1. Fraction: A fraction represents a part of a whole. The whole can be a group of objects or a single object.
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2. Proper Fraction: A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number). It represents a part of a whole.
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3. Improper Fraction: An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
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4. Mixed Fraction: A mixed fraction combines a whole number with a proper fraction.
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5. Equivalent Fractions: Fractions that represent the same value or part of a whole, even though they have different numerators and denominators. Equivalent fractions can be obtained by multiplying or dividing both the numerator and denominator by the same nonzero integer.
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6. Simplest Form: A fraction is in its simplest or lowest form if the numerator and denominator have no common factor other than 1. This can be found by dividing both the numerator and denominator by their highest common factor (HCF).
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7. Like Fractions: Fractions that have the same denominator.
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8. Unlike Fractions: Fractions that have different denominators.
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9. Comparing Fractions: To compare fractions, convert them to have a common denominator or convert them to decimal form.
For like fractions, the one with the greater numerator is larger.
For unlike fractions, find the least common multiple (LCM) of the denominators to compare.
10. Addition and Subtraction of Fractions:
For like fractions, add or subtract the numerators and keep the denominator the same.
Examples:
1) +
The two fractions are like fractions, so we add their numerators and keep the denominator the same.
+ = =
2) −
Here, the given fractions are like fractions. So, we subtract their numerators and keep the denominator the same.
− = =
For unlike fractions, first find the LCM of the denominators, convert to like fractions, then add or subtract the numerators.
Examples:
1) +
The given fractions are unlike fractions, so we first find LCM of their denominators.LCM of 8 and 24 = 2 × 2 × 2 × 3 = 24
Now, we convert the fractions into like fractions.
(Changing the denominator of fractions to 24)= and
+ = =
2) −
As the given fractions are unlike fractions, we find the LCM of their denominator.LCM of 15 and 27 = 3 × 3 × 3 × 5 = 135
Next, we convert the fractions into like fractions
(Fractions with the same denominator)= and =
 = =
11. Mixed fractions
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