1. To add unlike fractions, you must first find a common denominator.
2. The numerator is the bottom number of a fraction.
3. \(\frac{1}{2} + \frac{1}{3} = \frac{2}{5}\).
4. A common multiple of 3 and 4 is 12.
5. When you add fractions, you add both the numerators and the denominators.
✏️ 2. Fill in the Blanks
1. To add fractions with different denominators, you first need to find a denominator.
2. The of a fraction tells you how many parts of the whole you have.
3. The least common multiple (LCM) of the denominators is often used as the common denominator.
4. After finding a common denominator, you must change the of each fraction.
5. When adding fractions, the denominator of the sum will be the common denominator.
🔗 3. Matching
« Fractions that have different denominators.
« A shared multiple of the denominators of two or more fractions.
« The top number in a fraction, representing the number of parts being considered.
« The bottom number in a fraction, representing the total number of equal parts in the whole.
« The smallest positive integer that is a multiple of two or more integers.
✍️ 4. Short Answer Questions
1. Why is it necessary to find a common denominator before adding unlike fractions?
💡 Suggested Answer: It is necessary because fractions can only be added when they refer to parts of the same size. A common denominator ensures that all parts are equal in size.
2. What is the first step when adding \(\frac{1}{4} + \frac{2}{3}\)?
💡 Suggested Answer: The first step is to find the least common denominator (LCD) for 4 and 3, which is 12.
🎯 5. Multiple Choice
1. Which of the following is the least common denominator for \(\frac{1}{2}\) and \(\frac{3}{5}\)?
2. What is the sum of \(\frac{1}{3} + \frac{1}{6}\)?
3. Sarah ate \(\frac{1}{4}\) of a pizza, and Tom ate \(\frac{3}{8}\) of the same pizza. How much pizza did they eat in total?
📝 6. Open-Ended Questions
1. Add \(\frac{1}{2} + \frac{2}{5}\). Show your work.
💡 Solution Steps:
Step 1: Find the least common denominator (LCD) for 2 and 5. The LCD is 10.\\Step 2: Convert each fraction to an equivalent fraction with the LCD. \\ \(\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}\\) \\ \(\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}\\) \\Step 3: Add the new fractions. \\ \(\frac{5}{10} + \frac{4}{10} = \frac{5+4}{10} = \frac{9}{10}\\) \\The sum is \(\frac{9}{10}\).
2. Calculate \(\frac{3}{4} + \frac{1}{6}\). Simplify your answer if possible.
💡 Solution Steps:
Step 1: Find the least common denominator (LCD) for 4 and 6. Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... The LCD is 12.\\Step 2: Convert each fraction. \\ \(\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\\) \\ \(\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}\\) \\Step 3: Add the fractions. \\ \(\frac{9}{12} + \frac{2}{12} = \frac{9+2}{12} = \frac{11}{12}\\) \\The sum is \(\frac{11}{12}\). It cannot be simplified further.
3. A recipe calls for \(\frac{2}{3}\) cup of flour and \(\frac{1}{2}\) cup of sugar. How much flour and sugar are needed in total?
💡 Solution Steps:
Step 1: Identify the fractions to be added: \(\frac{2}{3}\) and \(\frac{1}{2}\).\\Step 2: Find the least common denominator (LCD) for 3 and 2. The LCD is 6.\\Step 3: Convert each fraction to an equivalent fraction with the LCD. \\ \(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\\) \\ \(\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}\\) \\Step 4: Add the new fractions. \\ \(\frac{4}{6} + \frac{3}{6} = \frac{4+3}{6} = \frac{7}{6}\\) \\Step 5: Convert the improper fraction to a mixed number (optional but good practice for word problems). \\ \(\frac{7}{6} = 1\frac{1}{6}\\) \\In total, \(\frac{7}{6}\) cups or \(1\frac{1}{6}\) cups of flour and sugar are needed.
Name Surname: .................................. Date: .... / .... / 202...
Add Unlike Fractions Worksheet
SCORE
A. True (T) / False (F)
( .... )
To add unlike fractions, you must first find a common denominator.
( .... )
The numerator is the bottom number of a fraction.
( .... )
\(\frac{1}{2} + \frac{1}{3} = \frac{2}{5}\).
( .... )
A common multiple of 3 and 4 is 12.
( .... )
When you add fractions, you add both the numerators and the denominators.
B. Fill in the Blanks
1)
To add fractions with different denominators, you first need to find a .................... denominator.
2)
The .................... of a fraction tells you how many parts of the whole you have.
3)
The least common multiple (LCM) of the denominators is often used as the .................... common denominator.
4)
After finding a common denominator, you must change the .................... of each fraction.
5)
When adding fractions, the denominator of the sum will be the .................... common denominator.
C. Matching Concepts
( .... )
Fractions that have different denominators.
- Denominator
( .... )
A shared multiple of the denominators of two or more fractions.
- Numerator
( .... )
The top number in a fraction, representing the number of parts being considered.
- Common Denominator
( .... )
The bottom number in a fraction, representing the total number of equal parts in the whole.
- Least Common Multiple (LCM)
( .... )
The smallest positive integer that is a multiple of two or more integers.
- Unlike Fractions
D. Short Answer Questions
1)
Why is it necessary to find a common denominator before adding unlike fractions?
2)
What is the first step when adding \(\frac{1}{4} + \frac{2}{3}\)?
E. Multiple Choice Questions
1)
Which of the following is the least common denominator for \(\frac{1}{2}\) and \(\frac{3}{5}\)?
A) 2B) 5C) 7D) 10
2)
What is the sum of \(\frac{1}{3} + \frac{1}{6}\)?
A) \(\frac{2}{9}\)B) \(\frac{2}{6}\)C) \(\frac{1}{2}\)D) \(\frac{3}{6}\)
3)
Sarah ate \(\frac{1}{4}\) of a pizza, and Tom ate \(\frac{3}{8}\) of the same pizza. How much pizza did they eat in total?
A) \(\frac{4}{12}\)B) \(\frac{4}{8}\)C) \(\frac{5}{8}\)D) \(\frac{1}{2}\)
F. Open-Ended Questions
1)
Add \(\frac{1}{2} + \frac{2}{5}\). Show your work.
2)
Calculate \(\frac{3}{4} + \frac{1}{6}\). Simplify your answer if possible.
3)
A recipe calls for \(\frac{2}{3}\) cup of flour and \(\frac{1}{2}\) cup of sugar. How much flour and sugar are needed in total?