Eureka Math Grade 5 Module 4 Lesson 8 Answer Key
Engage ny eureka math 5th grade module 4 lesson 8 answer key, eureka math grade 5 module 4 lesson 8 problem set answer key.
Question 1. Laura and Sean find the product of \(\frac{2}{3}\) × 4 using different methods. Laura: It’s 2 thirds of 4. \(\frac{2}{3}\) × 4 = \(\frac{4}{3}\) + \(\frac{4}{3}\) = 2 × \(\frac{4}{3}\) = \(\frac{8}{3}\)
Sean: It’s 4 groups of 2 thirds. \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = 4 × \(\frac{2}{3}\) = \(\frac{8}{3}\) Use words, pictures, or numbers to compare their methods in the space below. Answer: Laura: 2/3 * 4 = 4/3 + 4/3 = 2*4/3 = 8/3 Sean: 2/3 + 2/3 + 2/3 + 2/3 = 4 * 2/3 = 8/3 Both methods are correct. 2/3 *4 is 2 thirds of 4, and it will also have the same product as the 4 groups of 2 thirds.
Question 2. Rewrite the following addition expressions as fractions as shown in the example. Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\) a. \(\frac{7}{4}\) + \(\frac{7}{4}\) + \(\frac{7}{4}\) = Answer: 21/4
Explanation: The addition expression for the fraction given is : 7/4 + 7/4 + 7/4 = (3 × 7)/4 = 21/4
b. \(\frac{14}{5}\) + \(\frac{14}{5}\) = Answer: 28/5
Explanation: The addition expression for the fraction given is : 14/5 + 14/5 = (2×14)/5 = 28/5
c. \(\frac{4}{7}\) + \(\frac{4}{7}\) + \(\frac{4}{7}\) = Answer: 12/7
Explanation: 4/7 +4/7 +4/7 = (3×4)/7 = 12/7
b. \(\frac{3}{5}\) × 10 10 × \(\frac{3}{5}\) Answer: 6
Explanation: 3 ×10/5 = 3 × 2 = 6 10 × 3/5 = (10×3)/5 = 30/5 = 6
a. 14 × \(\frac{3}{7}\) 14 × \(\frac{3}{7}\) Answer: 6
Explanation: (14×3)/7 = (7×2×3)/7 = (7×6)/7 = 6 (14 × 3)/7 = (2×3)/1 = 6
b. \(\frac{3}{4}\) × 36 \(\frac{3}{4}\) ×36 Answer: 27
Explanation: (3×36)/4 = (3×4×9)/4 = (4×27)/4 = 27 (3×36)/4 = (3×9) = (3×9) = 27
c. 30 × \(\frac{13}{10}\) 30 × \(\frac{13}{10}\) Answer: 39
Explanation: (30×13)/10 = (10×3×13)/10 = (10×39)/10 = 39 (30 ×13)/10 = (3×13)/1 = 39
d. \(\frac{9}{8}\) ×32 \(\frac{9}{8}\) × 32 Answer: 36
Explanation: (9×32)/8 = (9×4×8)/8 = (36×8)/8 = 36 (9×32)/8 = (9×32)/8 = (9×4)/1 = 36
Question 5. Solve each problem any way you choose. a. \(\frac{1}{2}\) × 60 \(\frac{1}{2}\) minute = __________ seconds Answer: 30seconds
Explanation: The answer and the procedure are explained clearly in the below steps. 1 minute = 60 seconds (1×60)/2 = (1×30)/1 = 30
b. \(\frac{3}{4}\) × 60 \(\frac{3}{4}\) hour = __________ minutes Answer: 45 minutes
Explanation: The answer and the procedure are explained clearly in the below steps. 1 hour = 60 minutes (3×60)/4 = (3×15)/1 = 45
c. \(\frac{3}{10}\) × 1,000 \(\frac{3}{10}\) kilogram = __________ grams” Answer: 300 grams
Explanation: The answer and the procedure are explained clearly in the below steps. 1 kilogram = 1000 grams (3×1000)/1 = 300
d. \(\frac{4}{5}\) × 100 \(\frac{4}{5}\) meter = __________ centimeters Answer: 80 centimeters
Explanation: The answer and the procedure are explained clearly in the below steps. 1 meter (4×100)/5 = (4×20)/1 = 80
Eureka Math Grade 5 Module 4 Lesson 8 Exit Ticket Answer Key
