📄 5th Grade Math: Adding and Subtracting Fractions with Unlike Denominators Worksheet
📌 1. True / False
1. To add or subtract fractions, they must have a common denominator.
2. The least common multiple (LCM) of 3 and 5 is 8.
3. When you multiply the numerator and denominator of a fraction by the same non-zero number, you get an equivalent fraction.
4. The sum of \( \frac{1}{2} \) and \( \frac{1}{3} \) is \( \frac{2}{5} \).
5. A mixed number consists of a whole number and a fraction.
✏️ 2. Fill in the Blanks
1. Before you can add or subtract fractions with different denominators, you need to find a denominator.
2. The is the smallest number that is a multiple of two or more numbers.
3. To make equivalent fractions, you must multiply both the numerator and the by the same number.
4. When adding \( \frac{1}{4} \) and \( \frac{3}{8} \), the common denominator you would use is .
5. An fraction has a numerator that is greater than or equal to its denominator.
🔗 3. Matching
« A shared denominator for two or more fractions.
« Fractions that represent the same value even though they have different numerators and denominators.
« The smallest positive integer that is a multiple of two or more integers.
« The top number in a fraction that tells how many parts are being considered.
« The bottom number in a fraction that tells the total number of equal parts in the whole.
✍️ 4. Short Answer Questions
1. Why is it important to find a common denominator before adding or subtracting fractions?
💡 Suggested Answer: It is important because fractions represent parts of a whole. To add or subtract them, the 'wholes' (denominators) must be divided into the same number of equal parts so that the parts being combined or taken away are of the same size.
2. What is the least common multiple (LCM) of 6 and 9?
💡 Suggested Answer: The multiples of 6 are 6, 12, 18, 24, ... The multiples of 9 are 9, 18, 27, ... The least common multiple (LCM) of 6 and 9 is 18.
🎯 5. Multiple Choice
1. What is the sum of \( \frac{1}{2} \) and \( \frac{1}{4} \)?
2. Subtract: \( \frac{5}{6} - \frac{1}{3} \)
3. Which fraction is equivalent to \( \frac{2}{3} \) with a denominator of 12?
📝 6. Open-Ended Questions
1. Add the following fractions: \( \frac{3}{5} + \frac{1}{2} \)
💡 Solution Steps:
Step 1: Find the least common multiple (LCM) of the denominators 5 and 2. The LCM of 5 and 2 is 10. Step 2: Convert each fraction to an equivalent fraction with a denominator of 10. \( \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \) \( \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \) Step 3: Add the equivalent fractions. \( \frac{6}{10} + \frac{5}{10} = \frac{6+5}{10} = \frac{11}{10} \) Step 4: (Optional) Convert the improper fraction to a mixed number. \( \frac{11}{10} = 1 \frac{1}{10} \) Answer: \( 1 \frac{1}{10} \) or \( \frac{11}{10} \).
2. Subtract the following fractions: \( \frac{7}{8} - \frac{1}{4} \)
💡 Solution Steps:
Step 1: Find the least common multiple (LCM) of the denominators 8 and 4. The LCM of 8 and 4 is 8. Step 2: Convert each fraction to an equivalent fraction with a denominator of 8. (\( \frac{7}{8} \) already has a denominator of 8.) \( \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \) Step 3: Subtract the equivalent fractions. \( \frac{7}{8} - \frac{2}{8} = \frac{7-2}{8} = \frac{5}{8} \) Answer: \( \frac{5}{8} \).
3. Maria drank \( \frac{1}{3} \) of a liter of water in the morning and \( \frac{1}{2} \) of a liter in the afternoon. How much water did she drink in total?
💡 Solution Steps:
Step 1: Identify the operation needed. To find the total amount of water, we need to add the two fractions: \( \frac{1}{3} + \frac{1}{2} \). Step 2: Find the least common multiple (LCM) of the denominators 3 and 2. The LCM of 3 and 2 is 6. Step 3: Convert each fraction to an equivalent fraction with a denominator of 6. \( \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \) \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \) Step 4: Add the equivalent fractions. \( \frac{2}{6} + \frac{3}{6} = \frac{2+3}{6} = \frac{5}{6} \) Answer: Maria drank a total of \( \frac{5}{6} \) of a liter of water.
Name Surname: .................................. Date: .... / .... / 202...
Adding and Subtracting Fractions with Unlike Denominators Worksheet
SCORE
A. True (T) / False (F)
( .... )
To add or subtract fractions, they must have a common denominator.
( .... )
The least common multiple (LCM) of 3 and 5 is 8.
( .... )
When you multiply the numerator and denominator of a fraction by the same non-zero number, you get an equivalent fraction.
( .... )
The sum of \( \frac{1}{2} \) and \( \frac{1}{3} \) is \( \frac{2}{5} \).
( .... )
A mixed number consists of a whole number and a fraction.
B. Fill in the Blanks
1)
Before you can add or subtract fractions with different denominators, you need to find a .................... denominator.
2)
The .................... is the smallest number that is a multiple of two or more numbers.
3)
To make equivalent fractions, you must multiply both the numerator and the .................... by the same number.
4)
When adding \( \frac{1}{4} \) and \( \frac{3}{8} \), the common denominator you would use is .....................
5)
An .................... fraction has a numerator that is greater than or equal to its denominator.
C. Matching Concepts
( .... )
A shared denominator for two or more fractions.
- Numerator
( .... )
Fractions that represent the same value even though they have different numerators and denominators.
- Common Denominator
( .... )
The smallest positive integer that is a multiple of two or more integers.
- Denominator
( .... )
The top number in a fraction that tells how many parts are being considered.
- Equivalent Fractions
( .... )
The bottom number in a fraction that tells the total number of equal parts in the whole.
- Least Common Multiple (LCM)
D. Short Answer Questions
1)
Why is it important to find a common denominator before adding or subtracting fractions?
2)
What is the least common multiple (LCM) of 6 and 9?
E. Multiple Choice Questions
1)
What is the sum of \( \frac{1}{2} \) and \( \frac{1}{4} \)?
Add the following fractions: \( \frac{3}{5} + \frac{1}{2} \)
2)
Subtract the following fractions: \( \frac{7}{8} - \frac{1}{4} \)
3)
Maria drank \( \frac{1}{3} \) of a liter of water in the morning and \( \frac{1}{2} \) of a liter in the afternoon. How much water did she drink in total?