. What was the afternoon temperature?In the following exercises, solve the given applications. Temperature On January 4, the high temperature in Laredo, Texas was 78 degrees, and the high in Houlton, Maine was -28 degrees. What was the difference in temperature of Laredo and Houlton?In the following exercises, multiply. 94 In the following exercises, multiply. 5(7)In the following exercises, multiply. (11)(11)wIn the following exercises, multiply. 16 In the following exercises, divide. 56(8)In the following exercises, divide. 120(6)In the following exercises, divide. 9612 In the following exercises, divide. 96(16)In the following exercises, divide. 45(1)In the following exercises, divide. 162(1)In the following exercises, simplify each expression. 5(9)3(12)In the following exercises, simplify each expression. (2)5 In the following exercises, simplify each expression. 34 In the following exercises, simplify each expression. (3)(4)(5)(6)In the following exercises, simplify each expression. 424(69)In the following exercises, simplify each expression. (815)(93)In the following exercises, simplify each expression. 2(18)9 In the following exercises, simplify each expression. 45(3)12 In the following exercises, evaluate each expression. 7x3when x=9 In the following exercises, evaluate each expression. 162nwhen n=8 In the following exercises, evaluate each expression. 5x+8bwhen a=2, b=6 In the following exercises, evaluate each expression. x2+5x+4when x=3 In the following exercises, translate to an algebraic expression and simplify if possible. the product of -12 and 6 In the following exercises, translate to an algebraic expression and simplify if possible. the quotient of 3 and the sum of -7 and s In the following exercises, determine whether each number is a solution of the given equation. 5x1035 a. x=9 b. x=5 c. x=5 In the following exercises, determine whether each number is a solution of the given equation. 468.sw 8u+24=32 a. u=7 b. u=1 c. u=7 In the following exercises, solve. a+14=2 In the following exercises, solve. b9=15 In the following exercises, solve. c+(10)=17 In the following exercises, solve. d(6)=26 In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.In the following exercises, solve each equation using the division property of equality and check the solution. 8p=72 In the following exercises, solve each equation using the division property of equality and check the solution. 12q=48 In the following exercises, solve each equation using the division property of equality and check the solution. 16r=64 In the following exercises, solve each equation using the division property of equality and check the solution. 478.sw 5s=100 In the following exercises, translate and solve. The product of -6 and y is -42 In the following exercises, translate and solve. The diffe ence of z and -13 is -18.In the following exercises, translate and solve. Four more than m is -48.In the following exercises, translate and solve. The product of -21 and n is 63.In the following exercises, translate and solve. Everyday Math 483. Describe how you have used two topics from this chapter in your life outside of your math class during the past month.Locate and label 0, 2, -4, and -1 on a number line.In the following exercises, compare the numbers, using < or >or =. a. 63 b. 14 In the following exercises, compare the numbers, using < or >or =. a. 5|5| b. |2|2 In the following exercises, find the opposite of each number. 487.a. -7 b. 8 In the following exercises, simplify. (22)In the following exercises, simplify. |49|In the following exercises, simplify. 8+6 In the following exercises, simplify. 15+(12)In the following exercises, simplify. 7(3)In the following exercises, simplify. 10(56)In the following exercises, simplify. 38 In the following exercises, simplify. 6(9)In the following exercises, simplify. 70(7)wIn the following exercises, simplify. (2)3 In the following exercises, simplify. 42 In the following exercises, simplify. 163(57)In the following exercises, simplify. |216||8|In the following exercises, evaluate. 35awhen a=4 In the following exercises, evaluate. 502.sw (2r)2when r=3 In the following exercises, evaluate. 3m2nwhen m=6,n=8 In the following exercises, evaluate. |y|when y=17 In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible. the difference of -7 and -4 In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible. the quotient of 25 and the sum of m and n.In the following exercises, solve. Early one morning, the temperature in Syracuse was -8°F. By noon, it had risen 12°. What was the temperature at noon?In the following exercises, solve. Collette owed $128 on her credit card. Then she charged $65. What was her new balance?In the following exercises, solve. n+6=5 In the following exercises, solve. p11=4 In the following exercises, solve. 