Eureka Math Grade 5 Module 3 Lesson 3 Answer Key (2024)

Engage NY Eureka Math 5th Grade Module 3 Lesson 3 Answer Key

Eureka Math Grade 5 Module 3 Lesson 3 Sprint Answer Key

A
Find the Missing Numerator or Denominator

Question 1.
\(\frac{1}{2}\) = \(\frac{}{4}\)
Answer:
\(\frac{1}{2}\) = \(\frac{2}{4}\)
Explanation :
\(\frac{1}{2}\) = \(\frac{x}{4}\)
x = \(\frac{1}{2}\) × 4
x = \(\frac{4}{2}\)
x = 2 .

Question 2.
\(\frac{1}{5}\) = \(\frac{2}{}\)
Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Explanation :
\(\frac{1}{5}\) = \(\frac{2}{x}\)
x = \(\frac{5}{1}\) × 2
x = 10 .

Question 3.
\(\frac{2}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)
Explanation :
\(\frac{2}{5}\) = \(\frac{x}{10}\)
x = \(\frac{2}{5}\) × 10
x = \(\frac{20}{5}\)
x = 4 .

Question 4.
\(\frac{3}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{3}{5}\) = \(\frac{6}{10}\)
Explanation :
\(\frac{3}{5}\) = \(\frac{x}{10}\)
x = \(\frac{3}{5}\) × 10
x = \(\frac{30}{5}\)
x = 6 .

Question 5.
\(\frac{4}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)
Explanation :
\(\frac{4}{5}\) = \(\frac{x}{10}\)
x = \(\frac{4}{5}\) × 10
x = \(\frac{40}{5}\)
x = 8 .

Question 6.
\(\frac{1}{3}\) = \(\frac{2}{}\)
Answer:
\(\frac{1}{3}\) = \(\frac{2}{}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{2}{x}\)
x = \(\frac{3}{1}\) × 2
x = 3 × 2
x = 6 .

Question 7.
\(\frac{2}{3}\) = \(\frac{}{9}\)
Answer:
\(\frac{2}{3}\) = \(\frac{6}{9}\)
Explanation :
\(\frac{2}{3}\) = \(\frac{x}{9}\)
x = \(\frac{2}{3}\) × 9
x = \(\frac{18}{3}\)
x = 6 .

Question 8.
\(\frac{1}{3}\) = \(\frac{3}{}\)
Answer:
\(\frac{1}{3}\) = \(\frac{3}{9}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{3}{x}\)
x = \(\frac{3}{1}\) × 3
x = 3 × 3
x = 9 .

Question 9.
\(\frac{2}{3}\) = \(\frac{}{9}\)
Answer:
\(\frac{2}{3}\) = \(\frac{6}{9}\)
Explanation :
\(\frac{2}{3}\) = \(\frac{x}{9}\)
x = \(\frac{2}{3}\) × 9
x = \(\frac{18}{3}\)
x = 6 .

Question 10.
\(\frac{1}{4}\) = \(\frac{}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)
Explanation :
\(\frac{1}{4}\) = \(\frac{x}{8}\)
x = \(\frac{1}{4}\) × 8
x = \(\frac{8}{4}\)
x = 2 .

Question 11.
\(\frac{3}{4}\) = \(\frac{}{8}\)
Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)
Explanation :
\(\frac{3}{4}\) = \(\frac{x}{8}\)
x = \(\frac{3}{4}\) × 8
x = \(\frac{24}{4}\)
x = 6 .

Question 12.
\(\frac{1}{4}\) = \(\frac{3}{}\)
Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)
Explanation :
\(\frac{1}{4}\) = \(\frac{3}{x}\)
x = \(\frac{4}{1}\) × 3
x = 4 × 3
x = 12 .

Question 13.
\(\frac{3}{4}\) = \(\frac{9}{}\)
Answer:
\(\frac{3}{4}\) = \(\frac{9}{12}\)
Explanation :
\(\frac{3}{4}\) = \(\frac{9}{x}\)
x = \(\frac{4}{3}\) × 9
x = \(\frac{36}{3}\)
x = 12 .

