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)

FAQs

What grade does Eureka math go to? ›

Eureka Math offers a full complement of Prekindergarten through Grade 12 print materials including Teacher Editions, student workbooks, and more. Spanish language editions are available for Grades K–8.

Get More Info Here ›

What are the four core components of a Eureka Math TEKS lesson? ›

A typical Eureka lesson is comprised of four critical components: fluency practice, concept development (including a problem set), application problem, and student debrief (including the Exit Ticket).

Read On ›

What is math Eureka? ›

Eureka Math^® is a math program designed to advance equity in the math classroom by helping students build enduring math knowledge.

Show Me More ›

What is the hardest math in 5th grade? ›

Some of the hardest math problems for fifth graders involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines.

See Details ›

What is the hardest math grade? ›

The hardest math class you can take in high school is typically AP Calculus BC or IB Math HL. These courses cover a wide range of advanced mathematical concepts, including calculus, trigonometry, and statistics.

Show Me More ›

How long does an Eureka math lesson take? ›

Not all Eureka Math lessons are formatted in the same way, but lessons in the same grade-band all follow a similar structure. Lessons in A Story of Units (PK-5) are written for a 60-minute class period, except for Pre-K lessons, which are 25 minutes, and K lessons, which are 50 minutes*.

Discover More Details ›

Is Eureka math common core math? ›

Eureka Math is a Common Core math. Eureka Math's framework is entirely built on the Common Core Learning Standards and Progressions for the Common Core State Standards in Mathematics.

How many schools use Eureka Math? ›

California districts using the curriculum include Vista Unified School District, Montebello Unified School District, Riverside Unified School District, Palmdale Unified School District, Pomona Unified School District, Alameda Unified School District, Lincoln Unified School District, Mountain View Whisman School ...

Discover More Details ›

What math is 8th grade level? ›

Eighth-grade math is typically a course in pre-algebra to help prepare students for high school algebra.

Find Out More ›

What math level is 5th grade? ›

In fifth grade, students focus on adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Your kid will become fluent with computing these types of numbers and understanding the relationship between them. Students should also be able to use these numbers in real-world scenarios.

See Details ›

What grade level is go math for? ›

Go Math! (K-6) on Ed is an easy-to-implement core curriculum with an effective instructional approach that includes robust differentiation and assessment resources that engage all levels of learners and support all levels of teachers, from novice to master.

Get More Info ›

What is advanced math in 8th grade? ›

Students on the advanced math track will take Algebra. This standards-based class covers the second half of Math 8 as well as high school-level Algebra I and is designed to prepare students for geometry in ninth grade. Placement is based on prior grades, teacher recommendations, and district benchmark testing scores.

Tell Me More ›