what you'll learn...
overview
Multiplication is
multiplicand × multiplier multiplicand × multiplier =product=product
It is explained that
• When product is not changing, the multiplicand and the multiplier are in inverse variation.
illustrative examples
Consider
33 bananas
of price 22 coin per banana
with overall cost is 66 coins.
A person carries 66 coins. The price of the banana is increased to 3 coins per banana. The person can buy only 2 bananas with the 6 coins.
Increase in the price results in the decrease in the number of bananas one can buy, when the overall cost remains unchanged.
The price of the banana is decreased to 1 coin per banana. The person can buy 6 bananas.
Decrease in the price results in the increase in the number of bananas one can buy, when the overall cost remains unchanged.
Because of a change in price, the person could buy 6 bananas. The revised price of a banana is 66=1 coin.
Increase in the number of banana was the result of decrease in the price, when the overall cost remains unchanged.
Because of a change in price, the person could buy only 2 bananas. The revised price of a banana is 3 coins.
Decrease in the number of banana was the result of increase in the price, when the overall cost remains unchanged.
summarizing the above
The underlying mathematical operation for the problem is product of two quantities.
• Multiplicand: number of bananas
• Multiplier: price of a banana
• Product : Overall cost
number × price = overall cost
Multiplicand × Multiplier = Product
• when overall cost remains unchanged, increase in the price results in decrease in the number.
• when overall cost remains unchanged, increase in the number results in decrease in the price.
These two are inverse variations. Increase in the multiplier results in decrease in the multiplicand.. Similarly, Decrease in the multiplier results in increase in the multiplicand.
The word "inverse" means: opposite or reverse.
summary
Inverse Variation : If increase in one quantity causes a proportional decrease in another quantity, then these quantities are related by inverse variation.
Multiplicand × Multiplier = Product
When the product is constant.
• Increase in the multiplier results in decrease in the multiplicand.
• Decrease in the multiplier results in increase in the multiplicand.
Outline
The outline of material to learn "commercial arithmetics" is as follows.
Note: Click here for the detailed ouline of commercial arthmetics.
• Ratio, Proportion, Percentage
→ Comparing Quantities
→ Introduction to Ratio
→ Ration & Fraction Differences
→ ProportionsP
→ Percentages
→ Conversion to percentage
• Unitary Method
→ Introduction to Unitary Method
→ Direct Variation
→ Inverse Variation
→ DIV Pair
• Simple & Compound Interest
→ Story of Interest
→ Simple Interest
→ Compound Interest
• Rate•Span=Aggregate
→ Understanding Rate-Span
→ Speed • Time=Distance
→ Work-rate • time = Work-amount
→ Fill-rate • time = Filled-amount
• Profit-Loss-Discount-Tax
→ Profit-Loss
→ Discount
→ Tax
→ Formulas