Question 14.
\(\frac{2}{4}\) = \(\frac{}{2}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) = \(\frac{x}{2}\)
x = \(\frac{2}{4}\) × 2
x = \(\frac{4}{4}\)
x = 1 .

Question 15.
\(\frac{2}{6}\) = \(\frac{1}{}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) = \(\frac{1}{x}\)
x = \(\frac{6}{2}\) × 1
x = \(\frac{6}{2}\)
x = 3 .

Question 16.
\(\frac{2}{10}\) = \(\frac{1}{}\)
Answer:
\(\frac{2}{10}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{2}{10}\) = \(\frac{1}{x}\)
x = \(\frac{10}{2}\) × 1
x = 5 .

Question 17.
\(\frac{4}{10}\) = \(\frac{}{5}\)
Answer:
\(\frac{4}{10}\) = \(\frac{2}{5}\)
Explanation :
\(\frac{4}{10}\) = \(\frac{x}{5}\)
x = \(\frac{4}{10}\) × 5
x = \(\frac{20}{10}\)
x = 2 .

Question 18.
\(\frac{8}{10}\) = \(\frac{}{5}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) = \(\frac{x}{5}\)
x = \(\frac{8}{10}\) × 5
x = \(\frac{40}{10}\)
x = 4 .

Question 19.
\(\frac{3}{9}\) = \(\frac{}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) = \(\frac{x}{3}\)
x = \(\frac{3}{9}\) × 3
x = \(\frac{9}{9}\)
x = 1 .

Question 20.
\(\frac{6}{9}\) = \(\frac{}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) = \(\frac{x}{3}\)
x = \(\frac{6}{9}\) × 3
x = \(\frac{18}{9}\)
x = 2 .

Question 21.
\(\frac{3}{12}\) = \(\frac{1}{}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) = \(\frac{1}{x}\)
x = \(\frac{3}{12}\) × 1
x = 4 .

Question 22.
\(\frac{9}{12}\) = \(\frac{}{4}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) = \(\frac{x}{4}\)
x = \(\frac{9}{12}\) × 4
x = \(\frac{36}{12}\)
x = 3 .

Question 23.
\(\frac{1}{3}\) = \(\frac{}{12}\)
Answer:
\(\frac{1}{3}\) = \(\frac{4}{12}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{x}{12}\)
x = \(\frac{1}{3}\) × 12
x = \(\frac{12}{3}\)
x = 4 .

Question 24.
\(\frac{2}{3}\) = \(\frac{}{12}\)
Answer:
\(\frac{2}{3}\) = \(\frac{8}{12}\)
Explanation :
\(\frac{2}{3}\) = \(\frac{x}{12}\)
x = \(\frac{2}{3}\) × 12
x = \(\frac{24}{3}\)
x = 8 .

Eureka Math Grade 5 Module 3 Lesson 3 Problem Set Answer Key

Question 1.
Draw a rectangular fraction model to find the sum. Simplify your answer, if possible.
a. \(\frac{1}{2}\) + \(\frac{1}{3}\) =
b. \(\frac{1}{3}\) + \(\frac{1}{5}\) =
c. \(\frac{1}{4}\) + \(\frac{1}{3}\) =
d. \(\frac{1}{3}\) + \(\frac{1}{7}\) =
e. \(\frac{3}{4}\) + \(\frac{1}{5}\) =
f. \(\frac{2}{3}\) + \(\frac{2}{7}\) =
Answer:
a.
\(\frac{1}{2}\) + \(\frac{1}{3}\)
L.c.m of 2 and 3 is 6
\(\frac{3}{6}\) + \(\frac{2}{6}\) = \(\frac{5}{6}\) .

