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Course Content
GRADE 12 – Unit 5: Mathematical Applications in Business
About Lesson

Basic Mathematical Concepts in Business

 

  • Ratios

A ratio is a comparison of two numbers by division. It helps to determine the relationship between two quantities.

The ratio of aa to bb can be expressed as:

a:boraba : b quad text{or} quad frac{a}{b}

  • Rates

A rate, like a ratio, is a comparison of two quantities, but the quantities may have different units of measure. For example, speed is measured in km/hr, comparing distance and time.

A rate that has a denominator of 1 is called a unit rate.

The rate of change of a given quantity is used to measure how one quantity changes in relation to another:

 

Rate of Change=Final Amount – Original AmountOriginal Amounttext{Rate of Change} = frac{text{Final Amount – Original Amount}}{text{Original Amount}}

  • Proportions

A proportion is an equation that states that two ratios are equal.

In the proportion a:b=c:da : b = c : d, with b0b neq 0 and d0d neq 0, the four numbers are referred to as the terms of the proportion.

The first and last terms (aa and dd) are called the extremes, and the second and third terms (bb and cc) are called the means.

For three quantities aa, bb, and cc, if:

ab=bcb2=a×cfrac{a}{b} = frac{b}{c} quad Rightarrow quad b^2 = a times c

This is called the mean proportion between aa and cc.

 

  • Compound Proportions

A compound proportion is when one variable quantity depends on two or more other variable quantities.

Two quantities xx and yy are said to be in inverse proportion if an increase in xx causes a proportional decrease in yy:

 

x×y=k,where k is a constantx times y = k, quad text{where } k text{ is a constant}

If xx and yy vary directly (in direct proportion), then:

y=kx,where k is a constanty = kx, quad text{where } k text{ is a constant}

  • Percentages

A percentage is a number or ratio expressed as a fraction of 100. It is used widely in business to describe profit margins, discounts, and markups.

The difference between a product’s selling price and its cost is called markup:

Markup=Selling PricePurchase Pricetext{Markup} = text{Selling Price} – text{Purchase Price}

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