Engage NY Eureka Math 5th Grade Module 6 Lesson 27 Answer Key
Eureka Math Grade 5 Module 6 Lesson 27 Problem Set Answer Key
Question 1.
Use the RDW process to solve the word problems below.
a. Julia completes her homework in an hour. She spends \(\frac{7}{12}\) of the time doing her math homework and \(\frac{1}{6}\) of the time practicing her spelling words. The rest of the time she spends reading. How many minutes does Julia spend reading?
Answer :
Time taken by Julia to complete her home work = 1 hour .
Time spent in Doing Math Homework = \(\frac{7}{12}\)
Time spent in Practicing her spelling words = \(\frac{1}{6}\)
Time spent in Reading = x .
Time spent in Doing Math Homework + Time spent in Practicing spelling words + Time spent in Reading = 1hour
\(\frac{7}{12}\) + \(\frac{1}{6}\) + x = 1
\(\frac{7 + 2 + 12x }{12}\) = 1
9 +12x = 12
12x = 12 – 9
12x = 3
x = \(\frac{3}{12}\)
x = \(\frac{1}{4}\) .
Therefore Time spent in Reading = \(\frac{1}{4}\) hour .
b. Fred has 36 marbles. Elise has \(\frac{8}{9}\) as many marbles as Fred. Annika has \(\frac{3}{4}\) as many marbles as Elise. How many marbles does Annika have?
Answer:
Number of Marbles with Fred = 36
Number of Marbles with Elise =\(\frac{8}{9}\) as many marbles as Fred =\(\frac{8}{9}\) (36)= 32
Number of Marbles with Annika = \(\frac{3}{4}\) as many marbles as Elise = \(\frac{3}{4}\) (32) = 24 .
Therefore Number of marbles with Annika = 24 .
Question 2.
Write and solve a word problem that might be solved using the expressions in the chart below.
Expression  Word Problem 
Solution 
\(\frac{2}{3}\) × 18


(26 + 34) × \(\frac{5}{6}\)


7 – (\(\frac{5}{12}\) + \(\frac{1}{2}\))


Answer:
Expression  Word Problem 
Solution 
\(\frac{2}{3}\) × 18

John brought 18 cakes to his class . His classmates ate \(\frac{2}{3}\) of cakes. How many cakes are eaten ?  \(\frac{2}{3}\) × 18 = 12 cakes. Number of cakes eaten = 12 . 
(26 + 34) × \(\frac{5}{6}\)

Ruby is having 26 chocolates. Her sister gave 34 more chocolates to her . Ruby parents ate \(\frac{5}{6}\) of chocolates. How many chocolates did Ruby parents eaten ?  (26 + 34) × \(\frac{5}{6}\) = 60 × \(\frac{5}{6}\) = 50 Number of chocolates eaten by Ruby parents = 50 chocolates . 
7 – (\(\frac{5}{12}\) + \(\frac{1}{2}\))

Tina brought 7 pizzas cut into 12 slices each . Tina friend ate 5 slices and her Brother ate \(\frac{1}{2}\) of pizza . What fraction of pizzas left over ? 
7 – (\(\frac{5}{12}\) + \(\frac{1}{2}\)) = 7 – (\(\frac{5 + 6}{12}\)) = 7 – \(\frac{11}{12}\) = \(\frac{84 – 11}{12}\) = \(\frac{73}{12}\) =6\(\frac{1}{12}\) pizzas . 
Eureka Math Grade 5 Module 6 Lesson 27 Reflection Answer Key
How did teaching other students how to solve a word problem strengthen your skills as a problem solver? What did you learn about your problemsolving skills? What are your strengths and weaknesses as a problem solver?
Answer:
Skills of a problem solver
Active listening.
Analysis.
Research.
Creativity.
Communication.
Dependability.
Decision making.
Teambuilding.
Problemsolving model
a. Define the problem. The system.
b. Think about it. “Let it simmer”.
c. Plan a solution. Consider possible strategies.
d. Carry out the plan. Be patient.
e. Look back. Encourage students to reflect.
ProblemSolving Strengths:
Divergent thinking
Challenges assumptions
Stepbystep approach
Seeks practical information
Builds off others’ ideas
Looks for how the solution impacts people
Looks at the big picture
Checks for connections between different problems
Problem – Solving Weakness :
Inaccurate information of question
Different approaches to solve problem
Explanation with diagrams
Clear explanation so that everyone should understand .
Eureka Math Grade 5 Module 6 Lesson 27 Homework Answer Key
Question 1.
Use the RDW process to solve the word problems below.
a. There are 36 students in Mr. Meyer’s class. Of those students, \(\frac{5}{12}\) played tag at recess, \(\frac{1}{3}\) played kickball, and the rest played basketball. How many students in Mr. Meyer’s class played basketball?
Answer :
Number of Students in Mr. Meyer’s class = 36 students.
Number of students played tag at recess = \(\frac{5}{12}\) (36 ) = 15 .
Number of students played kickball = \(\frac{1}{3}\) (36 ) = 12.
Number of students played basket ball = Total students – students who played ( recess + kickball )= 36 – (15 +12 )
= 36 – 27 = 9 students.
Therefore, Number of students played basket ball = 9 students.
b. Julie brought 24 apples to school to share with her classmates. Of those apples, \(\frac{2}{3}\) are red, and the rest are green. Julie’s classmates ate \(\frac{3}{4}\) of the red apples and \(\frac{1}{2}\) of the green apples. How many apples are left?
Answer:
Number of Apples Julie brought = 24
Number of red apples = \(\frac{2}{3}\) ( 24) = 16 .
Number of green apples = total – red apples = 24 – 16 = 8.
Number of red apples eaten = \(\frac{3}{4}\) ( 16 ) = 12 apples.
Number of green apples eaten = \(\frac{1}{2}\) ( 8 ) = 4 apples .
Number of red apples left = total red apples – number of red apples eaten = 16 – 12 = 4 apples.
Number of green apples left = total green apples – number of green apples eaten = 8 – 4 = 4 apples.
Total number of apples left = Number of left red apples left +Number of left green apples = 4 + 4 = 8 apples.
Question 2.
Write and solve a word problem for each expression in the chart below.
Expression  Word Problem 
Solution 
Answer:
Expression  Word Problem 
Solution 
144 × \(\frac{7}{12}\)

Kristy is having 144 eggs. she used \(\frac{7}{12}\) of eggs to bake cakes . How many eggs are used for baking cakes?  144 × \(\frac{7}{12}\) = 84 eggs. Number of eggs used for baking a cake = 84 eggs. 
9 – (\(\frac{4}{9}\) + \(\frac{1}{23}\))

Gaurish having 9 apples cut into 9 peices. His brother Mourish ate \(\frac{4}{9}\) and his sister ate \(\frac{1}{23}\) of apples . How many Apples are left over ? 
9 – (\(\frac{4}{9}\) + \(\frac{1}{23}\)) = 9 – (\(\frac{92 – 9}{207}\)) = 9 – \(\frac{83}{207}\) = \(\frac{1863 – 83}{207}\) = \(\frac{1780}{207}\) 
\(\frac{3}{4}\) × (36 + 12)

Gourab having 36 color pencils . His Brother gave 12 more colorpencils to him . Gourab used \(\frac{3}{4}\) color pencils to draw a picture . How many color pencils are used ?

\(\frac{3}{4}\) × (36 + 12) = \(\frac{3}{4}\) × (48) = 36 color pencils. Number of color pencils used for picture = 36 color pencils . 