Explanation :
Divide the first rectangle into 2 parts using vertical lines as first fraction is \(\frac{1}{2}\) and each vertical section represents \(\frac{1}{2}\) and 1 part is shaded.
Divide the Second rectangle into 3 parts using horizontal lines as Second fraction is \(\frac{1}{3}\) and each horizontal fraction represent \(\frac{1}{3}\) and 1 part is shaded.
As 2 and 3 have 6 lcm now divide both the rectangles into 6 parts .
First rectangle divided into 6 parts by drawing 2 horizontal lines and second rectangle into 6 parts by drawing 1 vertical line
Write fraction of shaded parts and add them .

b.
\(\frac{1}{3}\) + \(\frac{1}{5}\)
L.c.m of 3 and 5 is 15 .
\(\frac{5}{15}\) + \(\frac{3}{15}\) = \(\frac{8}{15}\)

Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is \(\frac{1}{3}\) and each vertical section represents \(\frac{1}{2}\) and 1 part is shaded.
Divide the Second rectangle into 5 parts using horizontal lines as Second fraction is \(\frac{1}{5}\) and each horizontal fraction represent \(\frac{1}{5}\) and 1 part is shaded.
As 5 and 3 have 15 lcm now divide both the rectangles into 15 parts .
First rectangle divided into 15 parts by drawing 4 horizontal lines and second rectangle into 15 parts by drawing 2 vertical line
Write fraction of shaded parts and add them .

c.
\(\frac{1}{4}\) + \(\frac{1}{3}\)
l.cm of 4 and 3 is 12 .
\(\frac{3}{12}\) + \(\frac{4}{12}\) = \(\frac{7}{12}\)

Explanation :
Divide the first rectangle into 4 parts using vertical lines as first fraction is \(\frac{1}{4}\) and each vertical section represents \(\frac{1}{4}\) and 1 part is shaded.
Divide the Second rectangle into 3 parts using horizontal lines as Second fraction is \(\frac{1}{3}\) and each horizontal fraction represent \(\frac{1}{3}\) and 1 part is shaded.
As 4 and 3 have 12 lcm now divide both the rectangles into 12 parts .
First rectangle divided into 12 parts by drawing 2 horizontal lines and second rectangle into 12 parts by drawing 3 vertical line
Write fraction of shaded parts and add them .

d.
\(\frac{1}{3}\) + \(\frac{1}{7}\)
l.c.m of 3 and 7 is 21
\(\frac{7}{21}\) + \(\frac{3}{21}\) = \(\frac{10}{21}\)
Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is \(\frac{1}{3}\) and each vertical section represents \(\frac{1}{3}\) and 1 part is shaded.
Divide the Second rectangle into 7 parts using horizontal lines as Second fraction is \(\frac{1}{7}\) and each horizontal fraction represent \(\frac{1}{7}\) and 1 part is shaded.
As 7 and 3 have 21 lcm now divide both the rectangles into 21 parts .
First rectangle divided into 21 parts by drawing 6 horizontal lines and second rectangle into 21 parts by drawing 2 vertical line
Write fraction of shaded parts and add them .

e.
\(\frac{3}{4}\) + \(\frac{1}{5}\)
l.c.m of 4 and 5 is 20.
\(\frac{15}{20}\) + \(\frac{4}{20}\) = \(\frac{19}{20}\)

Explanation :
Divide the first rectangle into 4 parts using vertical lines as first fraction is \(\frac{3}{4}\) and each vertical section represents \(\frac{1}{4}\) and 3 parts are shaded.
Divide the Second rectangle into 5 parts using horizontal lines as Second fraction is \(\frac{1}{5}\) and each horizontal fraction represent \(\frac{1}{5}\) and 1 part is shaded.
As 5 and 4 have 20 lcm now divide both the rectangles into 20 parts .
First rectangle divided into 20 parts by drawing 3 horizontal lines and second rectangle into 20 parts by drawing 3 vertical line
Write fraction of shaded parts and add them .

