Podcast
Questions and Answers
What distinguishes a ratio from other mathematical relationships?
What distinguishes a ratio from other mathematical relationships?
- It is a comparison between two quantities of the same kind. (correct)
- It represents the area of a geometric shape.
- It involves only one quantity.
- It always results in a whole number.
If a classroom has 12 male students and 18 female students, what is the ratio of male students to total students in simplest form?
If a classroom has 12 male students and 18 female students, what is the ratio of male students to total students in simplest form?
- 2:3
- 3:2
- 2:5 (correct)
- 3:5
What condition must be met to determine if two ratios are equivalent?
What condition must be met to determine if two ratios are equivalent?
- They must compare different types of quantities.
- Their quantities must be different.
- They can be simplified or multiplied to be the same. (correct)
- One ratio must involve more than two quantities.
Which operation helps in simplifying ratios?
Which operation helps in simplifying ratios?
Ratios can be written as:
Ratios can be written as:
In what scenario is it most appropriate to use a ratio?
In what scenario is it most appropriate to use a ratio?
What is the primary characteristic of a proportion?
What is the primary characteristic of a proportion?
What does it mean for two fractions to 'reduce to the same value' in the context of proportions?
What does it mean for two fractions to 'reduce to the same value' in the context of proportions?
How can you find an unknown value in a proportion?
How can you find an unknown value in a proportion?
If 2 apples cost $3, how much will 8 apples cost, assuming a direct proportion?
If 2 apples cost $3, how much will 8 apples cost, assuming a direct proportion?
When using a proportion to solve for a missing quantity, what must be true of the fractions?
When using a proportion to solve for a missing quantity, what must be true of the fractions?
In a proportion problem, what is the significance of 'cross multiplying'?
In a proportion problem, what is the significance of 'cross multiplying'?
What is the ratio of the number of sides in a hexagon to the number of sides in a triangle?
What is the ratio of the number of sides in a hexagon to the number of sides in a triangle?
If two quantities are directly proportional, what happens to one quantity if the other is doubled?
If two quantities are directly proportional, what happens to one quantity if the other is doubled?
What does it mean for a ratio to be in its 'simplest form'?
What does it mean for a ratio to be in its 'simplest form'?
What distinguishes a ratio of three quantities from a proportion?
What distinguishes a ratio of three quantities from a proportion?
What must be consistent among the quantities being compared in a three-part ratio?
What must be consistent among the quantities being compared in a three-part ratio?
How does simplifying a three-part ratio compare to simplifying a two-part ratio?
How does simplifying a three-part ratio compare to simplifying a two-part ratio?
If the ratio of the ages of three siblings is 2:3:5 and the youngest is 4 years old, how old are the other two siblings?
If the ratio of the ages of three siblings is 2:3:5 and the youngest is 4 years old, how old are the other two siblings?
When is it appropriate to multiply each term in a ratio by 10, 100, or 1000?
When is it appropriate to multiply each term in a ratio by 10, 100, or 1000?
If the ratios A:B and B:C are known, how can the ratio A:B:C be determined?
If the ratios A:B and B:C are known, how can the ratio A:B:C be determined?
Determine if the ratios 3:5:7 and 9:15:21 are equivalent.
Determine if the ratios 3:5:7 and 9:15:21 are equivalent.
Determine if the ratios 1:2:3 and 2:3:4 are equivalent.
Determine if the ratios 1:2:3 and 2:3:4 are equivalent.
If the ratio of cats to tigers is 3:5, what does this tell you?
If the ratio of cats to tigers is 3:5, what does this tell you?
Consider a scenario where one needs to determine the ideal mix of cement, sand, and gravel for construction. Which mathematical concept would be most applicable?
Consider a scenario where one needs to determine the ideal mix of cement, sand, and gravel for construction. Which mathematical concept would be most applicable?
How would you approach simplifying the ratio 100:2000:36 to its lowest term?
How would you approach simplifying the ratio 100:2000:36 to its lowest term?
In a scenario involving snakes, cats and tigers, given a ratio of snakes to cats of 2:3 and a ratio of cats to tigers of 3:5, the combined ratio of snakes:cats:tigers will be?
In a scenario involving snakes, cats and tigers, given a ratio of snakes to cats of 2:3 and a ratio of cats to tigers of 3:5, the combined ratio of snakes:cats:tigers will be?
What adjustment needs to be made if the ratio of snakes to cats is 1:2 and the ratio of cats to tigers is 4:7 before they can be combined into Snakes:Cats:Tigers?
What adjustment needs to be made if the ratio of snakes to cats is 1:2 and the ratio of cats to tigers is 4:7 before they can be combined into Snakes:Cats:Tigers?
Which of the following is the simplified form of the ratio 4:6:8?
Which of the following is the simplified form of the ratio 4:6:8?
If a recipe requires a ratio of flour to sugar to butter as 5:3:2, and you want to make a larger batch using 15 cups of sugar, how many cups of flour will you need?
If a recipe requires a ratio of flour to sugar to butter as 5:3:2, and you want to make a larger batch using 15 cups of sugar, how many cups of flour will you need?
If one has a combination of red, blue, and yellow paints, one part red, three parts blue and 9 parts yellow, what mathematical concept facilitates understanding.
If one has a combination of red, blue, and yellow paints, one part red, three parts blue and 9 parts yellow, what mathematical concept facilitates understanding.
What does it signify if a ratio compares the cost of resources for each phase, facilitating budgeting and cost optimization in project management?
What does it signify if a ratio compares the cost of resources for each phase, facilitating budgeting and cost optimization in project management?
Given the ratio of the price of a Bungalow to a Semi-D to a Terrace house is 5:3:2, and the price of a bungalow is RM 1,200,000 and using proportions, what is the price of the terrace house?
