Problems Using Equivalent 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.
- 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 1
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 $5$5 parts and Keira gets $4$4 parts.
Do:
| Amir | gets | $5$5 parts |
| $=$= | $5\times\$80$5×$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$$720
$\$400+\$320=\$720$$400+$320=$720
Question 2
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 3
Divide 24 kilograms into the ratio $4:8$4:8.
a) Which is the larger value?
b) What is the smaller value?