f.
\(\frac{2}{3}\) + \(\frac{2}{7}\)
l.c.m of 3 and 7 is 21.
\(\frac{14}{21}\) + \(\frac{6}{21}\) = \(\frac{20}{21}\)

Explanation :
Divide the first rectangle into 3 parts using vertical lines as first fraction is \(\frac{2}{3}\) and each vertical section represents \(\frac{1}{3}\) and 2 parts are shaded.
Divide the Second rectangle into 7 parts using horizontal lines as Second fraction is \(\frac{2}{7}\) and each horizontal fraction represent \(\frac{1}{7}\) and 2 parts are shaded.
As 7 and 3 have 21 lcm now divide both the rectangles into 21 parts .
First rectangle divided into 21 parts by drawing 6 horizontal lines and second rectangle into 21 parts by drawing 2 vertical line
Write fraction of shaded parts and add them .

Solve the following problems. Draw a picture and write the number sentence that proves the answer. Simplify your answer, if possible.
Question 2.
Jamal used \(\frac{1}{3}\) yard of ribbon to tie a package and \(\frac{1}{6}\) yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?
Answer:

Explanation :
Length of ribbon used to tie package = \(\frac{1}{3}\) yard
Length of ribbon used to tie bow = \(\frac{1}{6}\) yard
Total length of ribbon used by jamal = \(\frac{1}{3}\) + \(\frac{1}{6}\) = \(\frac{2}{6}\) + \(\frac{1}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\) .

Question 3.
Over the weekend, Nolan drank \(\frac{1}{6}\) quart of orange juice, and Andrea drank \(\frac{3}{4}\) quart of orange juice. How many quarts did they drink together?
Answer :

Explanation :
Quantity of Orange juice drank by Nolan= \(\frac{1}{6}\) quart
Quantity of Orange juice drank by Andrea = \(\frac{3}{4}\) quart
Total Quantity of orange juice drank by both of them = \(\frac{1}{6}\) + \(\frac{3}{4}\) = \(\frac{2}{12}\) \(\frac{9}{12}\) = \(\frac{11}{12}\) quarts .

Question 4.
Nadia spent \(\frac{1}{4}\) of her money on a shirt and \(\frac{2}{5}\) of her money on new shoes. What fraction of Nadia’s money has been spent? What fraction of her money is left?
Answer:

consider total money = 1 whole .
Money spent on shirt = \(\frac{1}{4}\)
Money spent on new shoes = \(\frac{2}{5}\)
Total Money spent on Nadia = \(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{5}{20}\) + \(\frac{8}{20}\) = \(\frac{13}{20}\)
Fraction of money left = 1 – \(\frac{13}{20}\) = \(\frac{20}{20}\) – \(\frac{13}{20}\) = \(\frac{7}{20}\) .

Eureka Math Grade 5 Module 3 Lesson 3 Exit Ticket Answer Key

Solve by drawing the rectangular fraction model.
Question 1.
\(\frac{1}{2}\) + \(\frac{1}{5}\) =
Answer:
\(\frac{1}{2}\) + \(\frac{1}{5}\) = \(\frac{5}{10}\) + \(\frac{2}{10}\) = \(\frac{7}{10}\)

Question 2.
In one hour, Ed used \(\frac{2}{5}\) of the time to complete his homework and \(\frac{1}{4}\) of the time to check his email. How much time did he spend completing homework and checking email? Write your answer as a fraction. (Extension: Write the answer in minutes.)
Answer:
Time used by Ed to complete his home work = \(\frac{2}{5}\)
Time used by Ed to check his email = \(\frac{1}{4}\)
Total Time Spent by Ed = \(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{8}{20}\) +\(\frac{5}{20}\) = \(\frac{13}{20}\) .
1 hour = \(\frac{20}{20}\) = \(\frac{60}{60}\) multiplied by 3
\(\frac{13}{20}\) = \(\frac{39}{60}\) that means 39 minutes .

