Application and fractional relations — lesson. Mathematics CBSE, Class 7 New.

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Some problems involving fractions:

There are many word problems that involve fractions and use arithmetic operations like addition, subtraction, multiplication, and division.

Steps to work on word problems involving fractions:

First, understand the information given in the question.
Consider all the fractions and numbers given in the question.
Identify the arithmetic operation suitable for the given content.
Solve the fractions and write the answer with the given units.

Example:

Amritpal decides on a destination for his vacation. If he takes a train, it will take him \(5\frac{1}{6}\) hours to get there. If he takes a plane, it will take him \(\frac{1}{2}\) hour. How many hours does the plane save?

Solution:

Hours taken to reach the destination by train \(=5\frac{1}{6}\)

Hours taken to reach the destination by plane \(=\frac{1}{2}\)

Hours saved by travelling by plane = Hours taken by train - Hours taken by plane

\(=5\frac{1}{6}\)\(-\frac{1}{2}\)

\(=\frac{31}{6}\)\(-\frac{1}{2}\)

L.C.M of \(6\) and \(2\) is \(6\).

\(=\frac{31}{6}\)\(-\frac{1 \times 3}{2\times 3}\)

\(=\frac{31}{6}\)\(-\frac{3}{6}\)

\(=\frac{31-3}{6}\)

\(=\frac{28}{6}\)

\(=\frac{2 \times14}{2 \times 3}\)

\(=\frac{\not2 \times 14}{\not2 \times 3}\)

\(=\frac{14}{3}\)

\(=4\frac{2}{3}\)

Hence , The plane saves \(=4\frac{2}{3}\) hours.

Fractional Relations:

Let us understand this topic using the example below.

Here is the square with some lines

We need to find the fraction of the area of the whole square that is shaded.

Let the area of the whole square be \(1\) square unit.

From the figure we get, the top right square occupies \(\frac{1}{4}\) of the whole square.

Area of above top right square = \(\frac{1}{4}\) square units.

We can split the above square in this below way,

This yellow shade is detailed explanation of above figure.

Area of yellow triangle \(= \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \text{square units}\)

The shaded region in the question occupies \(\frac{3}{4}\) space in yellow region

Thus the area of shaded region \(= \frac{3}{4} \times \frac{1}{8} = \frac{3}{32} \text{square units}\)

A Dramma - tic Donation:

Around the \(12\)th century, several types of coins were in use in different kingdoms of the Indian subcontinent.

Most commonly used were:

Gold coins (called dinars/gadyanas and hunas),
Silver coins (called drammas/tankas),
Copper coins (called kasus/panas and mashakas),
and Cowrie shells.

The exact conversion rates between these coins varied depending on the region, time period, economic conditions, weights of coins and their purity.

Gold coins had high-value and were used in large transactions and to store wealth.
Silver coins were more commonly used in everyday transactions.
Copper coins had low-value and were used in smaller transactions.
Cowrie shells were the lowest denomination and were used in very small transactions and as change.

If \(1\) gold dinar = \(12\) silver drammas,

\(1\) silver dramma = \(4\) copper panas,

\(1\) copper pana = \(6\) mashakas, and

\(1\) pana = \(30\) cowrie shells.

Example:

How many gold dinar's make \(1\) copper pana?

Solution:

We know that,

\(1\) gold dinar = \(12\) silver drammas

\(= 12 \times 4\) copper panas

\(= 48\) copper panas

(i.e) \(1\) gold dinar = \(48\) copper panas