lesson 8 homework 4.5 answer key

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Eureka Math Grade 4 Module 5 Lesson 8 Answer Key

Engage ny eureka math 4th grade module 5 lesson 8 answer key, eureka math grade 4 module 5 lesson 8 problem set answer key.

Each rectangle represents 1.

Answer: 2/3 = 4/6.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 2/3 = 2 x 2/3 x 2. 2 x 2 = 4. 3 x 2 = 6. 2/3 = 4/6.

Answer: 3/4 = 9/16.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 3/4 = 3 x 3/4 x 4. 3 x 3 = 9. 4 x 4 = 16. 3/4 = 9/16.

Answer: 4/5 = 8/10.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 4/5 = 4 x 2/5 x 2. 4 x 2 = 8. 5 x 2 = 10. 4/5 = 8/10.

Answer: 5/6 = 10/12.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 5/6 = 5 x 2/6 x 2. 5 x 2 = 10. 6 x 2 = 12. 5/6 = 10/12.

Answer: 3/5 = 6/10.

Answer: 3/5 = 9/15.

Question 3. Draw area models to prove that the following number sentences are true. a. \(\frac{2}{5}\) = \(\frac{4}{10}\)

Answer: 2/5 = 4/10.

b. \(\frac{2}{3}\) = \(\frac{8}{12}\)

Answer: 2/3 = 8/12.

c. \(\frac{3}{6}\) = \(\frac{6}{12}\)

Answer: 3/6 = 6/12.

d. \(\frac{4}{6}\) = \(\frac{8}{12}\)

Answer: 4/6 = 8/12.

Question 4. Use multiplication to find an equivalent fraction for each fraction below. a. \(\frac{3}{4}\)

b. \(\frac{4}{5}\)

Answer: 4/5 = 8/15.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 4/5 = 4 x 2/5 x 3. 4 x 2 = 8. 5 x 3 = 15. 4/5 = 8/15.

c. \(\frac{7}{6}\)

Answer: 7/6 = 14/12.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 7/6 = 7 x 2/6 x 2. 7 x 2 = 14. 6 x 2 = 12. 7/6 = 14/12.

d. \(\frac{12}{7}\)

Answer: 12/7 = 24/14.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 12/7 = 12 x 2/7 x 2. 12 x 2 = 24. 7 x 2 = 14. 12/7 = 24/14.

Question 5. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence. a. \(\frac{4}{3}\) = \(\frac{8}{9}\)

Answer: 4/3 = 8/9.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 4/3 = 4 x 2/3 x 3. 4 x 2 = 8. 3 x 3 = 9. 4/3 = 8/9.

b. \(\frac{5}{4}\) = \(\frac{10}{8}\)

Answer: 5/4 = 10/8.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 5/4 = 5 x 2/4 x 2. 5 x 2 = 10. 4 x 2 = 8. 5/4 = 10/8.

c. \(\frac{4}{5}\) = \(\frac{12}{10}\)

Answer: 4/5 = 12/10 is wrong. 4/5 = 8/10 is correct.

d. \(\frac{4}{6}\) = \(\frac{12}{18}\)

Answer: 4/6 = 12/18.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 4/6 = 4 x 3/6 x 3. 4 x 3 = 12. 6 x 3 = 18. 4/6 = 12/18.

Eureka Math Grade 4 Module 5 Lesson 8 Exit Ticket Answer Key

Question 1. Use multiplication to create an equivalent fraction for the fraction below. \(\frac{2}{5}\)

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 2/5 = 2 x 2/5 x 2. 2 x 4 = 8. 5 x 2 = 10. 2/5 = 4/10.

Question 2. Determine if the following is a true number sentence. If needed, correct the statement by changing the right-hand side of the number sentence. \(\frac{3}{4}\) = \(\frac{9}{8}\)

Answer: 3/4 = 9/8.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 3/4 = 3 x 3/4 x 2. 3 x 3 = 9. 4 x 2 = 8. 3/4 = 9/8.