9r=54 In the following exercises, translate and solve. The product of 15 and x is 75.In the following exercises, translate and solve. Eight less than y is -32.TRY IT:: 4.1 Name the fraction of the shape that is shaded in each figure:TRY IT:: 4.2 Name the fraction of the shape that is shaded in each figure:TRY IT:: 4.3 Shade of the circle.TRY IT:: 4.4 Shade of the rectangle.TRY IT:: 4.5 Use fraction circles to make wholes with the following pieces: 3 thirds.TRY IT:: 4.6 Use fraction circles to make wholes with the following pieces: 8 eighths.TRY IT:: 4.7 Use fraction circles to make wholes with the following pieces: 5 thirds.TRY IT:: 4.8 Use fraction circles to make wholes with the following pieces: 5 halves.TRY IT:: 4.9 Name the improper fraction. Then write it as a mixed number.TRY IT:: 4.10 Name the improper fraction. Then write it as a mixed number.TRY IT:: 4.11 Draw a figure to model 76 .TRY IT:: 4.12 Draw a figure to model 65 .TRY IT:: 4.13 Use a model to rewrite the improper fraction as a mixed number: 97 .TRY IT:: 4.14 Use a model to rewrite the improper fraction as a mixed number: 74 .TRY IT:: 4.15 Use a model to rewrite the mixed number as an improper fraction: 138 .TRY IT:: 4.16 Use a model to rewrite the mixed number as an improper fraction: 156 .TRY IT:: 4.17 Convert the improper fraction to a mixed number: 137 .TRY IT:: 4.18 Convert the improper fraction to a mixed number: 149 .TRY IT:: 4.19 Convert the improper fraction to a mixed number: 237 .TRY IT:: 4.20 Convert the improper fraction to a mixed number: 4811 .TRY IT:: 4.21 Convert the mixed number to an improper fraction: 357 .TRY IT:: 4.22 Convert the mixed number to an improper fraction: 278 .TRY IT:: 4.23 Convert the mixed number to an improper fraction: 4611 .TRY IT:: 4.24 Convert the mixed number to an improper fraction: 1113 .TRY IT:: 4.25 Use fraction tiles to find equivalent fractions: How many eighths equal one-fourth?TRY IT:: 4.26 Use fraction tiles to find equivalent fractions: How many twelfths equal one-fourth?TRY IT:: 4.27 Find three fractions equivalent to 35 .TRY IT:: 4.28 Find three fractions equivalent to 45 .TRY IT:: 4.29 Find a fraction with a denominator of 21 that is equivalent to 67 .TRY IT: : 4.30 Find a fraction with a denominator of 100 that is equivalent to 310 .TRY IT:: 4.31 Locate and label the following on a number line: 13,54,74,235,92 .TRY IT:: 4.32 Locate and label the following on a number line: 23,52,94,114,325 .TRY IT:: 4.33 Locate and label each of the given fractions on a number line: 23,23,214,214,32,32 TRY IT:: 4.34 Locate and label each of the given fractions on a number line: 34,34,112,112,73,73 TRY IT:: 4.35 Order each of the following pairs of numbers, using < or >: a. 13 __ 1 b. 112 __ 2 c. 23 __ 13 d. 3 __ 73 TRY IT:: 4.36 Order each of the following pairs of numbers, using < or >: a. 3 __ 175 b. 214 __ 2 c. 35 __ 45 d. 4 __ 103 In the following exercises, name the fraction of each figure that is shaded. 1.In the following exercises, name the fraction of each figure that is shaded. 2.In the following exercises, shade parts of circles or squares to model the following fractions. 3. 12 In the following exercises, shade parts of circles or squares to model the following fractions. 4. 13 In the following exercises, shade parts of circles or squares to model the following fractions. 5. 34 In the following exercises, shade parts of circles or squares to model the following fractions. 6. 25 In the following exercises, shade parts of circles or squares to model the following fractions. 7. 56 In the following exercises, shade parts of circles or squares to model the following fractions. 8. 78 In the following exercises, shade parts of circles or squares to model the following fractions. 9. 58 In the following exercises, shade parts of circles or squares to model the following fractions. 710 In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 3 thirds In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 8 eighths In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 7 sixths In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 4 thirds In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 7 fifths In the following exercises, use fraction circles to make wholes, if possible, with the following pieces. 7 fourths In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number. 17.In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number. 18.In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number. 19.In the following exercises, draw fraction circles to model the given fraction. 33 In the following exercises, draw fraction circles to model the given fraction. 44 In the following exercises, draw fraction circles to model the given fraction. 74 In the following exercises, draw fraction circles to model the given fraction. 53 In the following exercises, draw fraction circles to model the given fraction. 116 In the following exercises, draw fraction circles to model the given fraction. 138 In the following exercises, draw fraction circles to model the given fraction. 103 In the following exercises, draw fraction circles to model the given fraction. 94 In the following exercises, rewrite the improper fraction as a mixed number. 32 In the following exercises, rewrite the improper fraction as a mixed number. 53 In the following exercises, rewrite the improper fraction as a mixed number. 114 In the following exercises, rewrite the improper fraction as a mixed number. 135 In the following exercises, rewrite the improper fraction as a mixed number. 256 In the following exercises, rewrite the improper fraction as a mixed number. 