When denominators are the same, add the numerators.
2/7 + 3/7 = (2 + 3)/7 = 5/7
5/7 is already in simplest form.
When denominators are the same, subtract the numerators.
5/8 - 2/8 = (5 - 2)/8 = 3/8
3/8 is already in simplest form.
We need to find an equivalent fraction for 2/5 with denominator 10.
Since 5 × 2 = 10, multiply both numerator and denominator by 2.
(2 × 2)/(5 × 2) = 4/10
So 2/5 = 4/10
Both fractions have the same denominator (4).
When denominators are the same, compare the numerators.
Since 3 is greater than 2, 3/4 is greater than 2/4.
There are 12 flowers total.
5 of them are red.
So 12 - 5 = 7 are not red.
The fraction that are not red is 7/12.
Find a common denominator. The LCD of 3 and 6 is 6.
Convert 1/3 to equivalent fraction with denominator 6: 1/3 = 2/6
Now add: 2/6 + 1/6 = (2 + 1)/6 = 3/6
Simplify: 3/6 = 1/2
The circle is divided into 8 equal parts.
5 parts are shaded: 5/8 is shaded.
3 parts are not shaded: 3/8 is not shaded.
Check: 5/8 + 3/8 = 8/8 = 1 whole
Find a common denominator. The LCD of 4 and 2 is 4.
Convert 1/2 to equivalent fraction with denominator 4: 1/2 = 2/4
Now subtract: 3/4 - 2/4 = (3 - 2)/4 = 1/4
To show they are equivalent, simplify 3/6.
Divide both numerator and denominator by their greatest common factor, which is 3.
3 ÷ 3 = 1, 6 ÷ 3 = 2
So 3/6 = 1/2
Therefore, 3/6 and 1/2 are equivalent.
The pizza has 8 slices total.
Tom ate 2 slices, Sarah ate 3 slices.
Total eaten: 2 + 3 = 5 slices.
Left: 8 - 5 = 3 slices.
Fraction left: 3/8.
Fraction: A number representing a part of a whole, written as numerator/denominator
Numerator: The top number showing how many parts are taken
Denominator: The bottom number showing how many equal parts the whole is divided into
Like Fractions: Fractions with the same denominator
Unlike Fractions: Fractions with different denominators
Equivalent Fractions: Different fractions that represent the same amount
Simplifying Fractions: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common factor
- Adding Like Fractions: Add numerators, keep denominator the same
- Subtracting Like Fractions: Subtract numerators, keep denominator the same
- Adding Unlike Fractions: Find common denominator, convert fractions, then add numerators
- Subtracting Unlike Fractions: Find common denominator, convert fractions, then subtract numerators
- Comparing Fractions: Find common denominator or compare numerators when denominators are the same
- Simplifying Fractions: Divide both numerator and denominator by their greatest common factor
• When denominators are the same: a/b + c/b = (a + c)/b
• When denominators are the same: a/b - c/b = (a - c)/b
• For different denominators, find a common denominator first
• Equivalent fractions: a/b = (a×n)/(b×n) for any non-zero n
• Simplifying: divide both numerator and denominator by their GCF
• The whole is always represented as b/b when the whole is divided into b equal parts
- Adding like: 1/5 + 2/5 = 3/5
- Subtracting like: 7/9 - 4/9 = 3/9 = 1/3
- Adding unlike: 1/2 + 1/3 = 3/6 + 2/6 = 5/6
- Equivalent: 2/4 = 4/8 = 1/2
- Comparison: 3/7 vs 2/7 → 3/7 > 2/7
- Adding or subtracting denominators along with numerators
- Forgetting to find a common denominator when adding/subtracting unlike fractions
- Not simplifying the final answer to lowest terms
- Making errors when converting fractions to equivalent forms
- Confusing the process for like vs unlike fractions
- Not checking if the answer makes sense in the context of the problem
Key Takeaways
- When denominators are the same, add or subtract numerators only
- When denominators are different, find a common denominator first
- Equivalent fractions represent the same value with different numerators and denominators
- Always simplify fractions to lowest terms when possible
- Visual models help understand fraction operations
- Check your work by verifying the answer makes sense
- Word problems require identifying the operation needed