Eureka Math Grade 4 Module 5 Lesson 8 Homework Answer Key

Answer: 3/4 = 6/8.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 3/4 = 3 x 2/4 x 2. 3 x 2 = 6. 4 x 2 = 8. 3/4 = 6/8.

Answer: 4/5 = 12/15.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 4/5 = 4 x 3/5 x 3. 4 x 3 = 12. 5 x 3 = 15. 4/5 = 12/15.

Answer: 7/8 = 14/16.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 7/8 = 7 x 2/8 x 2. 7 x 2 = 14. 8 x 2 = 16. 7/8 = 14/16.

Answer: 3/6 = 9/12.

Answer: 2/4 = 6/12.

Question 3. Draw area models to prove that the following number sentences are true. a. \(\frac{1}{3}\) = \(\frac{2}{6}\)

Answer: 1/3 = 2/6.

b. \(\frac{2}{5}\) = \(\frac{4}{10}\)

c. \(\frac{5}{7}\) = \(\frac{10}{14}\)

Answer: 5/7 = 10/14.

d. \(\frac{3}{6}\) = \(\frac{9}{18}\)

Answer: 3/6 = 9/18.

Question 4. Use multiplication to create an equivalent fraction for each fraction below. a. \(\frac{2}{3}\)

b. \(\frac{5}{6}\)

c. \(\frac{6}{5}\)

Answer: 6/5 = 12/10.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 6/5 = 6 x 2/5 x 2. 6 x 2 = 12. 5 x 2 = 10. 6/5 = 12/10.

d. \(\frac{10}{8}\)

Answer: 10/8 = 5/4.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 10/8 = 5 x 2/2 x 2. 5 x 2 = 10. 2 x 2 = 4. 10/8 = 5/4.

Question 5. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence. a. \(\frac{2}{3}\) = \(\frac{4}{9}\)

Answer: 2/3 = 4/9.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 2/3 = 2 x 2/3 x 3. 2 x 2 = 4. 3 x 3 = 9. 2/3 = 4/9.

b. \(\frac{5}{6}\) = \(\frac{10}{12}\)

c. \(\frac{3}{5}\) = \(\frac{6}{15}\)

Answer: 3/5 = 6/15 is wrong. 3/5 = 9/15 is correct.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 3/5 = 3 x 3/ 5 x 3. 3 x 3 = 9. 5 x 3 = 15. 3/5 = 9/15.

d. \(\frac{7}{4}\) = \(\frac{21}{12}\).

Answer: 7/4 = 21/12.

Explanation: In the above-given question, given that, the shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. 7/4 = 7 x 3/4 x 3. 7 x 3 = 21. 4 x 3 = 12. 7/4 = 21/12.

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( 3 , 2 ) ( 3 , 2 )

( 2 , 3 ) ( 2 , 3 )

( 3 , 4 ) ( 3 , 4 )

( 5 , −4 ) ( 5 , −4 )

no solution

infinitely many solutions

ⓐ no solution, inconsistent, independent ⓑ one solution, consistent, independent

( 6 , 1 ) ( 6 , 1 )

( −3 , 5 ) ( −3 , 5 )

( 2 , 3 2 ) ( 2 , 3 2 )

( − 1 2 , −2 ) ( − 1 2 , −2 )

( 2 , −1 ) ( 2 , −1 )

( −2 , 3 ) ( −2 , 3 )

( 1 , 3 ) ( 1 , 3 )

( 4 , −3 ) ( 4 , −3 )

( 6 , 2 ) ( 6 , 2 )

( 1 , −2 ) ( 1 , −2 )

ⓐ Since both equations are in standard form, using elimination will be most convenient. ⓑ Since one equation is already solved for x , using substitution will be most convenient.

ⓐ Since one equation is already solved for y , using substitution will be most convenient. ⓑ Since both equations are in standard form, using elimination will be most convenient.

