A fraction is a number that shows a part of a whole (a fraction of a big whole number). When you split something into equal pieces, each piece is a fraction of that whole. The fraction is written like this: Num/Deno.

• The numerator (upper number) indicates parts; that is, how many parts we have.
• The denominator (lower number) indicates the whole.

Think of a fraction as the whole being split into many parts.

Table of Contents:
•            Examples from daily life:

• Different Types of Fractions Explained in a Detailed Way

1. Proper Fractions
2. Improper Fractions
3. Mixed Fractions
4. Equivalent Fractions
5. Like Fractions
6. ]|

• How Fractions can be used in our daily lives

1. Cooking / Baking
2. Time
3. Sharing
4. Shopping / Discounts

• Use of Fractions in Workplaces and Industries

1. Construction / Carpentry
2. Printing / Graphics Design

• Numerical Problems Based on Fractions Concepts
• Word Problems Based on the Concepts of Fractions for 6th Graders

1. Riya’s Ribbon
2. Tailor’s Fabric
3. Factory Sheets

• FAQs based on the Topics of Fractions
  

Examples from daily life:

• Suppose you have one chocolate bar divided into 4 equal pieces, and you eat 1 piece. You’ve eaten 1/4th of the bar.
• If there are 8 slices of pizza, you take 3 slices, you will end up taking 3/8th of the pizza.
• Think of a water bottle divided into 5 equal parts (5 equal-segment markings with water). If the water reaches 2 marks out of 5 markings, we can say the bottle is ^th
• If you have a big cake and it is cut into 3 big slices. Then, if you eat 2 greedily, that will be equivalent to of the cake. But, unfortunately, only one will be the remaining slice that can be eaten by others.

So, fractions help us show parts of a whole--parts of objects, of quantities, of time, etc.

Different Types of Fractions Explained in a Detailed Way

1. Proper Fractions: The numerator is less than the denominator in this case. Hence, they show a partial amount out of the whole. Example: 3/5 means three parts out of five equal parts.
2. Improper Fractions: The numerator exceeds the denominator in such scenarios. One of the examples: 7/4. 7/4 is equal to one whole and three-quarters 1 3/4 (mixed fraction).
3. Mixed Fractions: A whole number gets added to a proper fraction (2 + 1/3), so multiply the denominator by the whole and add the sum to the numerator [(3x2) + 1]/3 = 7/3]. Another example: 3 added to one half (3 ½).
4. Equivalent Fractions: Different forms that equal the same portion. That is, equal types of fractions exist in different forms. Example: 1/2 equals 2/4; both represent the same half.
5. Like Fractions: In this case, fractional numbers share the same denominator and hence, numerators can be added easily. Also, the denominator being the same, the comparison as well as the addition becomes straightforward. Example: 2/7 and 3/7 use equal-sized parts; in this case, summing of numerator [(2+3)/7) = 5/7] is easy.

How Fractions can be used in our daily lives

Fractions are not just about dividing cakes or pizzas. They go beyond the eating items and can be used everywhere in ordinary life.

Cooking / Baking: Suppose, in a recipe, one may have to use1/2 teaspoon of sugar, 3/4 cup of milk. If you double a recipe, you might need the milk quantity to be: 3/4 x 2 = 6/4 = 1 2/4 or 1 1/2 cups.

Time: Suppose that a class lasts 1 hour and 15 minutes, that is, 1 15/60 = 1 1/4 hours. If you watch TV for 3/2 hours, that is 3/2 x 60 minutes = 90 minutes (since 1 hour = 60 mins).

Sharing: If you share 5 apples equally among 3 friends, each friend gets 5/3 apples (that is, 1 whole apple and 2/3 apple extra).

Shopping / Discounts: If an item is discounted by 2/5 of its price, and the original price is ₹500, you save 2/5 × 500 = ₹200. And hence, you pay 500 − 200 = ₹300

Use of Fractions in Workplaces and Industries

Construction / Carpentry

In construction, precision is everything in all ways. Thus, fractions form the bedrock of this craft without any doubt. Example: for making a wood-based item, a plank may require a 3/8-inch cut. It goes without saying that such thorough tasks demand immense care and a high level of precision.

Hence, this would be a process of precision-based material handling. Reason: accuracy decides the strength. In other words, any kind of minor errors will lead to ill-fitting joints. So, in case a door is required, one can expect a poorly-measured door leading to the creation of one that won’t close properly.

Similarly, even when it comes to shelves, wrong measurements in fractions may result in shaky shelves--improperly-cut-supports. This is nothing but a clear safety hazard that went ignored.

Imagine a new trainee may be given a task of making a desk. He might eye a cut, hacking off timber with less-than-ideal measurement. Thus, this would result in a desk that would be wobbly. Also, due to bad measurements, even its drawers would jam. Conversely, a seasoned carpenter shaves the plank with highly practiced skill.

