💡 5th Grade Math: Adding and Subtracting Fractions with Unlike Denominators Practice Questions

To add fractions with unlike denominators, we need to find a common denominator.

• 👉 Step 1: Find the Least Common Multiple (LCM) of the denominators.
  The denominators are 3 and 6. The LCM of 3 and 6 is 6.
• 👉 Step 2: Convert the fractions to equivalent fractions with the common denominator.
  \( \frac{1}{3} \) needs to be changed to have a denominator of 6. Multiply the numerator and denominator by 2:
  \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \)
  The fraction \( \frac{1}{6} \) already has the common denominator, so it stays the same.
• 👉 Step 3: Add the new fractions.
  Now that both fractions have the same denominator, we can add their numerators:
  \( \frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6} \)
• 👉 Step 4: Simplify the answer if possible.
  Both 3 and 6 are divisible by 3:
  \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \)

✅ So, \( \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \).

To subtract fractions with unlike denominators, we need a common denominator.

• 👉 Step 1: Find the LCM of the denominators.
  The denominators are 4 and 2. The LCM of 4 and 2 is 4.
• 👉 Step 2: Convert the fractions to equivalent fractions with the common denominator.
  \( \frac{3}{4} \) already has the common denominator.
  \( \frac{1}{2} \) needs to be changed to have a denominator of 4. Multiply the numerator and denominator by 2:
  \( \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \)
• 👉 Step 3: Subtract the new fractions.
  Now subtract the numerators:
  \( \frac{3}{4} - \frac{2}{4} = \frac{3-2}{4} = \frac{1}{4} \)
• 👉 Step 4: Simplify the answer if possible.
  The fraction \( \frac{1}{4} \) is already in its simplest form.

✅ So, \( \frac{3}{4} - \frac{1}{2} = \frac{1}{4} \).

Let's add these fractions with unlike denominators!

• 👉 Step 1: Find the LCM of the denominators.
  The denominators are 5 and 4. The LCM of 5 and 4 is 20.
• 👉 Step 2: Convert the fractions to equivalent fractions with the common denominator.
  For \( \frac{2}{5} \): Multiply numerator and denominator by 4 to get 20 in the denominator:
  \( \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \)
  For \( \frac{1}{4} \): Multiply numerator and denominator by 5 to get 20 in the denominator:
  \( \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \)
• 👉 Step 3: Add the new fractions.
  Add the numerators:
  \( \frac{8}{20} + \frac{5}{20} = \frac{8+5}{20} = \frac{13}{20} \)
• 👉 Step 4: Simplify the answer if possible.
  The fraction \( \frac{13}{20} \) cannot be simplified because 13 is a prime number and not a factor of 20.

✅ So, \( \frac{2}{5} + \frac{1}{4} = \frac{13}{20} \).

Let's subtract these fractions with different denominators!

• 👉 Step 1: Find the LCM of the denominators.
  The denominators are 6 and 9. Multiples of 6 are 6, 12, 18, 24... Multiples of 9 are 9, 18, 27... The LCM of 6 and 9 is 18.
• 👉 Step 2: Convert the fractions to equivalent fractions with the common denominator.
  For \( \frac{5}{6} \): Multiply numerator and denominator by 3:
  \( \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
  For \( \frac{2}{9} \): Multiply numerator and denominator by 2:
  \( \frac{2 \times 2}{9 \times 2} = \frac{4}{18} \)
• 👉 Step 3: Subtract the new fractions.
  Subtract the numerators:
  \( \frac{15}{18} - \frac{4}{18} = \frac{15-4}{18} = \frac{11}{18} \)
• 👉 Step 4: Simplify the answer if possible.
  The fraction \( \frac{11}{18} \) is in its simplest form because 11 is a prime number and not a factor of 18.

✅ So, \( \frac{5}{6} - \frac{2}{9} = \frac{11}{18} \).

This problem requires two steps: first, find the total sugar used, then subtract that from the initial amount.

• 👉 Step 1: Find the total amount of sugar used.
  Add the sugar used for cookies and cake:
  \( \frac{1}{2} + \frac{1}{3} \)
  The LCM of 2 and 3 is 6.
  Convert fractions: \( \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \) and \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \)
  Add: \( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)
  So, the baker used \( \frac{5}{6} \) cup of sugar in total.
• 👉 Step 2: Find the fraction of sugar left.
  The baker started with 1 full cup of sugar. We can write 1 as \( \frac{6}{6} \) (since our common denominator is 6).
  Subtract the total used from the starting amount:
  \( \frac{6}{6} - \frac{5}{6} = \frac{6-5}{6} = \frac{1}{6} \)

✅ The baker has \( \frac{1}{6} \) cup of sugar left.

This problem asks us to find the difference between the amount of grapes Emily has and the amount she uses.

• 👉 Step 1: Identify the operation needed.
  To find out how much is left, we need to subtract the amount used from the amount Emily has.
  \( \frac{7}{8} - \frac{3}{4} \)
• 👉 Step 2: Find the LCM of the denominators.
  The denominators are 8 and 4. The LCM of 8 and 4 is 8.
• 👉 Step 3: Convert the fractions to equivalent fractions with the common denominator.
  \( \frac{7}{8} \) already has the common denominator.
  For \( \frac{3}{4} \): Multiply numerator and denominator by 2:
  \( \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)
• 👉 Step 4: Subtract the new fractions.
  \( \frac{7}{8} - \frac{6}{8} = \frac{7-6}{8} = \frac{1}{8} \)
• 👉 Step 5: Simplify the answer if possible.
  The fraction \( \frac{1}{8} \) is already in its simplest form.

✅ Emily will have \( \frac{1}{8} \) cup of grapes left.

This is an addition problem, as we need to find the total distance.

• 👉 Step 1: Set up the addition problem.
  \( \frac{1}{2} + \frac{2}{5} \)
• 👉 Step 2: Find the LCM of the denominators.
  The denominators are 2 and 5. The LCM of 2 and 5 is 10.
• 👉 Step 3: Convert the fractions to equivalent fractions with the common denominator.
  For \( \frac{1}{2} \): Multiply numerator and denominator by 5:
  \( \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \)
  For \( \frac{2}{5} \): Multiply numerator and denominator by 2:
  \( \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)
• 👉 Step 4: Add the new fractions.
  \( \frac{5}{10} + \frac{4}{10} = \frac{5+4}{10} = \frac{9}{10} \)
• 👉 Step 5: Simplify the answer if possible.
  The fraction \( \frac{9}{10} \) is in its simplest form.

✅ Sarah walked a total of \( \frac{9}{10} \) mile.

This is a subtraction problem because we need to find the difference between what is needed and what is available.

• 👉 Step 1: Set up the subtraction problem.
  \( \frac{5}{6} - \frac{1}{3} \)
• 👉 Step 2: Find the LCM of the denominators.
  The denominators are 6 and 3. The LCM of 6 and 3 is 6.
• 👉 Step 3: Convert the fractions to equivalent fractions with the common denominator.
  \( \frac{5}{6} \) already has the common denominator.
  For \( \frac{1}{3} \): Multiply numerator and denominator by 2:
  \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \)
• 👉 Step 4: Subtract the new fractions.
  \( \frac{5}{6} - \frac{2}{6} = \frac{5-2}{6} = \frac{3}{6} \)
• 👉 Step 5: Simplify the answer if possible.
  Both 3 and 6 are divisible by 3:
  \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \)

✅ Mark needs \( \frac{1}{2} \) cup more milk for the recipe.