160 policies

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

The angle measures are 55 and 35.

The angle measures are 5 and 85.

The angle measures are 42 and 138.

The angle measures are 66 and 114.

The length is 60 feet and the width is 35 feet.

The length is 60 feet and the width is 38 feet.

It will take Clark 4 hours to catch Mitchell.

It will take Sally 1 1 2 1 1 2 hours to catch up to Charlie.

The rate of the boat is 11 mph and the rate of the current is 1 mph.

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

The speed of the jet is 235 mph and the speed of the wind is 30 mph.

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

206 adults, 347 children

42 adults, 105 children

13 dimes and 29 quarters

19 quarters and 51 nickels

3 pounds peanuts and 2 pounds cashews

10 pounds of beans, 10 pounds of ground beef

120 ml of 25% solution and 30 ml of 50% solution

125 ml of 10% solution and 125 ml of 40% solution

$42,000 in the stock fund and $8000 in the savings account

$1750 at 11% and $5250 at 13%

Bank $4,000; Federal $14,000

$41,200 at 4.5%, $24,000 at 7.2%

ⓐ C ( x ) = 15 x + 25 , 500 C ( x ) = 15 x + 25 , 500

ⓑ R ( x ) = 32 x R ( x ) = 32 x

ⓓ 1,500 1,500 ; when 1,500 benches are sold, the cost and revenue will be both 48,000

ⓐ C ( x ) = 120 x + 150,000 C ( x ) = 120 x + 150,000

ⓑ R ( x ) = 170 x R ( x ) = 170 x

ⓓ 3,000 3,000 ; when 3,000 benches are sold, the revenue and costs are both $510,000

( 2 , −1 , 3 ) ( 2 , −1 , 3 )

( −2 , 3 , 4 ) ( −2 , 3 , 4 )

( −3 , 4 , −2 ) ( −3 , 4 , −2 )

( −2 , 3 , −1 ) ( −2 , 3 , −1 )

infinitely many solutions ( x , 3 , z ) ( x , 3 , z ) where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

The fine arts department sold 75 adult tickets, 200 student tickets, and 75 child tickets.

The soccer team sold 200 adult tickets, 300 student tickets, and 100 child tickets.

ⓐ [ 3 8 −3 2 5 −3 ] [ 3 8 −3 2 5 −3 ] ⓑ [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ] [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ]

ⓐ [ 11 9 −5 7 5 −1 ] [ 11 9 −5 7 5 −1 ] ⓑ [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ] [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ]

{ x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0 { x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0

{ x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3 { x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3

ⓐ [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] ⓑ [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] ⓒ [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ] [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ]

ⓐ [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] ⓑ [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] ⓒ [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ] [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ]

[ 1 −1 2 0 −3 −4 ] [ 1 −1 2 0 −3 −4 ]

[ 1 −1 3 0 −5 8 ] [ 1 −1 3 0 −5 8 ]

The solution is ( 4 , −1 ) . ( 4 , −1 ) .

The solution is ( −2 , 0 ) . ( −2 , 0 ) .

( 6 , −1 , −3 ) ( 6 , −1 , −3 )

( 5 , 7 , 4 ) ( 5 , 7 , 4 )

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number.

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number.

ⓐ −14 ; −14 ; ⓑ −28 −28

ⓐ 2 ⓑ −15 −15

ⓐ 3 ⓑ 11 ⓒ 2

ⓐ −3 −3 ⓑ 2 ⓒ 3

( − 15 7 , 24 7 ) ( − 15 7 , 24 7 )

( −2 , 0 ) ( −2 , 0 )

( −9 , 3 , −1 ) ( −9 , 3 , −1 )

( −6 , 3 , −2 ) ( −6 , 3 , −2 )

infinite solutions

The solution is the grey region.

No solution.

