Fraction
What is a Fraction?
A fraction represents a part of a whole. It is made up of two numbers:
1. Numerator: The number on the top of the fraction, which shows how many parts we have.
2. Denominator: The number on the bottom of the fraction, which shows how many equal parts the whole is divided into.
For example, in the fraction 3/4:
– 3 is the numerator, meaning you have 3 parts.
– 4 is the denominator, meaning the whole is divided into 4 equal parts.
How to Understand Fractions
– Imagine a pizza cut into 4 equal slices. If you eat 3 slices, you have eaten 3/4 of the pizza.
– Fractions can be less than 1 (like 1/2, 3/4) or equal to 1 (like 4/4, which means the whole thing).
Types of Fractions:
1. Proper Fractions: The numerator is smaller than the denominator (e.g., 1/2, 3/5).
2. Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 5/4, 7/3).
3. Mixed Fractions: A whole number combined with a fraction (e.g., 1 1/2, meaning one whole and half).
Key Points:
– Half (1/2) means something is divided into two equal parts, and you take one part.
– Quarter (1/4) means something is divided into four equal parts, and you take one part.
– The larger the denominator, the smaller the pieces, because the whole is divided into more parts.
Numerator and Denominator
When we write a fraction, it looks like this: 1/2 or 3/4.
– Numerator: The number on the top of the fraction.
– Denominator: The number on the bottom of the fraction.
Example:
Imagine you have a pizza that is cut into 4 slices. If you eat 1 slice, you have eaten 1/4 of the pizza.
– Numerator (top number): How many pieces of the pizza you ate. In this case, it’s 1.
– Denominator (bottom number): How many total pieces the pizza was cut into. In this case, it’s 4.
So, in the fraction 1/4:
– The numerator (1) tells you how many parts you have.
– The denominator (4) tells you how many total parts make up the whole pizza.
It’s like saying: “Out of 4 pieces of pizza, I ate 1.”
Halves, third and quarter
1. Halves (1/2)
– When something is divided into two equal parts, each part is called a half.
– The fraction for one half is written as 1/2.
Example:
Imagine you have an apple, and you cut it into 2 equal parts. Each part is half of the apple. If you eat 1 part, you ate 1/2 of the apple.
2. Thirds (1/3)
– When something is divided into three equal parts, each part is called a third.
– The fraction for one third is written as 1/3.
Example:
Imagine you have a chocolate bar, and you divide it into 3 equal pieces. Each piece is a third. If you eat 1 piece, you ate 1/3 of the chocolate bar.
3. Quarters (1/4)
– When something is divided into four equal parts, each part is called a quarter (or sometimes a fourth).
– The fraction for one quarter is written as 1/4.
Example:
If you cut a sandwich into 4 equal parts, each part is a quarter of the sandwich. If you eat 1 part, you ate 1/4 of the sandwich.
Fraction on number line
Adding Fractions to the Number Line
1. Dividing the Space Between Whole Numbers:
– To represent fractions, we divide the space between two whole numbers into equal parts.
– For example, to show 1/2, divide the space between 0 and 1 into 2 equal parts.
2. Locating Simple Fractions:
– 1/2: Find the midpoint between 0 and 1. This point is 1/2.
– 1/4: Divide the space between 0 and 1 into 4 equal parts. The first point is 1/4, the second point is 2/4 (or 1/2), the third is 3/4, and the fourth point is 1 (which is 4/4).
3. Example:
– Draw a number line from 0 to 2.
– Divide the space between 0 and 1 into 4 equal parts to show quarters.
– Mark the points: 0, 1/4, 2/4 (1/2), 3/4, and 1.
– Do the same between 1 and 2 to show fractions like 5/4, 6/4 (3/2), 7/4, and 2.
Fraction of collection of objects
Understanding Fraction of a Collection
– When we talk about a fraction of a collection, we’re focusing on part of a group of objects, not just a single object.
How to Explain:
1. Start with a Simple Collection:
– Begin with a collection of objects, like 8 apples.
– Ask the student to count the total number of objects. In this case, there are 8 apples.
2. Introducing Fractions:
– If you want to show 1/2 of the collection, explain that this means you are dividing the collection into 2 equal groups.
– Split the 8 apples into 2 equal groups. Each group will have 4 apples.
– So, 1/2 of 8 apples is 4 apples.
3. Using Other Fractions:
– 1/4 of a Collection: If you have 12 objects and you want to find 1/4 of the collection, divide the collection into 4 equal parts.
– 12 objects divided into 4 groups gives 3 objects in each group. So, 1/4 of 12 objects is 3 objects.
4. Practice with Examples:
– Take 10 pencils. Ask, “What is 1/2 of these pencils?” (Answer: 5 pencils)
– Take 12 candies. Ask, “What is 1/3 of these candies?” (Answer: 4 candies, since 12 divided by 3 equals 4)
– Take 16 blocks. Ask, “What is 1/4 of these blocks?” (Answer: 4 blocks)
Comparision of fraction
How to Compare Fractions:
When comparing fractions, we want to know which fraction is larger or smaller. There are two main ways to compare fractions:
1. Same Denominator:
– Denominator: The bottom number of the fraction, which shows how many equal parts the whole is divided into.
– Numerator: The top number, which shows how many parts we have.
– Example: Compare 3/8 and 5/8.
– Since the denominators (8) are the same, we just compare the numerators.
– 5 is greater than 3, so 5/8 is greater than 3/8.
2. Different Denominators:
– When the denominators are different, it’s a bit trickier. We can use two methods:
a) Convert to Common Denominator:
– Find a common denominator (a number that both denominators can divide into).
– Example: Compare 1/2 and 1/3.
– The common denominator for 2 and 3 is 6.
– Convert: 1/2 = 3/6, 1/3 = 2/6.
– Now, compare: 3/6 is greater than 2/6, so 1/2 is greater than 1/3.
Important Tips:
– Remember: A bigger numerator usually means a bigger fraction if the denominators are the same.
– If the denominators are different, make them the same by finding a common denominator or by comparing using visuals.