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Halves and quarters are the portions of a whole, and whole means the entire thing. An entire pizza, the complete birthday cake, an entire chocolate bar, etc., are examples of the whole. In mathematics, we represent halves and quarters using the concept of fractions. This topic deals with defining and finding the relationship between the halves and the quarters and their whole.

This article will elaborate on using models to divide a whole into half parts and quarter parts. It will also help solve some questions that will help practise the concepts and learn how to deal with quarters and halves in real life.

Before we learn about halves and quarters, we need to know about the whole. Whole means something which is complete and which is not divided into parts. We can consider an entire pizza, a whole birthday cake, a whole watermelon, a whole orange etc. are examples of the whole.The parts are the portions of a whole. When we divide a whole into two equal parts, we will get halves.For example, if we divide a certain quantity of sugar into two equal portions, each portion obtained is half of the whole amount of the sugar.

Similarly, if we divide one orange into four equal parts, each part is one-fourth of the orange. Now, one-fourth of a whole is called a quarter.Now, half and a quarter represent a part of the whole quantity, which are called fractions.

A fraction is a quantity that expresses a part of the whole. Let us further learn what fractions exactly are.

The term fraction expresses a numerical quantity that is part of a whole thing. Suppose we have a large piece of pie, and we divide it into \(6\) equal portions and colour five parts in light pink and one part in dark pink. Then each part of the paper is only \(\frac{1}{6}^{\text {th }}\) of the total pie. Here, \(\frac{1}{6}\) is a fraction.

We call the above upper part of the fraction the numerator and the below part the denominator. In the above example \(\frac{1}{6}, 1\) is known as the numerator, and \(6\) is known as the denominator. We don’t always deal with whole objects in our regular life. We deal with parts or portions of whole things very often. To quantify them, we need fractions.

We can represent half as a fraction as half is also part of a whole quantity. We already discussed how we could define a part of a whole in a fraction form. Similarly, suppose we divide a whole quantity into two equal parts. In that case, the upper part of the fraction expresses what we have, that is \(1\) and, the lower part of the fraction represents the number into which the whole object is divided, that is \(2\).

So, the numerator will be \(1\), and the denominator will be \(2\) if we represent a half into fraction form.

We can represent quarter as a fraction as it is also a part of a whole quantity. If we divide a whole quantity into four equal parts, then the upper part of the fraction expresses what we have, i.e., \(1\) and, the lower part of the fraction says the number into which the whole object is divided, i.e., \(4\).

So, the numerator will be \(1\) and, the denominator will be \(4\) if we represent a quarter into fraction form.

If we divide a whole into exactly two equal parts, then these parts are called halves of the whole. Each part is called half of the whole.For example, half of an orange, half of a circular piece of paper, half glass of water, half of a watermelon.

Let us take some geometrical figures and see their half parts. We can divide a triangle, a square, a circle into two halves.

Let us take an example of a number and explain. Number \(8\) is a whole number, and we can divide it into two equal parts that are \(4\) and \(4\). So, number \(8\) is a whole, and \(4\) and \(4\) are the parts of number \(8\). In other words, we can say if we add two numbers \(4\) and \(4\), we will get the whole as \(8\). That means two \(4 \mathrm{~s}\) which we got after breaking \(8\) into two equal parts, are the halves of \(8\).

If we divide a whole into four equal parts, these parts are called quarters of the whole. Each part is known as a quarter of the whole. For example, a quarter of an orange.

Let us take some geometrical figures and see their quarter part. We can divide a square, a circle, into four quarters.

In the above figure, the blue shaded part is a quarter of the whole circle.

In the above figure, the orange shaded part is a quarter of a rectangle.

Let us take number \(8\) and explain its quarters. Number \(8\) is a whole number, and we can divide it into four equal parts are \(2, 2, 2\) and \(2\). So, number \(8\) is a whole, and four \(\text {2s}\) are the parts of number \(8\).

In other words, we can say if we add these four numbers, we will get the whole as \(8\). That means four \(\text {2s}\) which we got after breaking \(8\) into four equal parts, are the quarters of \(8\).