ⓐ { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 ⓑ

ⓐ { a ≥ p + 5 a + 2 p ≤ 400 { a ≥ p + 5 a + 2 p ≤ 400 ⓑ

ⓐ { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 ⓑ

ⓐ { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 ⓑ

Section 4.1 Exercises

( 0 , 2 ) ( 0 , 2 )

( 2 , 4 ) ( 2 , 4 )

( −2 , 2 ) ( −2 , 2 )

( 3 , 3 ) ( 3 , 3 )

( 6 , −4 ) ( 6 , −4 )

No solutions, inconsistent, independent

1 point, consistent and independent

infinite solutions, consistent, dependent

( 1 , −4 ) ( 1 , −4 )

( −3 , 2 ) ( −3 , 2 )

( −1 / 2 , 5 / 2 ) ( −1 / 2 , 5 / 2 )

( −5 , 4 ) ( −5 , 4 )

( 0 , 10 ) ( 0 , 10 )

( 4 , −2 ) ( 4 , −2 )

( 4 , 0 ) ( 4 , 0 )

( 4 , 5 ) ( 4 , 5 )

( 7 , 12 ) ( 7 , 12 )

( −3 , −5 ) ( −3 , −5 )

( 2 , −3 ) ( 2 , −3 )

( −11 , 2 ) ( −11 , 2 )

( 6 / −9 , 24 / 7 ) ( 6 / −9 , 24 / 7 )

infinitely many

ⓐ substitution ⓑ elimination

ⓐ elimination ⓑ substituion

Answers will vary.

Section 4.2 Exercises

−7 −7 and −19 −19

22 and −67 −67

Eighty cable packages would need to be sold to make the total pay the same.

Mitchell would need to sell 120 stoves for the companies to be equal.

8 and 40 gallons

1000 calories playing basketball and 400 calories canoeing

Oranges cost $2 per pound and bananas cost $1 per pound

Package of paper $4, stapler $7

Hot dog 150 calories, cup of cottage cheese 220 calories

Owen will need 80 quarts of water and 20 quarts of concentrate to make 100 quarts of lemonade.

53.5 53.5 degrees and 36.5 36.5 degrees

16 degrees and 74 degrees

134 degrees and 46 degrees

37 degrees and 143 degrees

16 ° 16 ° and 74 ° 74 °

45 ° 45 ° and 45 ° 45 °

Width is 41 feet and length is 118 feet.

Width is 10 feet and length is 40 feet.

1.5 1.5 hour

Boat rate is 16 mph and current rate is 4 mph.

Boat rate is 18 mph and current rate is 2 mph.

Jet rate is 265 mph and wind speed is 22 mph.

Jet rate is 415 mph and wind speed is 25 mph.

Section 4.3 Exercises

110 adult tickets, 190 child tickets

6 good seats, 10 cheap seats

92 adult tickets, 220 children tickets

13 nickels, 3 dimes

42 dimes, 8 quarters

17 $10 bills, 37 $20 bills

80 pounds nuts and 40 pounds raisins

9 pounds of Chicory coffee, 3 pounds of Jamaican Blue Mountain coffee

10 bags of M&M’s, 15 bags of Reese’s Pieces

7.5 7.5 liters of each solution

80 liters of the 25% solution and 40 liters of the 10% solution

240 liters of the 90% solution and 120 liters of the 75% solution

$1600 at 8%, 960 at 6%

$28,000 at 9%, $36,000 at 5.5 % 5.5 %

$8500 CD, $1500 savings account

$55,000 on loan at 6% and $30,000 on loan at 4.5 % 4.5 %

ⓐ C ( x ) = 5 x + 6500 C ( x ) = 5 x + 6500

ⓑ R ( x ) = 10 x R ( x ) = 10 x

ⓓ 1,500; when 1,500 water bottles are sold, the cost and the revenue equal $15,000

Section 4.4 Exercises

( 4 , 5 , 2 ) ( 4 , 5 , 2 )

( 7 , 12 , −2 ) ( 7 , 12 , −2 )

