The Maths Prof: Ratio EXAM QUESTIONS

The Maths Prof
21 Jun 201713:30
EducationalLearning
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TLDRThe video script provides a detailed explanation of solving ratio problems involving both money and class sizes. The first part of the script focuses on dividing a total sum of money ($785) among individuals based on their respective shares, which are represented by parts of a whole. The explanation involves calculating the value of one part and then determining each person's share by multiplying the value of one part by the number of parts each person has. The second part of the script deals with a similar ratio problem but with different context, involving heights in meters and parts of a whole. The process involves converting the given height into parts and then calculating the total height of another individual based on their parts. The third part of the script involves a class scenario where the total number of students is known, and the task is to find out the number of girls and boys in the class based on given ratios. The script also covers how to calculate the ratio of girls to boys across two different classes, emphasizing the importance of simplifying ratios to their simplest form. The video script is an educational resource for understanding and solving ratio problems in a step-by-step manner.

Takeaways
  • 💡 To find the total amount of money, you need to understand the ratio of parts each person gets and then calculate the value of each part.
  • 🧮 When calculating shares, first find the value of one part by dividing the total amount by the total number of parts.
  • 🤔 For ratios where the total amount isn't given, you may need to equate parts to a known value and then find the value of other parts based on that.
  • 📊 In ratio problems, it's essential to work out the value of one part before calculating the value of multiple parts.
  • 🔢 To find the total number of parts in a ratio, simply add up the individual parts that each person or group gets.
  • 📌 When you have a ratio and a total amount, you can equate the total to the sum of the parts multiplied by the value of one part.
  • 👧👦 To find the total number of students in a class, you can use the ratio of girls to boys and the known number of one group to calculate the other.
  • 📘 If you're given the number of parts and the total, you can find the value of each part and then calculate the share for each part of the ratio.
  • 📌 When calculating ratios, it's important to show your work, including dividing by the number of parts to find one part's value.
  • 📝 For checking your work in ratio problems, you can use a known total to verify that your calculations result in the correct sum.
  • ✅ Always simplify your ratios to their simplest form by finding the greatest common factor that can divide both numbers in the ratio.
Q & A

  • What is the total amount of money that needs to be divided according to the first exam question?

    -The total amount of money to be divided is seven hundred and eighty-five dollars ($785).

  • How many parts does the ratio consist of in the first exam question?

    -The ratio consists of five parts in total.

  • What is the value of one part in the first exam question?

    -The value of one part is one hundred and fifty-seven dollars ($157), which is obtained by dividing the total amount ($785) by the total number of parts (5).

  • What is the share that 'Pit' gets in the first exam question?

    -Pit gets a share of six hundred and twenty-eight dollars ($628), which is calculated by multiplying the value of one part ($157) by four parts.

  • In the second example question, what is the height of one part in meters?

    -The height of one part is zero point two meters (0.2 m), found by dividing one point four meters (1.4 m) by seven parts.

  • What is the total number of students in the class according to the second part of the script?

    -The total number of students in the class is thirty-two (32).

  • How many girls are there in the class according to the second part of the script?

    -There are twenty (20) girls in the class.

  • What is the ratio of girls to boys in Mr. Patel's class?

    -The ratio of girls to boys in Mr. Patel's class is three to two (3:2), with 24 girls and 16 boys.

  • What is the total number of parts in the ratio for the third question regarding the horse?

    -The total number of parts in the ratio is nine, consisting of three parts, four parts, and two parts.

  • How much does each person pay for the horse in the third question?

    -Each person pays different amounts based on their parts: two parts pay $4,800, three parts pay $7,200, and four parts pay $9,600.

  • What is the simplified form of the ratio of the total number of girls to the total number of boys?

    -The simplified form of the ratio of the total number of girls to boys is twenty-two to sixteen (22:16).

  • How does one find the value of one part in a ratio problem?

    -To find the value of one part in a ratio problem, you divide the known total amount or quantity by the total number of parts in the ratio.

  • What is the importance of simplifying ratios?

    -Simplifying ratios is important to express the relationship between two quantities in the simplest form, making it easier to understand and compare.

Outlines
00:00
💰 Division of Money Based on Ratios

This paragraph explains how to divide a total amount of money ($785) according to a given ratio. The ratio is 4 parts for one person and 1 part for another (Anna). By calculating the total number of parts (5 parts in total), the speaker determines the value of one part ($157) and then multiplies it by the respective number of parts to find each person's share. The person with 4 parts receives $628.

05:01
📏 Ratio Calculations Using Heights

In the second example, the speaker is given a height of 1.4 meters corresponding to 7 parts of a ratio. To find the height corresponding to 9 parts, the speaker first calculates the value of one part by dividing the given height by 7, which results in 0.2 meters per part. Multiplying this by 9 gives the height for 9 parts, which is 1.8 meters. This method is applied to solve similar ratio problems involving total amounts and parts.

