# Computing Commissions

by Ike Prudente

Before we started MATH-Inic, I planned to organize mental Math classes for parents so that they can teach their children at home. To promote my courses I thought of inviting them to free seminars, where I showed them examples of mental calculations.

A good friend, Past President Rosanna Panque of the Kiwanis Club of Siete Lagos who is a Unit Manager at Insular Life asked me to give an ice breaker at one of meetings of her associates. After discussing some short cuts, I asked my audience what they usually compute. As expected, they told me that they often want to know their commissions as soon as their clients bought a policy.

I asked them for an example which we can compute. They told me about a popular policy where the agent gets 45% of the first premium:

VYP: Ok, give me an amount of first premium.

Agent 1: P18,000

VYP: Can you compute  45% of P18,000 ?

Audience: (Silent)

VYP: What is P18,000 times 0.45?

Audience: (Silent)

VYP:  OK. Let us first divide P18,000 by 2. What do we get?

Audience: P9,000

VYP: Then we double 0.45. What do we get?

Audience: 0.90

VYP: So now we changed the problem to .90 x 9,000. Now, can you mentally compute that?

Audience: (Silent)

VYP: If we multiply 0.90 by 10 we get 9 and when we divide 9,000 by 10 we get 900. So our problem now becomes 9 x 900. Now can you compute that?

Agent 1: Yes! 9 x 9 is 81, so that is P8,100.

VYP: Correct! So you see, you can use doubling and halving to make calculations easier. Let us have another example. Give me another amount.

Agent 2: P 25,000!

I quickly realized that halving P25,000 would give P12,500 which has more non zero digits than the original number. So a different solution is needed.

VYP: Can you compute 45% of P25,000 ?

Audience: (Silent)

VYP: Let us try another solution. What is 10% of P25,000?

Audience: P2,500.

VYP: Deduct P2,500 from P25,000. What do we get?

Audience: P22,500.

VYP: Correct! Now since we deducted 10%, what remains is 90%. Now half 90% is 45%. What is half of P22,500?

Audience: P 11,250!

VYP: Do you have any other questions?

Agents: When will your Math-Inic classes start?

How much is the tuition fee?

Are you offering Math-Inic in Tiaong?

VYP’s Thoughts: Yes!Ayos! Panalo!

Note: Shortly after that, I realized that there are other shortcuts to computing 45% of P25,000.

1)      Halving and doubling together(MSC 7)

45% of P25,000 =  25% of P45,000

= .25 x 45,000

= .50 x 22,500

= 1 x 11,250

2)      Multiplying numbers ending in 5

45% of P25,000 = .45 x 25,000

= 45 x 250

Momentarily disregarding the ending zero in 250, we have

45 x 25 = (4×2)+(4+2)/2| 5 x 5

= 8+3|25

= 1125

We then attach the zero to give a final answer of 11,250. Further examples of this type of calculations will be given in MSC 23.