All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 10 Lesson 8 Problem-Solving Investigation: Extra or Missing Information will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 10 Lesson 8 Problem-Solving Investigation: Extra or Missing Information
Learn the Strategy
On the first day, Gabriella’s family traveled \(\frac{3}{10}\) of a road trip. On the second day, they traveled \(\frac{27}{100}\) of the trip. They traveled 4 days. What part of their trip did they travel in the first two days?
1. Understand
What facts do you know?
Gabriella’s family traveled \(\frac{3}{10}\) of a road trip on the first day and \(\frac{27}{100}\) of the trip on the second day. They traveled 4 days.
What do you need to find?
the part of their trip that they traveled in the first two days
2. Plan
The fact that they traveled 4 days is extra information. Find \(\frac{3}{10}\) + \(\frac{27}{100}\).
3. Solve
\(\frac{3}{10}+\frac{27}{100}=\frac{30}{100}+\frac{27}{100}=\frac{30+27}{100}=\frac{57}{100}\) Write \(\frac{3}{10}\) as \(\frac{30}{100}\). Then add.
So, Gabriella’s family traveled 
of their trip ¡n the first two days.
4. Check
Does your answer make sense? Explain.
Answer: 
Practice the Strategy
Charlotte walked \(\frac{6}{10}\) mile to school. After school, she walked \(\frac{24}{100}\) mile to her friend’s house. How much time does it take Charlotte to walk to school and to her friend’s house?
1. Understand
What facts do you know?
What do you need to find?
2. Plan
3. Solve
4. Check
Does your answer make sense? Explain.
Answer:
1. Understand
What facts do you know?
Charlotte walked \(\frac{6}{10}\) mile to school. After school, she walked \(\frac{24}{100}\) mile to her friend’s house.
What do you need to find?
The time taken for Charlotte to walk to school and to her friend’s house
2. Plan
No information was given regarding to individual time taken by Charlotte to walk to her school and then to her friend’s place.
The question was mentioned distance travelled by Charlotte, not time.
Apply the Strategy
Determine if there is extra or missing information to solve each problem. Then solve if possible.
Question 1.
There are 100 movies at the store. \(\frac{30}{100}\) are action movies, \(\frac{50}{100}\) are comedies, and \(\frac{20}{100}\) are adventure movies. What part of the movies are action or comedies?
Answer: \(\frac{80}{100}\)
There is no extra or missing information.
1) Understand
What facts do you know?
Total movies = 100
Action movies = \(\frac{30}{100}\)
Comedy movies = \(\frac{50}{100}\)
Adventure movies = \(\frac{20}{100}\)
What do you need to find?
The part of the movies that are action or comedies
2. Plan
The part of the movies that are action or comedies = \(\frac{30}{100}\) + \(\frac{50}{100}\)
3. Solve
\(\frac{30}{100}\) + \(\frac{50}{100}\)= \(\frac{50 +30}{100}\) = \(\frac{80}{100}\)
So, The part of the movies that are action or comedies =\(\frac{80}{100}\)
4. Check
Checked and it makes sense.
Question 2.
Mathematical PRACTICE Keep Trying In a basketball game, the red team scored \(\frac{3}{10}\) of the baskets during the first half and \(\frac{4}{10}\) of the baskets during the second half. The blue team had 10 players. How many baskets did the red team score during the first half and second half of the game?
Answer: The number of baskets scored by the Red team during the first half and second half of the game is \(\frac{7}{10}\)
There is an extra information.
1) Understand
What facts do you know?
the red team scored \(\frac{3}{10}\) of the baskets during the first half and \(\frac{4}{10}\) of the baskets during the second half. The blue team had 10 players.
What do you need to find?
The number of baskets scored by the Red team during the first half and second half of the game
2. Plan
The blue team had 10 players is the extra information. We need to find \(\frac{3}{10}\) + \(\frac{4}{10}\)
3. Solve
\(\frac{3}{10}\) + \(\frac{4}{10}\) = \(\frac{3 + 4}{10}\) =\(\frac{7}{10}\)
Therefore, The number of baskets scored by the Red team during the first half and second half of the game is \(\frac{7}{10}\)
4. Check
Checked and it makes sense.
Question 3.
Alexia and her family went on vacation. They walked \(\frac{1}{10}\) mile to the beach and \(\frac{2}{10}\) mile to the
souvenir shop. How far did they walk to the beach and to the souvenir shop?
