Vocabulary
Define ratio
A ratio is an ordered pair of numbers which are not both zero. A ratio is denoted A:B to indicate the order of the numbers-- the number A is first and the number B is second.
Write two ratios that are equivalent to 1:1.
Answers will vary. Ex. 2:2 or 50:50
Pam and her brother both open savings accounts. Each begin with a balance of zero dollars. For every two dollars that Pam saves in her account, her brother saves five dollars in his account.
a.) Determine a ratio to describe the money in Pam's account to the money in her brother's account.
2:5
What is the ratio for the following description:
Kaleel made three times as many baskets as John during basketball practice.
A ratio of 3:1.
What sweet food made by bees using nectar from flowers?
Honey
Define tape diagrams
• a rectangular visual model resembling a piece of tape with
divisions used to assist mathematical calculations.
• also known as a divided bar model, fraction strip,
length model or strip diagram.
Write two ratios that are equivalent to 3:11.
Answers will vary. Ex. 6:22; 9:33
Pam and her brother both open savings accounts. Each begin with a balance of zero dollars. For every two dollars that Pam saves in her account, her brother saves five dollars in his account.
b.) If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to support your answer.
Pam's brother has 100 dollars in his account.
Describe a ratio for the following description:
For every 6 cups of flour in a bread recipe, there are 2 cups of milk.
A ratio of 6:2; or the equivalent ratio of 3:1.
What country is home to the kangaroo?
Australia
Define value of a ratio
The value of the ratio A:B is the quotient A/B as long as B is not zero.
-simplified ratio to its lowest terms
Use the value of the ratio to determine which ratios are equivalent to 7:15.
a. 21:45
b. 14:45
c. 3:5
d. 63:135
Both (a) and (d) are equivalent to 7:15.
When Carla looked out at the school parking lot, she noticed that for every 2 minivans, there were 5 other types of vehicles. If there are 161 vehicles in the parking lot, how many of them are not minivans?
5 out of 7 vehicles are not minivans. 7 x 23 = 161. So, 5 x 23 = 115.
115 of the vehicles are not minivans.
There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is 5:7. Is Lonnie correct? Why or why not?
No, Lonnie is not correct. The ratios 5:7 and 35:42 are not equivalent. They are not equivalent because 5 x 7 = 35, but 7 x 7 = 49, not 42.
From what tree do acorns come?
Oak
Define equivalent ratios
Equivalent ratios are ratios that make the same comparison of numbers.
Ex.
4:8 = 1:2
Prove that 3:8 is equivalent to 12:32.
Use a tape diagram to support your answer.
12 is 3 times 4; 32 is 8 times 4.
Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1. If the same number of boys and girls were surveyed, and 90 boys enjoy soccer, how many girls enjoy each sport?
(Hint: Before and after tape diagrams)
The girl survey would show that 210 girls enjoy soccer, and 30 girls enjoy basketball.
You created a new playlist, and 100 of your friends listened to it and shared if they liked the new playlist of not. Nadhii said the ratio of the number of people who liked the playlist to the number of people who did not like the playlist is 75:25. Dylan said that for every 3 people who liked the playlist, one person did not.
Do Nadhii and Dylan agree? Prove your answer using the values of the ratios (simplify the fraction).
Dylan and Nadhii agree. The value of both of their ratios is equivalent, so their ratios are also equivalent.
What is the name of the bear in The Jungle Book?
Baloo
Define ratio relationships
A ratio relationship is the set of all ratios that are equivalent ratios.
Ex.
1/2 = 4:8 = 16/32
The ratio of Isabella's money to Shane's money is 3:11. If Isabella has $33, how much money do Shane and Isabella have together? Use a diagrams to to illustrate your answer.
Isabella has $33, and Shane has $121. $33 + $121 = $154. Together, Isabella and Shane have $154.
At the beginning of Grade 6, the ratio of the number of advanced math students to the number of regular math students was 3:8. However, after taking placement tests, students were moved around changing the ratio of the number of advanced math students to the number of regular math students to 4:7.
How many students started in regular math and advanced math if there were 92 students in advanced math after the placement tests?
There were 69 students in advanced math and 184 students in regular math before the placement tests.
During first semester, the ratio of the number of students in art class to the number of students in gym class was 2:7. However, the art classes were really small, and the gym classes were large, so the principal changed students’ classes for second semester. In second semester, the ratio of the number of students in art class to the number of students in gym class was 5:4.
If 75 students were in art class second semester, how many were in art class and gym class first semester?
(Hint: Before and after tape diagrams)
There were 30 students in art class and 105 students in gym class during during first semester.
How many wives did Henry VIII have?
6