( −3 , −5 , 4 ) ( −3 , −5 , 4 )

( 2 , −3 , −2 ) ( 2 , −3 , −2 )

( 6 , −9 , −3 ) ( 6 , −9 , −3 )

( 3 , −4 , −2 ) ( 3 , −4 , −2 )

( −3 , 2 , 3 ) ( −3 , 2 , 3 )

( −2 , 0 , −3 ) ( −2 , 0 , −3 )

x = 203 16 ; y = –25 16 ; z = –231 16 ; x = 203 16 ; y = –25 16 ; z = –231 16 ;

( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

$20, $5, $10

Section 4.5 Exercises

ⓐ [ 2 4 −5 3 −2 2 ] [ 2 4 −5 3 −2 2 ] ⓑ [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ] [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ]

ⓐ [ 2 −5 −3 4 −3 −1 ] [ 2 −5 −3 4 −3 −1 ] ⓑ [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ] [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ]

{ 2 x − 4 y = −2 3 x − 3 y = −1 { 2 x − 4 y = −2 3 x − 3 y = −1

{ 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2 { 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2

ⓐ [ 3 2 1 4 −6 −3 ] [ 3 2 1 4 −6 −3 ] ⓑ [ 12 8 4 4 −6 −3 ] [ 12 8 4 4 −6 −3 ] ⓒ [ 12 8 4 24 −10 −5 ] [ 12 8 4 24 −10 −5 ]

ⓐ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓑ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓒ [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ] [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ]

[ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ] [ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ]

( 1 , −1 ) ( 1 , −1 )

( −2 , 5 , 2 ) ( −2 , 5 , 2 )

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 1 2 z + 4 ; y = 1 2 z − 6 ; z x = 1 2 z + 4 ; y = 1 2 z − 6 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

Section 4.6 Exercises

ⓐ 6 ⓑ −14 −14 ⓒ −6 −6

ⓐ 9 ⓑ −3 −3 ⓒ 8

( 7 , 6 ) ( 7 , 6 )

( −9 , 3 ) ( −9 , 3 )

inconsistent

Section 4.7 Exercises

ⓐ false ⓑ true

ⓐ { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 ⓑ

ⓐ { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c ⓑ

ⓐ { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 ⓑ

ⓐ { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 ⓑ

Review Exercises

( 3 , −1 ) ( 3 , −1 )

one solution, consistent system, independent equations

( 3 , 1 ) ( 3 , 1 )

( 4 , −1 ) ( 4 , −1 )

elimination

50 irises and 150 tulips

10 calories jogging and 10 calories cycling

35 ° 35 ° and 55 ° 55 °

the length is 450 feet, the width is 264 feet

1 2 1 2 an hour

the rate of the jet is 395 mph, the rate of the wind is 7 mph

41 dimes and 11 pennies

46 2 3 46 2 3 liters of 30% solution, 23 1 3 23 1 3 liters of 60% solution

$29,000 for the federal loan, $14,000 for the private loan

( −3 , 2 , −4 ) ( −3 , 2 , −4 )

[ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ] [ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ]

{ x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3 { x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3

ⓐ [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] ⓑ [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] ⓒ [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ] [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ]

( −2 , 5 , −2 ) ( −2 , 5 , −2 )

ⓐ { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 ⓑ

Practice Test

( 2 , 1 ) ( 2 , 1 )

( 2 , −2 , 1 ) ( 2 , −2 , 1 )

15 liters of 1% solution, 5 liters of 5% solution

The candy cost $20; the cookies cost $5; and the popcorn cost $10.

ⓐ { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C ⓑ

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Texas Go Math Grade 5 Lesson 4.5 Answer Key 2-Digit Divisors

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The annual rainfall in Greensville is 4.32 inches. What is the average monthly rainfall in Greensville?