We can divide a whole into halves as well as into quarters. There must be a relation between halves and quarters. Let us use some real-life examples and try to relate halves and quarters with each other.

From the above image, it is visible that if we cut one whole tomato into two equal pieces, we get \(\frac{1}{2}\) of the tomato and, if we again cut the half part into two identical pieces, we get \(\frac{1}{4}\) of tomato. So, \(\frac{1}{4}\) of a tomato is equal to half of \(\frac{1}{2}\) of a tomato. In other words, we can say two quarters make one half.

Q.1. Express half as a fraction.Ans: We can represent half as a fraction. Suppose we are dividing a whole quantity into two equal parts. In that case, the upper part of the fraction expresses what we have, i.e., \(1\) and, the lower part of the fraction represents the number into which the whole object is divided, i.e., \(2\).Therefore, the fraction form of half is \(\frac{1}{2}\).

Q.2. Express a quarter as a fraction.Ans: We can represent a quarter as we can divide an entire amount into four equal parts. In this case, the numerator will be \(1\) and, the denominator will be \(4\). Therefore, the fraction form of a quarter is \(\frac{1}{4}\).

Q.3. How many pieces will we get from the halves of a lemon?Ans: If we divide a whole into exactly two equal parts, then these parts are called halves of the whole. Each part is known as half of the whole.So, if we divide a lemon into halves, we will get two pieces of lemon.

Q.4. Find the quarter of \(20\).Ans: We know that a quarter of a whole means one-fourth of a whole.Therefore, \(\frac{1}{4} \times 20=5\)Hence, a quarter of \(20\) is \(5\).

Q.5. Find half of \(12\).Ans: We know that a half of a whole means \(\frac{1}{2}\) of a whole.Therefore, \(\frac{1}{2} \times 12=6\)Hence, half of \(12\) is \(6\).

In this article, we have learned about halves and quarters, the relation between halves and quarters. We have seen some examples of halves and quarters. We learned that we could represent half and a quarter using fractions. We have also solved some problems related to the topic.

Q.1. What are quarters and halves?Ans: When we divide a whole into two equal parts, we call these parts halves, and when we divide a whole into four equal parts, we call these parts quarters.

Q.2. Do halves have to be equal?Ans: Yes, halves have to be equal. If we divide a whole into two unequal parts then, these parts can not be called halves.

Q.3. What is the difference between halves and quarters?Ans: When we divide a whole into two equal parts, we call these parts halves, and when we divide a whole into four equal parts, we call these parts quarters.So, the halves mean each part is \(\frac{1}{2}\) of a whole and the quarters means each piece is \(\frac{1}{4}\) of a whole.

Q.4. What is the relation between a half and a quarter?Ans: A quarter means one-fourth that we can represent as \(\frac{1}{4}\) and two quarters means \(2 \times \frac{1}{4}=\frac{1}{2}\). So, two quarters mean one half.Now, if we divide \(\frac{1}{2}\) into two parts, we will get \(\frac{1}{2} \div 2=\frac{1}{4}\).So, half of one half is one quarter.

DSV A/S[1] is a Danish transport and logistics company offering global transport services by road, air, sea and train as well as logistics solutions. Since its foundation in 1976 by nine independent Danish hauliers, the company has achieved rapid expansion and international presence, predominantly through a series of strategic competitor acquisitions, some of the most important ones being Samson Transport (1997), DFDS Dan Transport Group (2000), J.H.Bachmann (2004), Frans Maas (2006), ABX LOGISTICS (2008), UTi Worldwide, Inc. (2016), Panalpina Welttransport (Holding) AG (2019) and Agility Global Integrated Logistics (GIL) (2021).

