Rates and Ratios

Question 1

What are rates?

Answer 1

Rates show the relationship between 2 different units.

Question 2

What are ratios?

Answer 2

Ratios compare units of the same type of quantity with the same unit

Question 3

How do you calculate $2.55 for 5 minutes into cents/mins?

Answer 3

2.55 divide by 5 = 51 c/min

Question 4

What are common forms of rates?

Answer 4

Speed: S = d/t
Density: D = m/v
Where m=mass and v=volume.
Concentration: C = Solute/solvent
Where solvent is liquid and solute is solid.

Question 5

What is a distance-time graph?

Answer 5

A journey or a trip that can be repsented by a distance/time graph called a travel graph.
Distance is shown on y-axis and time is taken to show on the x-axis.
A straight line shows a constant speed (Linear).
A horizontal lines means subject is stationary.

Question 6

How do you calculate the gradient? And what is an example of it?

Answer 6

Gradient = Rise/Run
Rise: Vertical distance
Run: Horizontal distance

Gradient is a measure of steepness. A gradient of 1 means for every 1 across. We go up by 1.

Question 7

What is the constant of proportionality?

Answer 7

To find the constant of proportionality is to find the link to x to y (As seen in the box or graph).

The formula for constant of porportionality is y = Kx where K is the constant (the rate) and y is the y-axis and the x is the x-axis.

Example: A tank uses 7.5L of petrol every 3km.
What is the rate: 2.5L/km
What is the constant: 2.5
What is the rule (The link/formula): y = 2.5x

Question 8

How do you calculate percentage?

Answer 8

Divide the fraction by each other and then x by 100.

For example,
Find the percentage of cleaned area if the rectangle is 2800 and the cleaned area is 1308.99.

You divide 1308.99/2800 x 100 which equals to 46.7%

Question 9

How do you divide a number into a ratio?

Answer 9

For example, divide 80$ into 2:3

Step 1: Add up ratio 2+3=5
Step 2: divide the whole number by the ratios number. 80/5=16
Step 3: Times the ratios original no.s by answer before. 2x16=32, 3x16=48.

Question 10

How do you simplify ratios if they are in a fraction or are decimal.

Answer 10

Decimal -

Multiply the number by 10 to get a whole number do the same to the other number then simplify.

Fraction -

Convert the fractions so that they have the same denominator.
And then the nominative is your answer. Or.
Multiply the fractions by the common denominator.
Simplify.

Question 11

What are some common form of rates?

Answer 11

Flow = litres/minute

Typing speed = words/minute

Heart Rate = beats/minutes

Cost = price/kg

Question 12

How do you calculate the mass from volume and density?

Answer 12

To get mass from volume and density multiply density and volume together.

Question 13

Leanna works in a donut van and sells on average 60 donuts every 15 min. How long is it likely to take her to sell 800 donuts?

Answer 13

Step 1: Selling rate = 60donuts / 15min so divide 60 by 15 which equals 4.

Step 2: The 4 means she makes 4 donuts every minute. So to find the amount of time she takes to make 800 you divide 800 by 4 which equals to 200 minutes.

Question 14

When converting rates into simpler rates such as, the question,

Change $15/h into c/min

Answer 14

Step 1: Change 15$ into cents
15 x 100 = 1500
Step 2: Change hours to minutes
So 1 Hour is 60 minutes.
Step 3: Divide the cents by minutes,
1500/60 = 25c/min