Printing / Graphics Design

In printing, even the page is like a canvas that is governed by fractional rules. Precisely, a margin might claim 1/8th of space; the text occupies 3/4.

These are the seemingly small details that cannot be ignored. Importantly, the inclusion of such in-depth calculations would yield a balanced final design that could be pleasing to the eye. Also, with care, readability and aesthetics are in place from these fractional relationships.

Example: junior graphic designers who have been assigned the task of assembling a new sales brochure. If margins have gone askew, even by a small amount, the whole text will look jumbled.

Numerical Problems Based on Fractions Concepts

Problem 1: Add 2/5 plus 3/5 and find the answer, and give an explanation for your answer. Answer: The answer turns out to be: 5/5 equals 1. The explanation or logic is: Denominators match (even-same-sized); add numerators, keep the denominator.

Problem 2: 4/7 minus 2/7 and find the answer, and give an explanation for your answer.

Answer: The answer turns out to be: 2/7, and the step is (4-2)/7 = 2/7. Explanation: Same denominator (even-same-sized); subtract numerators; the denominator remains constant.

Problem 3: Solve the problem: 3/4 multiplied by 2/3 and provide logic behind the solution. Answer: When both 3/4 and 2/3 are multiplied, we get 6/12, which can be further simplified to 1/2. Logic behind solving the problem: Multiply numerators and denominators across (3 x 2 / 4 x 3) = 6 / 12 = 1/2; then simplify by common factors.

Problem 4: Find out what happens when 5/6 is divided by 2/3 and offer an explanation. 

Answer: 5/6 divided by 2/3 = (5 x 3)/(6x2) =15/12=5/4, which equals 1 1/4. Explanation: Division becomes multiplication by reciprocal; flip the second fraction, then multiply.

Problem 5: You have to add 2/3 to 5/4 and give an explanation of how you found the answer. 

Answer: The solution is 23/12, which is 1 11/12. Explanation: Find LCM 12; convert each fraction to twelfths, then add the numerators.

Word Problems Based on the Concepts of Fractions for 6^th Graders

Riya’s Ribbon

Q1: Riya had a 2 m ribbon; she used three-quarters for a gift. She donated one-eighth of the remaining ribbon. Find the part she donated?
Answer: 0.0625 m (6.25 centimeters), and here is how we solve it:
Step 1: Three-quarters of two meters equals one point five meters (3/4 x 2 = 6/4 = 3/2 = 1.5m).
Step 2: The Remaining ribbon equals two minus one point five (2 – 1.5 = 0.5), thus zero point five.
Step 3: One-eighth of the remainder equals zero point five divided by eight. Dividing: 0.5 ÷ 8 equals 0.0625 meters. Convert to centimeters: multiply by one hundred; result equals 6.25 cm. This small piece needs careful handling [steady-handed-precise].

Tailor’s Fabric

Q2: A tailor had seven yards of fabric; he used two-fifths for shirts. He then used one-third of the remaining fabric for pants. Find the remaining length of fabric?
Answer: 2.8 yards remain.
Step 1: Two-fifths of seven equals fourteen-fifths (2/5 x 7 = 2.8), which is two point eight.

Step 2: Remainder equals seven minus two point eight; therefore, four point two (7 - 2.8 = 4.2). Step 3: One-third of the remainder for pants equals four point two divided by three (4.2/3 = 1.4). Division gives one point four yards used for pants.
Final remainder equals four point two minus one point four; equals two point eight (4.2 – 1.4 = 2.8).

Factory Sheets

Q3: A factory produced 1,200 sheets; three-eighths were defective. One-fifth of the good sheets were exported. So, how many sheets were exported?
Answer: 168 sheets exported.
Step 1: Calculate defective: 1,200 × 3/8 equals 360 defective sheets.
Step 2: Good sheets equal 1,200 minus 360; that equals 840.
Step 3: Exported equals one-fifth of 840; compute: 840 ÷ 5. Division gives 168 exported sheets.

FAQs based on the Topics of Fractions
1. Q: What is an equivalent fraction, and why do we use it?  

 A: Equivalent fractions show the same part with different numbers, and they help in comparing and adding.

2. Q: How do you convert an improper fraction into a mixed fraction?  

A: Divide numerator by denominator; quotient is whole; remainder/denominator is fraction.

3. Q: When adding unlike fractions, what’s the rule?  

A: Find the common denominator, convert the fractions, then add the numerators.

4. Q: How to subtract fractions when the first is smaller than the second?  

A: Convert to improper, find the common denominator, subtract, and simplify.

5. Q: What is the reciprocal of a fraction, and why is it useful?  

 A: Reciprocal is the numerator/denominator flipped, which is used for dividing fractions.