RATIO AND PROPORTIONS + UNIT CONVERSIONS

0.0(0)
studied byStudied by 6 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/14

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

15 Terms

1
New cards

What is a ratio?

A ratio is a comparison between two or more quantities or magnitudes

2
New cards

What does ratio tell us?

  • A ratio gives us information about how parts of a whole relate to each other, and how those parts relate to the whole

  • A ratio only portrays a relationship between quantities. By itself, it doesn’t provide the actual numbers of those quantities

3
New cards

What is a ratio multiplier?

A ratio multiplier is a value multiplied by both the numerator and denominator of a ratio to represent the actual amounts of two quantities

4
New cards

How can we determine the ratio multiplier?

  • When we are given the quantity of one of the items

  • We are given the quantity of all the items in the ratio

Sum of the quantities of each item must equal the total number of items being considered in the ratio. Sometimes the ratio multiplier is not an integer

5
New cards

How do you calculate multipart ratio?

  • Find the common variable between the two ratios

  • Make the common variable same by taking the LCM

6
New cards

Are we able to add/subtract/multiply/divide a quantity to get the desired ratio?

  • To be able to add/subtract/multiply/divide a quantity to get the desired ratio, we must find the actual quantity of each component first. This is applicable for both part-to-part ratios as well as part-to-total ratios

7
New cards

What is proportion?

  • 2 equal ratios are called proportions.

  • If a/b = c/d, then we have a proportion and it must be true that ad = bc

8
New cards

What is direct variation?

  • Describes the relationship between 2 variables

  • If y varies directly with x i.e. if x increases or decreases by a factor, y will increase or decrease by the same factor

  • Can be represented by y = kx, where k is constant

9
New cards

What is inverse variation?

  • Describes the relationship between 2 variables

  • When we have inverse variation between 2 variables x and y, then they can be related by the equation y = k/x, where k is a positive constant. When x increases by a factor, y will decrease by the same factor.

  • On the other hand, when x decreases by a factor, y will increase by the same factor

10
New cards

What is combined variation?

  • Single variable can have both direct and inverse variation with one variable and inverse variation with another.

  • In such situations, both relationships can be combined into one equation

  • For eg: If y varies directly with x and inversely with z, then the 3 variables are related by the equation y = kx/z, where k is a constant

11
New cards

What is joint variation?

  • Variable varies directly jointly with 2 other variables if it varies directly with each of them

  • Eg: If y varies directly jointly with x and z, then the three variables are related by the equation y = kxz, where k is a constant.

  • A single variable can also vary inversely with 2 other variables simultaneously.

  • Eg: If y varies inversely jointly with x and z, then the three variables are related by the equation y = k/xz, where k is a constant

12
New cards

Convert from LHS → RHS:

  • Dollar to cents

  • Metres to Km

  • Quarts to pints

  • 1$ = 100cents

  • 1000m = 1Km

  • 1 Quart = 2 Pints

13
New cards

How do you tackle a unit conversion problem in which we need the final answer in squared units?

  • We raise both sides of the original unit to the second power, and then convert the squared units

14
New cards

How do you tackle a unit conversion problem in which we need the final answer in cubic units?

  • We raise both sides of the original unit to the third power, and then convert the cubic units

15
New cards

Answer the following questions:
what is:

  • Area of rectangle

  • Area of square

  • Volume of box

  • Volume of cube

  • Surface area of box

  • Surface area of cube

  • Area of rectangle = Length x width

  • Area of square = (side)²

  • Volume of box = length x width x height

  • Volume of cube = (edge)³

  • Surface area of box = 2(length x width) + 2(width x height) + 2(length x height)

  • Surface area of cube = 6(edge)³