💡 5th Grade Math: Add Unlike Fractions Practice Questions

Here's how to solve \( \frac{1}{3} + \frac{1}{6} \):

• Step 1: Find a common denominator. The smallest common multiple of 3 and 6 is 6.
• Step 2: Convert the fractions to have the common denominator.
• \( \frac{1}{3} \) needs to be converted. Multiply the numerator and denominator by 2: \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \).
• \( \frac{1}{6} \) already has the denominator 6.
• Step 3: Add the fractions with the common denominator.
• \[ \frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6} \]
• Step 4: Simplify the answer (if possible).
• \( \frac{3}{6} \) can be simplified by dividing both numerator and denominator by 3: \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \).

✅ The answer is \( \frac{1}{2} \).

Let's add \( \frac{2}{5} + \frac{1}{10} \):

• Step 1: Find the common denominator. The least common multiple of 5 and 10 is 10.
• Step 2: Convert the fractions.
• \( \frac{2}{5} \) becomes \( \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \).
• \( \frac{1}{10} \) stays the same.
• Step 3: Add the numerators.
• \[ \frac{4}{10} + \frac{1}{10} = \frac{4+1}{10} = \frac{5}{10} \]
• Step 4: Simplify.
• \( \frac{5}{10} \) simplifies to \( \frac{1}{2} \) (divide by 5).

✅ The sum is \( \frac{1}{2} \).

Here's how to add \( \frac{1}{4} + \frac{2}{3} \):

• Step 1: Find the common denominator. The LCM of 4 and 3 is 12.
• Step 2: Convert the fractions.
• \( \frac{1}{4} \) becomes \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \).
• \( \frac{2}{3} \) becomes \( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \).
• Step 3: Add the numerators.
• \[ \frac{3}{12} + \frac{8}{12} = \frac{3+8}{12} = \frac{11}{12} \]
• Step 4: Simplify (if possible).
• \( \frac{11}{12} \) cannot be simplified further.

✅ The result is \( \frac{11}{12} \).

Let's add \( \frac{3}{8} + \frac{1}{6} \):

• Step 1: Find the common denominator. The LCM of 8 and 6 is 24.
• Step 2: Convert the fractions.
• \( \frac{3}{8} \) becomes \( \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \).
• \( \frac{1}{6} \) becomes \( \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \).
• Step 3: Add the numerators.
• \[ \frac{9}{24} + \frac{4}{24} = \frac{9+4}{24} = \frac{13}{24} \]
• Step 4: Simplify (if possible).
• \( \frac{13}{24} \) cannot be simplified.

✅ The sum is \( \frac{13}{24} \).

Sarah is not correct.

• Explanation: Adding numerators and denominators directly, like \( \frac{1+1}{2+4} = \frac{2}{6} \), does not follow the rules of fraction addition. This method does not account for the fact that the fractions represent different-sized pieces. To add fractions, they must have a common denominator, meaning they are broken into the same number of equal parts.
• Correct Solution:
• Step 1: Find a common denominator for \( \frac{1}{2} \) and \( \frac{1}{4} \). The LCM of 2 and 4 is 4.
• Step 2: Convert \( \frac{1}{2} \) to an equivalent fraction with a denominator of 4. \( \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \).
• Step 3: Add the fractions with the common denominator. \( \frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4} \).

✅ Sarah's answer \( \frac{2}{6} \) (which simplifies to \( \frac{1}{3} \)) is incorrect. The correct answer is \( \frac{3}{4} \).

Let's find the value of each sum:

• Sum 1: \( \frac{1}{3} + \frac{1}{2} \)
• Common denominator of 3 and 2 is 6.
• Convert: \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \) and \( \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \).
• Add: \( \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \).
• Sum 2: \( \frac{1}{4} + \frac{1}{2} \)
• Common denominator of 4 and 2 is 4.
• Convert: \( \frac{1}{4} \) stays the same and \( \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \).
• Add: \( \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \).
• Compare the sums: We need to compare \( \frac{5}{6} \) and \( \frac{3}{4} \).
• Find a common denominator for 6 and 4, which is 12.
• Convert: \( \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \) and \( \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \).
• Comparing \( \frac{10}{12} \) and \( \frac{9}{12} \), we see that \( \frac{10}{12} \) is greater.

✅ Therefore, \( \frac{1}{3} + \frac{1}{2} \) is greater than \( \frac{1}{4} + \frac{1}{2} \).

To find the total amount of flour and sugar, we need to add the fractions:

\[ \frac{1}{2} \text{ cup} + \frac{1}{3} \text{ cup} \]

• Step 1: Find a common denominator for 2 and 3. The LCM is 6.
• Step 2: Convert the fractions.
• \( \frac{1}{2} \) becomes \( \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \).
• \( \frac{1}{3} \) becomes \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \).
• Step 3: Add the converted fractions.
• \[ \frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6} \]

✅ Maria needs a total of \( \frac{5}{6} \) cup of flour and sugar.

To find out how much pizza they ate together, we add the fractions:

\[ \frac{1}{4} + \frac{1}{3} \]

• Step 1: Find the common denominator for 4 and 3. The LCM is 12.
• Step 2: Convert the fractions to have a denominator of 12.
• \( \frac{1}{4} \) becomes \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \).
• \( \frac{1}{3} \) becomes \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \).
• Step 3: Add the numerators.
• \[ \frac{3}{12} + \frac{4}{12} = \frac{3+4}{12} = \frac{7}{12} \]

✅ David and Emily ate \( \frac{7}{12} \) of the pizza altogether.