Commercial Arithmetics : Ratio & Fraction Differences

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Ratio & Fraction Differences

what you'll learn...

overview

Ratio and Fraction are two methods to specifying relative magnitude of quantities. Eg: $12$ $12$ and $24$ $24$ are in $1 : 2$ $1:2$ ratio

OR $12$ $12$ is $\frac{1}{2}$ $1/2$ of $24$ $24$ .

Understanding the differences in these two representation is explained.

ratio vs fraction

Consider $4$ apples and $6$ oranges. And there are pieces of a cake. The cake was cut into $6$ pieces and only $4$ pieces are remaining.

• ratio of apples to oranges is $4:6$ which is equivalently $2:3$
A ratio represents comparison of two quantities given as the magnitude of one to the magnitude of another.

• number of apples is $4/6$ fraction of number of oranges. which is equivalently $2/3$ .
A fraction can be used for comparing two quantities.

• number of cakes is $4/6$ fraction of the whole, which is equivalently $2/3$ .
A fraction can be ised to specify a quantity.

Note that the fraction can be used both for comparing quantities and to specify a quantity.

context

Consider $4$ apples and $6$ oranges.

• ratio of apples to oranges is $4:6$ which is equivalently $2:3$

• ratio of apples to fruits is $4:10$ which is equivalently $2:5$

• number of apples is $4/6$ fraction of number of oranges. which is equivalently $2/3$ .

• fraction of apples in the fruit basket is $4/10$ which is equivalently $2/5$ .

Students should always pay attention to the context under which ratio or fraction is given.

making sense of ratios & fractions

Consider: Distance-to-school is $3$ km in the east and distance-to-hospital is $9$ km in the north.

• ratio of distance-to-school to distance-to-hospital is $3:9$ which is equivalently $1:3$

• distance-to-school is $3/9$ fraction of distance to hospital.

• fraction of distance to school to the total distance does not make sense. The distances cannot be added unless specifically required in the given problem.

For example, consider that a person traveled to school first and returned to home. And then he traveled to hospital and returned home. In this case, the total distance traveled can be worked out.

Ratio Vs Fraction : comparison of two quantities given as magnitude of one to magnitude of another is ratio.

Fractions are also used to represent comparison of two quantities given as magnitude of one over magnitude of another.

Fractions specify one quantity that is part of a whole given as magnitude of the part to magnitude of whole.

examples

Convert $2:3$ into a fraction.

The answer is " $2//3$ "

convert $11/14$ into a ratio

The fraction $11/14$ can mean two possibilities

• Two quantities are in $11:14$ ratio

• one quantity is specified as $11/14$ part of the whole.

In the context of ratio, the fraction is taken to be in the form of comparison of two quantities, unless specified in the question. So, the answer is " $11:14$ ".

The number of apples are $2/3$ of the number of oranges. What is the ratio of apples to oranges?

The given fraction specifies the comparison of apples to oranges.

Number of apples is $2/3$ of the number of oranges. Which means, for every orange, there are $2/3$ apples.
So the ratio of apples to oranges is $2/3 : 1$ , which is equivalently $2:3$ . So, the answer is " $2:3$ ".

A basket has $2/3$ apples and rest oranges. What is the ratio of apples to oranges?

The given fraction specifies the quantity of apples.

Quantity of apples $2/3$
Quantity of oranges $1 - 2/3 = 1/3$
So the ratio of apples to oranges is $2/3 : 1/3$ which is equivalently $2:1$ . So the answer is " $2:1$ ".

summary

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