289 In the following exercises, rewrite the improper fraction as a mixed number. 4213 In the following exercises, rewrite the improper fraction as a mixed number. 4715 In the following exercises, rewrite the mixed number as an improper fraction. 123 In the following exercises, rewrite the mixed number as an improper fraction. 125 In the following exercises, rewrite the mixed number as an improper fraction. 214 In the following exercises, rewrite the mixed number as an improper fraction. 256 In the following exercises, rewrite the mixed number as an improper fraction. 279 In the following exercises, rewrite the mixed number as an improper fraction. 257 In the following exercises, rewrite the mixed number as an improper fraction. 347 In the following exercises, rewrite the mixed number as an improper fraction. 359 In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many sixths equal one-third?In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many twelfths equal one-third?In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many eighths equal three-fourths?In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many twelfths equal three-fourths?In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many fourths equal three-halves?In the following exercises, use fraction tiles or draw a figure to find equivalent fractions. How many sixths equal three-halves?In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 50. 14 In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 51. 13 In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 52. 38 In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 53. 56 In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 54. 27 In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 55. 59 In the following exercises, plot the numbers on a number line. 23,54,125 In the following exercises, plot the numbers on a number line. 13,74,135 In the following exercises, plot the numbers on a number line. 14,95,113 In the following exercises, plot the numbers on a number line. 710,52,138,3 In the following exercises, plot the numbers on a number line. 213,213 In the following exercises, plot the numbers on a number line. 134,135 In the following exercises, plot the numbers on a number line. 34,34,123,123,52,52 In the following exercises, plot the numbers on a number line. 25,25,134,134,83,83 In the following exercises, order each of the following pairs of numbers, using < or >. 1 __ 14 In the following exercises, order each of the following pairs of numbers, using < or >. 1 __ 13 In the following exercises, order each of the following pairs of numbers, using < or >. 212 __ 3 In the following exercises, order each of the following pairs of numbers, using < or >. 134 __ 2 In the following exercises, order each of the following pairs of numbers, using < or >. 512 __ 712 In the following exercises, order each of the following pairs of numbers, using < or >. 910 __ 310 In the following exercises, order each of the following pairs of numbers, using < or >. 3 __ 135 In the following exercises, order each of the following pairs of numbers, using < or >. 4 __ 236 Music Measures A choreographed dance is broken into counts. A 11 count has one step in a count, a 12 count has two steps in a count and a 13 count has three steps in a count. How many steps would be in a 15 count? What type of count has four steps in it?Music Measures Fractions are used often in music. In 44 time, there are four quarter notes in one measure. a. How many measures would eight quarter notes make? b. The song “Happy Birthday to You” has 25 quarter notes. How many measures are there in “Happy Birthday to You?”Baking Nina is making five pans of fudge to serve after a music recital. For each pan, she needs 12 cup of walnuts. a. How many cups of walnuts does she need for five pans of fudge? b. Do you think it is easier to measure this amount when you use an improper fraction or a mixed number? Why?Give an example from your life experience (outside of school) where it was important to understand fractions.Explain how you locate the improper fraction 214 on a number line on which only the whole numbers from 0 through 10 are marked.TRY IT:: 4.37 Simplify: 812 .TRY IT:: 4.38 Simplify: 1216 .TRY IT:: 4.39 Simplify: 2128 .TRY IT:: 4.40 Simplify: 1624 .TRY IT:: 4.41 Simplify: 5442 .TRY IT:: 4.42 Simplify: 8145 .TRY IT:: 4.43 Simplify: 69120 .TRY IT:: 4.44 Simplify: 120192 .TRY IT:: 4.45 Simplify: 7x7y .TRY IT:: 4.46 Simplify: 9a9b .TRY IT:: 4.47 Use a diagram to model: 1235 .TRY IT:: 4.48 Use a diagram to model: 1256 .TRY IT:: 4.49 Multiply, and write the answer in simplified form: 1325 .TRY IT:: 4.50 Multiply, and write the answer in simplified form: 3578 .TRY IT:: 4.51 Multiply, and write the answer in simplified form: 47(58) .TRY IT:: 4.52 Multiply, and write the answer in simplified form: 712(89) .TRY IT:: 4.53 Multiply, and write the answer in simplified form: 1028815 .TRY IT:: 4.54 Multiply, and write the answer in simplified form: 920512 .TRY IT:: 4.55 Multiply, and write the answer in simplified form: a. 1872 b. 113(9a)TRY IT:: 4.56 Multiply, and write the answer in simplified form: a. 3864 b. 16x1112

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