a. \(\frac{2}{3}\) × 15 \(\frac{2}{3}\) × 15 Answer: 10
Explanation: By solving the given question in two methods we could get the same answer i.e 10. The Explanation is given below. 2/3 × 15 = (2 ×15)/3 = 30/3 = 10 2/3 ×15 = (2×15)/3 = (2×5) = 10
b. \(\frac{5}{4}\) × 12 \(\frac{5}{4}\) × 12 Answer: 15
Explanation: By solving the given question in two methods we could get the same answer i.e 15. The process for the question is done below. 5/4 × 12 = (5×12)/4 = (60)/4 =15 5/4 ×12 = ( 5×12)/4 = (5×3) =15
Eureka Math Grade 5 Module 4 Lesson 8 Homework Answer Key
Question 1. Rewrite the following expressions as shown in the example. Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\)
a. \(\frac{5}{3}\) + \(\frac{5}{3}\) + \(\frac{5}{3}\) Answer: 5
Explanation: (\(\frac{3 × 5}{3}\)) = \(\frac{15}{3}\) =5
b. \(\frac{13}{5}\) + \(\frac{13}{5}\) Answer: \(\frac{26}{5}\)
Explanation: (\(\frac{2 × 13}{5}\)) = \(\frac{26}{5}\)
c. \(\frac{9}{4}\) + \(\frac{9}{4}\) + \(\frac{9}{4}\) Answer: \(\frac{27}{4}\)
Expalanation: (\(\frac{3 × 9}{4}\)) = \(\frac{27}{4}\)
a. \(\frac{3}{4}\) × 16 \(\frac{3}{4}\) × 16 Answer: 12
Explanation: (\(\frac{3 × 16}{4}\)) = \(\frac{48}{4}\) = 12 (\(\frac{3 × 16}{4}\)) = \(\frac{3 × 4}{1}\) = 12
b. \(\frac{4}{3}\) × 12 \(\frac{4}{3}\) × 12 Answer: 16
Explanation: (\(\frac{4 × 12}{3}\)) = \(\frac{48}{3}\) = 16 (\(\frac{4 × 12}{3}\)) = \(\frac{4 × 12}{1}\) = 16
c. 40 × \(\frac{11}{10}\) 40 × \(\frac{11}{10}\) Answer: 44
Explanation: (\(\frac{40 × 11}{10}\)) = \(\frac{440}{10}\) = 44 (\(\frac{40× 11}{10}\)) = \(\frac{4 × 11}{1}\) = \(\frac{44}{1}\) = 44
d. \(\frac{7}{6}\) × 36 \(\frac{7}{6}\)× 36 Answer: 42
Explanation: (\(\frac{7 × 36}{6}\)) = \(\frac{252}{6}\) = 42 (\(\frac{7 × 36}{6}\)) = \(\frac{7 × 6}{1}\) = 42
e. 24 × \(\frac{5}{8}\) 24 × \(\frac{5}{8}\) Answer: 15
Explanation: (\(\frac{24 × 5}{8}\)) = \(\frac{126}{8}\) = 15 (\(\frac{24 × 5}{8}\)) = \(\frac{3 × 5}{1}\) = 15
f. 18 × \(\frac{5}{12}\) 18 × \(\frac{5}{12}\) Answer: 7 1/2
Explanation: (\(\frac{18 × 5}{12}\)) = \(\frac{90}{12}\) = 7 6/12 = 7 1/2 (\(\frac{18 × 5}{12}\)) = \(\frac{3 × 5 }{2}\) = \(\frac{15}{2}\)= 7 1/2
g. \(\frac{10}{9}\) × 21 \(\frac{10}{9}\) × 21 Answer: 23 3/9 = 23 1/3
Explanation: (\(\frac{10 × 21}{9}\)) = \(\frac{210}{9}\) = 23 3/9 = 23 1/3 (\(\frac{10 × 21}{9}\)) = \(\frac{10 × 7}{3}\) = \(\frac{70}{3}\) = 23 1/3
Question 3. Solve each problem any way you choose.
a. \(\frac{1}{3}\) × 60 \(\frac{1}{3}\) minute = _________ seconds Answer: 20 seconds
Explanation: (\(\frac{1 × 60}{3}\)) = \(\frac{60}{3\) = 20
b. \(\frac{4}{5}\) × 60 \(\frac{4}{5}\) hour = _________ minutes Answer: 48 minutes
Explanation: (\(\frac{4 × 60}{5}\)) = \(\frac{48}{1\) = 48
c. \(\frac{7}{10}\) × 1000 \(\frac{7}{10}\) kilogram = _________ grams Answer: 700 grams
Explanation: (\(\frac{7 × 1000}{10}\)) = \(\frac{700}{1\) = 700
d. \(\frac{3}{5}\)× 100 \(\frac{3}{5}\) meter = _________ centimeters Answer: 60 centimeres
Explanation: (\(\frac{3 × 100}{5}\)) = \(\frac{60}{1\) = 60
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