Eureka Math Grade 5 Module 3 Lesson 3 Homework Answer Key

Question 1.
Draw a rectangular fraction model to find the sum. Simplify your answer, if possible.
a. \(\frac{1}{4}\) + \(\frac{1}{3}\) =
b. \(\frac{1}{4}\) + \(\frac{1}{5}\) =
c. \(\frac{1}{4}\) + \(\frac{1}{6}\) =
d. \(\frac{1}{5}\) + \(\frac{1}{9}\) =
e. \(\frac{1}{4}\) + \(\frac{2}{5}\) =
f. \(\frac{3}{5}\) + \(\frac{3}{7}\) =
Answer:
a. \(\frac{1}{4}\) + \(\frac{1}{3}\) = \(\frac{3}{12}\) + \(\frac{4}{12}\) =\(\frac{7}{12}\)

b. latex]\frac{1}{4}[/latex] + \(\frac{1}{5}\) = latex]\frac{5}{20}[/latex] + \(\frac{4}{20}\) = latex]\frac{9}{20}[/latex]

c. \(\frac{1}{4}\) + \(\frac{1}{6}\) =\(\frac{3}{12}\) + \(\frac{2}{12}\) = \(\frac{5}{12}\)

d. \(\frac{1}{5}\) + \(\frac{1}{9}\) =\(\frac{9}{45}\) + \(\frac{5}{45}\) = \(\frac{13}{45}\)

e. latex]\frac{1}{4}[/latex] + \(\frac{2}{5}\) = latex]\frac{5}{20}[/latex] + \(\frac{8}{20}\) = latex]\frac{13}{20}[/latex]

f. \(\frac{3}{5}\) + \(\frac{3}{7}\) = \(\frac{21}{35}\) + \(\frac{15}{35}\) = \(\frac{36}{35}\) = 1\(\frac{1}{35}\)

Solve the following problems. Draw a picture, and write the number sentence that proves the answer. Simplify your answer, if possible.
Question 2.
Rajesh jogged \(\frac{3}{4}\) mile and then walked \(\frac{1}{6}\) mile to cool down. How far did he travel?
Answer:

Distance traveled by Rajesh by jogging = \(\frac{3}{4}\) mile
Distance traveled by Rajesh by walking = \(\frac{1}{6}\) mile
Total Distance traveled by Rajesh = \(\frac{3}{4}\) + \(\frac{1}{6}\) = \(\frac{9}{12}\) + \(\frac{2}{12}\) = \(\frac{11}{12}\)

Question 3.
Cynthia completed \(\frac{2}{3}\) of the items on her to-do list in the morning and finished \(\frac{1}{8}\) of the items during her lunch break. What fraction of her to-do list is finished by the end of her lunch break? (Extension: What fraction of her to-do list does she still have to do after lunch?)
Answer:

Work done by Cynthia in the morning = \(\frac{2}{3}\)
Work done by Cynthia in the lunch break = \(\frac{1}{8}\)
Total work done = \(\frac{2}{3}\) + \(\frac{1}{8}\) = \(\frac{16}{24}\) + \(\frac{3}{24}\) = \(\frac{19}{24}\).

Question 4.
Sam read \(\frac{2}{5}\) of her book over the weekend and \(\frac{1}{6}\) of it on Monday. What fraction of the book has she read? What fraction of the book is left?
Answer :

Fraction of her book read by weekend = \(\frac{2}{5}\)
Fraction of her read by Monday = \(\frac{1}{6}\)
Fraction of book read = \(\frac{2}{5}\) + \(\frac{1}{6}\) = \(\frac{12}{30}\) + \(\frac{5}{30}\) = \(\frac{17}{30}\)
Fraction of book left to read = 1 – \(\frac{17}{30}\) = \(\frac{30 }{30}\) – \(\frac{17}{30}\) = \(\frac{13}{30}\) .

Eureka Math Grade 5 Module 3 Lesson 3 Answer Key (2024)

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