With headquarters in Hedehusene (near Copenhagen), Denmark, and offices in more than 80 countries, DSV employs more than 75,000 people and collaborates with partners and agents globally.[1] The company is listed on NASDAQ OMX Copenhagen (Copenhagen Stock Exchange) and included in the OMXC25 index as one of the 25 most traded stocks.[2]

The company is structured in three divisions, Road, Air & Sea, and Solutions. Its main activities lie within road transport (trucking) networks in Europe, North America and South Africa, global air and sea freight forwarding business, and contract logistics solutions across the globe. As part of an asset-light financial strategy to maintain fixed costs at a minimum and be able to quickly respond to market fluctuations, the group does not own any ships or aeroplanes and only a relatively small fleet of trucks and trailers.[1]

Jens Bjørn Andersen became CEO in August 2008. In 2022, the company reported a net revenue of DKKm 235,665.[1]

In 1976, Leif Tullberg and nine independent haulers established DSV, an initialism for “De Sammensluttede Vognmænd af 13-7 1976 A/S” (The Joint Hauliers of 13-7 1976).[3] Leif Tullberg remained CEO until his retirement in 2005.

He was succeeded by Kurt Larsen who became Chairman of the Board of Directors in 2008 when Jens Bjørn Andersen took over as CEO.

During the first decade the company mainly functioned as a cartage department for the owners, handling contract haulage and deliveries.[3]

Seeking a foothold on the international market, DSV bought two competing export companies in 1989, Borup Autotransport A/S and Hammerbro A/S-Bech Trans. The next acquisitions on the road to becoming Pan-European were Samson Transport Co. A/S in 1997 and Svex Group A/S in 1999.[3]

The purchase of the DFDS Dan Transport Group in 2000 provided DSV with important road transport activities in Scandinavia, the UK, several Mainland European countries and the Baltics plus a global network including a logistics set-up.[3] The purchase of J.H. Bachmann in 2005 reinforced the company's position within international air and sea transport.

The acquisition of the Dutch Frans Maas Group in 2006 placed DSV as a truly Pan-European road transport and logistics supplier – and one of the three largest in Europe.[4] With the acquisition of ABX LOGISTICS in 2008, DSV got a foothold in South America and is now represented on six continents.[3] With the acquisition of UTi Worldwide, Inc. in 2016 and Panalpina Welttransport (Holding) AG in 2019,[1] the company became one of the world's four largest transport and logistics companies).[1]

On 1 April 2019, an acquisition agreement with Swiss Panalpina was announced valued at CHF 4.6 billion (€ 4.1 billion).[5] On 19 August 2019, DSV announced that the acquisition of Panalpina was completed.[6]

In July 2020, DSV announced its plans to invest approx. DKK2bn in a new logistics centre near Horsens, Europe’s largest with just one leaseholder.[7]

On 27 April 2021, DSV announced its plans to acquire "Agility Global Integrated Logistics (GIL)".[8]. The acquisition was completed 19 August 2021, making the company a global top-three transport and logistics provider. With this acquisition, the company gained a stronger foothold in the Middle East and added additional capacity to all its divisions: Air & Sea, Road and Solutions.

When in 2000 DSV A/S acquired DFDS Dan Transport Group A/S, the new joint company's activities continued under the DFDS Transport name, while the parent company remained De Sammensluttede Vognmænd (In English: The joint Hauliers) af 13-7 1976 A/S. In 2003, it was formally shortened to DSV A/S.[3]

In 2007, the name of the company's transport activities were also changed to DSV, to create a global brand and avoid confusion.

On 24 September 2019, at an Extraordinary General Meeting following the acquisition of Panalpina Welttransport (Holding) AG, it was decided to change the company name from DSV A/S to DSV Panalpina A/S while maintaining DSV A/S as a second name.[9] The name change only applied to the parent company. The DSV logo remained unchanged.

On 8 September 2021, the name of parent company, DSV Panalpina A/S, was changed back to DSV A/S. [10]

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• Use Corn Flour Or Rice Flour.
• Use Semolina To Get The Right Texture.
• Use Baking Soda.
• Fry The Vadas On A High Flame.
• Deep Fry The Vadas.
• Place The Vadas In A Bowl.
• Do Not Add Vegetables While Making Vadas.