Given the ratio of the price of a Bungalow to a Semi-D to a Terrace house is 5:3:2, and the price of a bungalow is RM 1,200,000 and using proportions, what is the price of the terrace house?
A curtain of length 810m must have three parts of different materials, in the ratio 4:2:3 what is the value of PQ relative to the rest?
A curtain of length 810m must have three parts of different materials, in the ratio 4:2:3 what is the value of PQ relative to the rest?
A curtain of length 810m has three parts with different materials. The ratio of the lengths of PQ to QR to RS is 4:2:3. What is the length of PQ?
A curtain of length 810m has three parts with different materials. The ratio of the lengths of PQ to QR to RS is 4:2:3. What is the length of PQ?
The ratio of the sides AB, BC and AC of triangle ABC are in the ratio 7:5:6. Find the length of side AB if the difference of the sides AB and BC is 4 cm
The ratio of the sides AB, BC and AC of triangle ABC are in the ratio 7:5:6. Find the length of side AB if the difference of the sides AB and BC is 4 cm
The ratio of the sides DE, EF and FD of triangle DEF are in the ratio 11:9:5. Find the sum of the three sides if the difference of the sides DE and DF is 18cm.
The ratio of the sides DE, EF and FD of triangle DEF are in the ratio 11:9:5. Find the sum of the three sides if the difference of the sides DE and DF is 18cm.
Flashcards
What is a ratio?
What is a ratio?
A comparison between two quantities of the same kind.
What is an equivalent ratio?
What is an equivalent ratio?
A ratio where both quantities are multiplied or divided by the same number.
What is a proportion?
What is a proportion?
An equation stating that two ratios are equal.
Ratio of three quantities
Ratio of three quantities
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State ratio in lowest term
State ratio in lowest term
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Study Notes
- Chapter 5 focuses on ratios, rates, and proportions
- The lesson objectives include using ratios, determining equivalent ratios, and writing ratios in their simplest form
Ratio of Two Quantities
- A ratio compares two quantities of the same kind
- Written as a : b, and read as 'a is to b'
Examples of Ratios
- The ratio of men to women in an image is 3:2
- The ratio of women to men in the same image is 2:3
- The ratio of blue balls to pink balls can be 9:3, or simplified to 3:1
- The ratio of pink balls to blue balls can be 9:6, or simplified to 3:2
Equivalent Ratios
- Equivalent ratios are obtained by multiplying or dividing both quantities in a ratio by the same number
- For example, 2:1 and 6:3 are equivalent because we multiplied each side ×3
- 8:12 and 2/3 are equivalent because we divided each side ÷4
Proportions
- A proportion is an equation stating that two ratios are equal
- In simple proportions, examine the fractions
- A proportion is true if both fractions reduce to the same value
Determining Proportionality
- To determine if two ratios are proportional, simplify each ratio
- 5/15 and 2/6 are proportional because they both reduce to 1/3
Solving for an Unknown in a Proportion
- Cross multiply to determine the unknown value
- For example, to solve 2/3 = x/9, cross multiply
- (3)(x) = (2)(9), 3x = 18, x = 6
Problem Solving with Proportions
- If 4 tickets cost $9.00, the cost of 14 tickets can be found using proportions
- If a house appraised for $10,000 pays $300 in taxes, the tax on a $15,000 house can be determined using proportions
Finding a Quantity Given Ratio and Sum
- A house painter mixes yellow and blue paint with a ratio of 5:3
- If the difference in volume is 500ml, volume of paint can be solved
- This requires determining what one unit is worth, and scaling
Ratio of Three Quantities
- A ratio of three quantities is achieved by comparing three quantities having the same unit of measurement
- The ages of three children are 10, 11 and 13 years leading to a ratio of 10:11:13
Determining Equivalent Ratios of Three Quantities
- 1:5:7 and 4:20:28 are equivalent ratios
- 2:3:5 and 10:14:20 are not equivalent ratios
Stating the Ratio in its Lowest terms
- State ratio in the lowest term using whole or mixed numbers
- Divide each by HCF(Highest Common Factor)
Decimals
- For decimals, multiply each term by 10, 100, 1000
- 0.1:2:0.036 can be expressed as 100:2000:36
Ratio of three quantities
- Given the ratio of A:B and B:C, find the ratio of A:B:C
- Snakes : cats : 2:3, Cats : Tigers : 3:5, leading to Snakes : Cats : Tigers : 2:3:5
Finding a Value Given Ratio and Value of Another
- Given ratio Bungalow:Semi-D:Terrace=5:3:2,
- If a property for bungalow is RM 1 200 000, the property for semi-detached house can be determined
Finding Value of Quantity Given Ratio and Sum
- With a curtain of length 810m with three parts (PQ to QR to RS is 4:2:3) the length of PQ can then be derived
- The solution requires that 9 parts = 810m, 1 part is therefore 90m and, finally, PQ = 360
Finding Value Given Ratio and Difference between Two Quantities
- AB:BC:AC of triangle ABC are in ratio 7:5:6, also the difference of the sides AB & BC equals 4cm, so AB can be derived:
- AB-BC = 4cm which means that 2 parts represent 4cm, therefore 1 part is 2cm, with AB = 7 parts × 2cm, AB has to be 14cm
Finding the sum of three quantities
- Given the Ratio and Difference between Two Quantities,
- DE, EF and FD of triangle DEF are in ratio 11:9:5 and that the difference of the sides DE and DF is 18 cm, the sum of sides can be discovered
- DE ─ DF = 11 ─ 5 = 6, meaning (6 parts represent = 18 cm), so 1 part must be 3cm
- Sum of all sides = 11 + 9 + 5 = 25 parts. = 25 parts × 3cm which means = 75 cm
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