Answer: The distance they walked to the beach and to the souvenir shop = \(\frac{3}{10}\)
There is no extra or missing information
1) Understand
What facts do you know?
Alexia and her family went on vacation. They walked \(\frac{1}{10}\) mile to the beach and \(\frac{2}{10}\) mile to the souvenir shop.
What do you need to find?
The distance they walked to the beach and to the souvenir shop
2. Plan
\(\frac{1}{10}\) +\(\frac{2}{10}\)
3. Solve
\(\frac{1}{10}\) +\(\frac{2}{10}\)Â = \(\frac{1+2}{10}\)Â = \(\frac{3}{10}\)
Therefore, The distance they walked to the beach and to the souvenir shop = \(\frac{3}{10}\)
4. Check
Checked and it makes sense.
Review the Strategies
Use any strategy to solve each problem.
- Determine extra or missing information.
- Use logical reasoning.
- Look for a pattern.
- Make a model.
Question 4.
Trina is making friendship bracelets. One tenth of the bracelets are blue. Some of the bracelets are red and some are purple. How many bracelets are blue and purple?
Answer: There is missing information
1) Understand
What facts do you know?
Trina is making friendship bracelets. One tenth of the bracelets are blue. Some of the bracelets are red and some are purple.
What do you need to find?
Number of bracelets that are in blue and purple
2) Plan
We have information on number of blue colored bracelets. But, we don’t have information on purple bracelets. They mentioned some are in purple in the question, but, they haven’t mentioned the accurate number. Because of missing information, this question cannot be solved.
Question 5.
Mathematical PRACTICE Repeated Reasoning Find the next number in the pattern below. Explain how you found the number. \(\frac{15}{100}\), \(\frac{3}{10}\), \(\frac{45}{100}\), \(\frac{6}{10}\), \(\frac{75}{100}\),…….
Answer: \(\frac{9}{10}\)
latex]\frac{15}{100}[/latex], \(\frac{3}{10}\), \(\frac{45}{100}\), \(\frac{6}{10}\), \(\frac{75}{100}\),..
Represent all the number in the form of denominator of 100.
Therefore, latex]\frac{15}{100}[/latex], \(\frac{30}{100}\), \(\frac{45}{100}\), \(\frac{60}{100}\), \(\frac{75}{100}\),..
If we observe the pattern above, all the numbers in the numerator are multiples of 15.
So, the next number in the series is \(\frac{90}{100}\) = \(\frac{9}{10}\)
Question 6.
The fourth grade classes voted on their favorite flavor of ice cream. Three tenths of the students voted for strawberry, \(\frac{21}{100}\) of the students voted for vanilla, and \(\frac{4}{10}\) of the students voted for chocolate. How many students voted for vanilla or chocolate?
Answer: Total No. of students who voted for vanilla or chocolate = \(\frac{61}{100}\)
1. Understand
What facts do you know?
No. of students who voted for strawberry = three tenths = \(\frac{3}{10}\)
No. of students who voted for vanilla = \(\frac{21}{100}\)
No. of students who voted for chocolate = \(\frac{4}{10}\)
What do you need to find?
Total No. of students who voted for vanilla or chocolate
2. Plan
No. of students who voted for strawberry are extra information here. Total No. of students who voted for vanilla or chocolate = \(\frac{21}{100}\) + \(\frac{4}{10}\)
3. Solve
\(\frac{21}{100}\) + \(\frac{4}{10}\) = \(\frac{21}{100}\) + \(\frac{40}{100}\) = \(\frac{21 +40}{100}\) = \(\frac{61}{100}\)
Therefore, Total No. of students who voted for vanilla or chocolate = \(\frac{61}{100}\)
4. Check
Checked and it makes sense.
Question 7.
Harper and his mom are making trail mix for a party. Two tenths of the trail mix is pretzels and \(\frac{32}{100}\) of the trail mix is cereal. The party starts at 1:00 P.M. How much of the trail mix is pretzels or cereal?
Answer: The amount of trail mix which is pretzels or cereal = \(\frac{52}{100}\)
There is an extra information here.
1. Understand
What facts do you know?
Two tenths, which is \(\frac{2}{10}\) of the trail mix is pretzels and \(\frac{32}{100}\) of the trail mix is cereal. The party starts at 1:00 P.M.
What do you need to find?