10:03
📊 Solving Ratios for Total Payments

The third paragraph involves calculating individual payments for a horse that costs $21,600, based on a ratio of 2, 3, and 4 parts. The total number of parts is 9. The speaker calculates the value of one part by dividing the total cost by 9, which equals $2,400. Then, each person's payment is found by multiplying their respective number of parts by the value of one part, resulting in payments of $4,800 for two parts, $7,200 for three parts, and $9,600 for four parts.

Mindmap
Keywords
💡Total Amount
The term 'Total Amount' refers to the overall sum of money or parts involved in a given situation. In the video, it is used to establish the basis for dividing money or parts according to a given ratio. For example, the script mentions 'the total amount of money seven hundred and eighty five dollars' which is then divided into parts to determine individual shares.
💡Ratio
A 'Ratio' is a mathematical expression that shows the relationship between two quantities. In the context of the video, ratios are used to determine how a total amount is distributed among different parties. The script uses ratios like 'four parts' and 'one part' to explain how the total amount is divided between different individuals.
💡Parts
'Parts' in this context refers to the individual segments or portions into which a whole is divided, especially in the process of proportionate distribution. The video discusses dividing a total amount into parts, such as 'five parts', to calculate shares based on the ratio of these parts.
💡Divide
To 'Divide' is a mathematical operation that separates a whole into equal parts. In the video, division is used to find the value of one part when the total amount and the number of parts are known, as illustrated by 'divide it by 5' to find the value of one part of the total amount of money.
💡Multiply
The term 'Multiply' refers to a mathematical operation that combines a number by another a certain number of times. In the video, multiplication is used to calculate the share of an individual based on their number of parts, such as 'multiply that answer by 4' to find the share of a person who has four parts.
💡Share
A 'Share' in this context is the portion of a total amount that an individual is entitled to, based on a ratio or agreement. The video script discusses calculating shares for different individuals, such as 'the share that people get', which is determined by multiplying the value of their parts.
💡Height
In the video, 'Height' is used metaphorically to represent a certain measure that is equivalent to a given number of parts in a ratio. For example, it mentions 'the height of at one point four meters so when I live, in the Bay Area and pipes is the professor and scientist of seven parts', which is used to establish a relationship between physical height and parts in a ratio.
💡Value
The 'Value' of a part refers to its worth or the quantity it represents in a given context. The video emphasizes finding the value of a single part, which is crucial for calculating the overall shares or amounts. It is used in calculations such as 'what the value of four part of it is' and 'what one part is equal to'.
💡Students
'Students' are the individuals being counted or considered in a class or educational context. The video uses the term in the context of calculating the total number of students in a class using ratios, such as 'there are 20 girls in her class' and 'the total number of students that she had'.
💡Boys and Girls
The terms 'Boys' and 'Girls' are used to categorize students by gender in the video. They are important for establishing the ratio of students in a class, as seen in the script where it discusses 'the number of boys in their class' and 'the number of girls in this club'.
💡Simplify Ratios
To 'Simplify Ratios' means to reduce the ratio to its simplest form by dividing both terms by their greatest common factor. In the video, this process is mentioned in the context of finding the simplest form of the ratio of girls to boys, such as 'the ratio in its simplest form we can't simplify it again because there's no common factor in those two numbers'.
Highlights

In the first exam question, the total amount of money is given, which requires finding the total number of parts based on the ratio of four parts for Pit and one part for Anna.

By adding the parts for Pit and Anna, the total number of parts is determined to be five.

The total amount of money, $785, is then divided by the total number of parts to find the value of one part, which is $157.

Pit's share is calculated by multiplying the value of one part by four, resulting in $628.

In the second example, the total number of parts is not given, so the height of one point four meters is used to represent seven parts.

The value of one part is found by dividing the height of one point four meters by seven, which equals 0.2 meters.

Ben's height, representing nine parts, is calculated by multiplying the value of one part by nine, resulting in 1.8 meters.

The third question involves calculating the amount each person paid for a horse, given the total amount of $21,600 and the parts in the ratio.

The value of one part is determined by dividing the total amount of money by the total number of parts in the ratio, which is nine.

Individual payments are calculated by multiplying the value of one part by the number of parts each person has in the ratio.

For the first part of the ratio question, the total number of students in a class is determined without using the number thirty-two, which is used to check the final answer.

The ratio of girls to boys in a class is calculated by dividing the number of girls by the value of one part, which is found by dividing the total number of parts by five.

The total number of students in Mr. Patel's class is calculated by dividing the total number of students by the value of one part, which is eight in this case.

The number of boys and girls in Mr. Patel's class is determined by multiplying the value of one part by the respective parts in the ratio.

The ratio of the total number of girls to boys in both classes is simplified by dividing both numbers by their common factor, which is two.

The final ratio of girls to boys in its simplest form is 22:16, which cannot be simplified further.

Transcripts

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Ratio CalculationProportion ProblemsMathematical ThinkingEducational ContentProblem SolvingFinancial SharesHeight RatiosClassroom ScenariosGender RatiosSimplification