What's compound ratio , duplicate ratio , triplicate ratio , subduplicate ratio , subtriplicate ratio ?
Answers
1. Compounded ratio: For two or more ratios, if we take antecedent as product of antecedents of the ratios and consequent as product of consequents of the ratios, then the ratio thus formed is called mixed or compound ratio. As, compound ratio of m : n and p : q is mp : nq.
In other words,
When two or more ratios are multiplies termwise; the ratio thus obtained is called compound ratio.
For example:
The compounded ratio of the two ratios a : b and c : d is the ratio ac : bd, and that of a : b, c : d and e : f is the ratio ace : bdf.
For ratios m : n and p : q; the compound ratio is (m × p) : (n × q).
For ratio m : n, p : q and r : s; the compound ratio is (m × p × r) : (n × q × s).
2. Duplicate ratio: Duplicate ratio is the ratio of two equal ratios.
For example:
The duplicate ratio of the ratio x : y is the ratio x22 : y22.
In other words,
The duplicate ratio of the ratio m : n = Compound ratio of m : n and m : n
= (m × m) : (n × n)
= m22 : n22
Therefore, the duplicate ratio of 4 : 7 = 422 : 722 = 16 : 49
3. Triplicate ratio: The triplicate ratio is the compound ratio of three equal ratios.
The triplicate ratio of the ratio a : b is the ratio a33 : b33.
In other words,
The triplicate ratio of the ratio m : n = Compound ratio of m : n, m : n and m : n
= (m × m × m) : (n × n × n)
= m33 : n33
Therefore, the triplicate ratio of 4 : 7 = 433 : 733 = 64 : 343.
4. Subduplicate ratio: The subduplicate ratio m : n is the ratio √m : √n. So, the subduplicate ratio of the ratio m22 : n22 is the ratio m : n.
For example:
The subduplicate ratio of 25 : 81 = √25 : √81 = 5 : 9.
5. Subtriplicate ratio: The subtriplicate ratio m : n is the ratio √m : √n. So, the subduplicate ratio of the ratio m−−√3m3 : n−−√3n3 is the ratio m : n.
For example:
The subtriplicate ratio of 125 : 729 = 125−−−√31253 : 729−−−√37293 = 5 : 9
Answer:
Compounded ratio: For two or more ratios, if we take antecedent as product of antecedents of the ratios and consequent as product of consequents of the ratios, then the ratio thus formed is called mixed or compound ratio. As, compound ratio of m : n and p : q is mp : nq.
In other words,
When two or more ratios are multiplies termwise; the ratio thus obtained is called compound ratio.
For example:
The compounded ratio of the two ratios a : b and c : d is the ratio ac : bd, and that of a : b, c : d and e : f is the ratio ace : bdf.
For ratios m : n and p : q; the compound ratio is (m × p) : (n × q).
For ratio m : n, p : q and r : s; the compound ratio is (m × p × r) : (n × q × s).
Step-by-step explanation: