Working Mathematically

Working Mathematically

Lesson

Rates

A rate is a ratio between two measurements with different units. A common example of a rate is speed (which is written in kilometres per hour or km/h). You can see that this describes a relationship between two measurements- kilometres and hours.

Examples

Question 1

Evaluate: If I drive at $55$55km/hour, how far will I travel in $4$4 hours?

Think: $55$55km represents the distance traveled in one hour, so to work out how far I went in $4$4 hours, I would need to multiply this distance by $4$4.

Do: $55\times4=220$55×4=220km

These questions don't always use multiplication. Sometimes we need to use division.

Evaluate: If Lee paid $\$11.85$$11.85 for 33kg of apples, how much did he pay per kilogram? Think: To find out what 11kg costs, we need to divide the weight by 33. So we also need to divide the cost by 33. Do:11.85\div3=\3.9511.85÷​3=3.95 /kg/kg Converting rates We can also change the units of measurement that our rates are expressed in. For example kilometres/hour can be changed to metres/second. We just need to be aware of how the values are changing when we are converting the quantities as we need to keep our rate in the same proportion. Examples Question 3 Convert: 1313 L/hr to L/day. Think: How are our units of measurement are changing. We only need to change one of our units of measurement- that is, we need to change hours to days. Since there are 2424 hours in a day, we need to multiply both sides of our rate by 2424. Do:  1313 L/hr == 312312 L/ 24 hrs multiply by 24 to get 24hrs == 312312 L/day We may need to change both units of measurement in some questions. Question 4 Convert 300300 mL/hr to mL/min. Ratios Ratios tell us about the relative sizes of two or more values. They are often used in everyday life, whether it's for dividing up money, betting odds, cooking or mixing cement! So knowing how to apply your knowledge about ratios is really important. You need to know! - How to calculate the total number of parts (by adding all the numbers in the ratio). - How to calculate what one part is worth (by dividing a value by the total number of parts) and - How to calculate what each share of the ratio is worth (by multiplying what one part is worth with each number in the ratio) Examples Question 5 Evaluate: Amir and Keira shared \720$$720 in the ratio $5:4$5:4. How much did each person get?

Think: There are $9$9 parts in total $\left(5+4\right)$(5+4) and $720\div9$720÷​9 is $80$80.

That means that one part is worth $\$80$$80. Amir gets 55 parts and Keira gets 44 parts. Do:  Amir gets 55 parts == 5\times\805×80 == \400$$400 Keira gets $4$4 parts $=$= $4\times\$80$4×$80 $=$= $\$320$$320 Check: The total of Amir and Keira's amounts should sum to the total amount ( \720$$720 )

$\$400+\$320=\$720400+$320=$720

Question 6

Evaluate: Divide $60$60cm in the ratio $1:2:3$1:2:3

Think: There are $6$6 parts in total  $\left(1+2+3\right)$(1+2+3) and $60\div6$60÷​6 is $10$10. This means that one part is worth $10$10cm.

Do: $60$60cm divided in the ratio $1:2:3$1:2:3 would be $10$10cm:$20$20cm:$30$30cm.

Question 7

Divide $24$24 kilograms into the ratio of $4:8$4:8.

1. What is the larger value?

2. What is the smaller value?

Outcomes

NA5-1

Reason with linear proportions.