The amount of trail mix which is pretzels or cereal
2. Plan
The party starts at 1:00 P.M is the extra information here. The amount of trail mix which is pretzels or cereal = \(\frac{2}{10}\) + \(\frac{32}{100}\)
3. Solve
\(\frac{2}{10}\) + \(\frac{32}{100}\) = \(\frac{20}{100}\) + \(\frac{32}{100}\) = \(\frac{20 + 32}{100}\) = \(\frac{52}{100}\)
Therefore, The amount of trail mix which is pretzels or cereal = \(\frac{52}{100}\)
4. Check
Checked and it makes sense.
McGraw Hill My Math Grade 4 Chapter 10 Lesson 8 My Homework Answer Key
Determine if there is extra or missing information to solve each problem. Then solve if possible.
Question 1.
Janice bought her mother a bunch of 10 flowers. Two of the flowers are daisies. One half of the remaining flowers are tulips. Write the fraction of the flowers that are daisies.
Answer: The fraction of the flowers that are daisies = \(\frac{2}{10}\)
There is an extra information here.
1. Understand
What facts do you know?
Janice bought her mother a bunch of 10 flowers.
Two of the flowers are daisies.
One half of the remaining flowers are tulips
What do you need to find?
The fraction of the flowers that are daisies.
2. Plan
The information regarding tulips are extra information here. The fraction of the flowers that are daisies are 2 out of total flowers
3. Solve
The fraction of the flowers that are daisies are 2 out of 10 total flowers = \(\frac{2}{10}\)
Question 2.
Mathematical PRACTICE Make a Plan There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
Answer:Â There is missing information here
1. Understand
What facts do you know?
Make a Plan There are 100 books in the library. There are non-fiction and fiction books.
What do you need to find?
The fraction of the books that are fiction
2. Plan
There is no proper information regarding number of fiction and non-fiction books. So, there is missing information here, there hence we cannot calculate the fraction of the books that are fiction.
Question 3.
Sean has a collection of coins. One tenth of the coins are from Europe. Thirty-two hundredths are from Asia. The rest are from Africa. Write a decimal to show the total part of the coins that are from Europe or Asia.
Answer: The decimal number to show the total part of the coins that are from Europe or Asia = 0.42
There is an extra information here.
1. Understand
What facts do you know?
One tenth of the coins are from Europe. Thirty-two hundredths are from Asia. The rest are from Africa.
What do you need to find?
The decimal number to show the total part of the coins that are from Europe or Asia.
2. Plan
One tenth of the coins are from Europe, which is \(\frac{1}{10}\)
Thirty-two hundredths are from Asia, which is \(\frac{32}{100}\)
the total part of the coins that are from Europe or Asia = \(\frac{1}{10}\) + \(\frac{32}{100}\)
3. Solve
\(\frac{1}{10}\) + \(\frac{32}{100}\) = \(\frac{10}{100}\) + \(\frac{32}{100}\)Â = \(\frac{10 + 32}{100}\) = \(\frac{42}{100}\)
Therefore, The total part of the coins that are from Europe or Asia = \(\frac{42}{100}\) = 0.42 in decimal
4. Check
Checked and it makes sense.
Question 4.
Kenley has 100 songs on her digital music player. Of the songs, seventeen-hundredths are country songs, two-tenths are musicals, and four-tenths are classical music songs. What part of the songs are either country or musicals? Write as a decimal.
Answer: The part of the songs are either country or musicals = \(\frac{37}{100}\) = 0.37 in decimal
There is an extra information here
1. Understand
What facts do you know?
Kenley has 100 songs on her digital music player. Of the songs, seventeen-hundredths are country songs, two-tenths are musicals, and four-tenths are classical music songs.
What do you need to find?
The part of the songs are either country or musicals
2. Plan
seventeen-hundredths are country songs, which is \(\frac{17}{100}\)
two-tenths are musicals, which is \(\frac{2}{10}\)
The information regarding classical music songs are extra information here.
The part of the songs are either country or musicals = \(\frac{17}{100}\) + \(\frac{2}{10}\)
3. Solve
\(\frac{17}{100}\) + \(\frac{2}{10}\) = \(\frac{17}{100}\) + \(\frac{20}{100}\) = \(\frac{17 + 20}{100}\) =Â \(\frac{37}{100}\)
therefore, The part of the songs are either country or musicals = \(\frac{37}{100}\) = 0.37 in decimal