One Way Use place value. Divide. 4.32 ÷ 12

So, the average monthly rainfall in Greenville is ___________ inch. Answer:

Divide. 43 tenths ÷ 12 Multiply. 12 × 3 tenths Subtract. 43tenths – 36tenths Check.7 tenths cannot be shared among 12 groups.

So, the average monthly rainfall in Greenville is 0.36 inch.

Math Talk Mathematical Processes

Explain how you would model 10.32 ÷ 12 using base-ten blocks. Answer:

Another Way Use an estimate.

Divide as you would with whole numbers. Divide. $40.89 ÷ 47

• Divide the tenths.
• Divide the hundredths. When the remainder is zero and there are no more digits in the dividend, the division is complete.
• Use your estimate to place the decimal point. Place a zero to show there are no ones.

Explain how you used the estimate to place the decimal point in the quotient. Answer: Estimated to place the decimal point. Placed a zero to show there are no ones. the decimal point is placed in the  product  so that the number of decimal places in the product is the sum of the decimal places in the  factors.

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Problem Solving

Go Math Lesson 4.5 5th Grade Answer Key Question 6. Write Math what’s the Error? Darla divided 812.5 by 50. She says the quotient is 1.625. Describe Darla’s error. Answer: 16.25 Explanation: She placed the decimal point wrong

Question 7. Jin makes trail mix with apricots and walnuts. A package of dried apricots weighs 25.5 ounces. Jin divides the apricots equally among 34 bags of trail mix. How many ounces of apricots are in each bag? Answer: 0.75 ounces Explanation: Jin makes trail mix with apricots and walnuts. A package of dried apricots weighs 25.5 ounces. Jin divides the apricots equally among 34 bags of trail mix. 2.5 ÷ 34 = 0.75

Question 9. Multi-Step Maya trains 5 days each week for a triathlon. In 5 weeks she logs 24.6 miles in the pool. 445.45 miles on the bike, and 167.45 miles running. On average, how many miles did Maya cover each day? Answer: 318.5miles Explanation: Maya trains 5 days each week for a triathlon. In 5 weeks she logs 24.6 miles in the pool. 445.45 miles on the bike, and 167.45 miles running. 24.6 + 445.45 + 167.45 = 637.5 To find the average we have to divide the total with 2 637.5 ÷ 2 = 318.5

Daily Assessment Task

Fill in the bubble completely to show your answer.

Question 10. A scientist conducting a dig spent $37.95 on 23 packets of hand wipes for her team of volunteers. What was the price of each packet? (A) $16.50 (B) $16.05 (C) $1.60 (D) $1.65 Answer: D Explanation: A scientist conducting a dig spent $37.95 on 23 packets of hand wipes for her team of volunteers. the price of each packet is $1.65

Division with 2-Digit Divisors Lesson 4.5 Answer Key Question 11. Calvin needs to buy carpet to cover the floor of a rectangular room with an area of 170.8 square feet. Calvin measures the room’s length to be 14 feet. He then divides the room’s area by its length to find the room’s width. How many decimal places will the quotient have? (A) 0 (B) 1 (C) 2 (D) 3 Answer: C Explanation: Calvin needs to buy carpet to cover the floor of a rectangular room with an area of 170.8 square feet. Calvin measures the room’s length to be 14 feet. He then divides the room’s area by its length to find the room’s width. The quotient is 12.2 so, the decimal point is 2

Question 12. Multi-Step Farmer Lee grows tomatoes and squash. He harvests 49.92 kilograms of tomatoes and 65.92 kilograms of squash. He distributes the tomatoes and squash into 32 farm share baskets. How many more kilograms of squash than tomatoes does each basket contain? (A) 2.06 kilograms (B) 0.5 kilogram (C) 1.56 kilograms (D) 3.62 kilograms Answer: 0.5 kilograms Explanation: Farmer Lee grows tomatoes and squash. He harvests 49.92 kilograms of tomatoes and 65.92 kilograms of squash. He distributes the tomatoes and squash into 32 farm share baskets. 49.92 ÷ 32 = 2.06 65.92 ÷ 32 = 1.56 2.06 – 1.56 = 0.5 0.5 more kilograms of squash than tomatoes in each basket contain.

Texas Test Prep

Question 13. Jasmine uses 14.24 pounds of fruit for 16 servings of fruit salad. If each serving contains the same amount of fruit, how much fruit is in each serving? (A) 0.089 pound (B) 1.76 pounds (C) 0.89 pound (D) 17.6 pounds Answer: C Explanation: Jasmine uses 14.24 pounds of fruit for 16 servings of fruit salad. If each serving contains the same amount of fruit, the fruit in each serving is 0.89 pounds

Texas Go Math Grade 5 Lesson 4.5 Homework and Practice Answer Key

Question 13. Carla’s car travels 412.5 miles on a tank of gas. The tank holds 15 gallons of gas. How many miles can Carla go on each gallon? Answer: 27.5miles Explanation: Carla’s car travels 412.5 miles on a tank of gas. The tank holds 15 gallons of gas. Carla can go on each gallon of gas is 27.5 miles

Question 14. Muffins cost $35.40 for a dozen or $18.72 for a half dozen. Which is the better buy? Explain. Answer: Dozen = $2.95 Half dozen = $3.12 Explanation: The better buy is dozen as it cost per piece is $2.95

Lesson Check

Question 15. Anita pays $20.70 to copy an 18 page report. What is the cost for each page? (A) $1.05 (B) $1.03 (C) $1.15 (D) $1.10 Answer: C Explanation: Anita pays $20.70 to copy an 18 page report. the cost for each page is $1.15

Question 16. A florist sells a dozen roses for $29.88. What is the cost of one rose? (A) $2.41 (B) $2.49 (C) $2.40 (D) $2.08 Answer: B Explanation: A florist sells a dozen roses for $29.88. cost of one rose $2.49 since dozen equals to 12. So 29.88 ÷ 12 = 2.49

Question 17. Cameron has a stack of 13 identical books that is 30.55 centimeters tall. He divides the total height by the number of books to find the width of one book. How many decimal places will the quotient have? (A) 3 (B) 2 (C) 1 (D) 0 Answer: Explanation: Cameron has a stack of 13 identical books that is 30.55 centimeters tall. He divides the total height by the number of books to find the width of one book. So width of each book is 2.35cm.  Since 30.55 ÷13 = 2.35. So 2 decimal places will the quotient have.

Question 18. Kiera makes 188.6 ounces of punch for a pool party. She has 23 guests attending the party. How many ounces of punch does she make for each guest? (A) 8.2 ounces (B) 9.4 ounces (C) 8.1 ounces (D) 7.2 ounces Answer: A Explanation: Kiera makes 188.6 ounces of punch for a pool party. She has 23 guests attending the party. So She made the 8.2 ounces of punch for each guest. Since 188.6 ÷ 23 = 8.2

Question 19. Multi-Step Last year, Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pickup. What was his average cost per month for phone service and garbage pickup? (A) $8.20 (B) $6.60 (C) $1.48 (D) $14.80 Answer: D Explanation: Last year, Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pickup. So total paid per year is $177.6. 12 months in a year. So his average cost per month phone service and garbage pick up is 14.80. Since 177.60 ÷12 = 14.80

Question 20. Multi-Step Isabel worked 20 hours last week and earned $145.80. Nan worked 15 hours last week and earned $112.50. How much more does Nan earn per hour? (A) $2.22 (B) $3.30 (C) $0.39 (D) $0.21 Answer: D Explanation: Isabel worked 20 hours last week and earned $145.80. So Isabel  earn $7.29 per hour. Since 145.80 ÷20 = 7.29. Nan worked 15 hours last week and earned $112.50. So Nan earn $7.50 per hour. Since $112.50 ÷15 = 7.50. Nan Earned $0.21 more than Isabel per hour.

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