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5th Grade Fractions Quiz: Adding & Subtracting Unlike Denominators

SORU 1

Add the following fractions: \(\frac{1}{3} + \frac{1}{6}\).


A) \(\frac{1}{2}\)
B) \(\frac{2}{6}\)
C) \(\frac{2}{9}\)
D) \(\frac{1}{3}\)
Açıklama:

To add \(\frac{1}{3}\) and \(\frac{1}{6}\), we first need to find a common denominator. The least common multiple (LCM) of \(3\) and \(6\) is \(6\).

Convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of \(6\):
\(\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)

Now, add the fractions with the common denominator:
\(\frac{2}{6} + \frac{1}{6} = \frac{2+1}{6} = \frac{3}{6}\)

Simplify the result by dividing both the numerator and the denominator by their greatest common divisor, which is \(3\):
\(\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}\)

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🚀 Adding and Subtracting Fractions with Unlike Denominators!

Hey amazing mathematicians! Today, we're going on an exciting adventure with fractions! We'll learn how to add and subtract fractions that have different (or "unlike") bottoms, also known as denominators. It's like trying to add apples and oranges – you need to make them the same kind first!

📌 What are Unlike Denominators?

Imagine you have a pizza cut into \(4\) slices, and your friend has a pizza cut into \(8\) slices. If you have \(\frac{1}{4}\) of your pizza and your friend has \(\frac{1}{8}\) of their pizza, these fractions have unlike denominators (\(4\) and \(8\)). To add or subtract them, we need to make sure they're talking about the same size pieces!

💡 The Super Important First Step: Finding a Common Denominator

Before we can add or subtract fractions with unlike denominators, we MUST find a common denominator. This means finding a number that both original denominators can divide into evenly. The best one to find is the Least Common Multiple (LCM)!

✅ How to Find a Common Denominator and Create Equivalent Fractions

Let's say we want to add \(\frac{1}{2}\) and \(\frac{1}{3}\).

  1. List Multiples:
    • Multiples of \(2\): \(2, 4, 6, 8, 10, ...\)
    • Multiples of \(3\): \(3, 6, 9, 12, ...\)
    The smallest number they share is \(6\). So, our common denominator is \(6\).
  2. Create Equivalent Fractions: Now, we change each fraction so they both have \(6\) as their denominator.
    • For \(\frac{1}{2}\): What do we multiply \(2\) by to get \(6\)? We multiply by \(3\). So, we multiply both the top and bottom by \(3\): \(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\).
    • For \(\frac{1}{3}\): What do we multiply \(3\) by to get \(6\)? We multiply by \(2\). So, we multiply both the top and bottom by \(2\): \(\frac{1 \times 2}{3 \times 2} = \frac{2}{6}\).
Teacher's Tip: Remember, whatever you do to the bottom (denominator), you MUST do to the top (numerator) to keep the fraction equivalent! It's like multiplying by \(\frac{3}{3}\) or \(\frac{2}{2}\), which is just multiplying by \(1\)!

➕ Adding Fractions with Unlike Denominators

Follow these steps:

  1. Find the LCM of the denominators. This will be your common denominator.
  2. Create Equivalent Fractions for each fraction using the common denominator.
  3. Add the Numerators (the top numbers). Keep the common denominator the same.
  4. Simplify your answer if possible (reduce the fraction to its lowest terms).

➖ Subtracting Fractions with Unlike Denominators

The steps are almost the same as adding!

  1. Find the LCM of the denominators. This will be your common denominator.
  2. Create Equivalent Fractions for each fraction using the common denominator.
  3. Subtract the Numerators (the top numbers). Keep the common denominator the same.
  4. Simplify your answer if possible.

✍️ Worked Examples

Example 1: Adding Fractions

Let's add \(\frac{1}{3} + \frac{1}{4}\).

  1. Find the LCM of \(3\) and \(4\):
    • Multiples of \(3\): \(3, 6, 9, 12, 15, ...\)
    • Multiples of \(4\): \(4, 8, 12, 16, ...\)
    The LCM is \(12\).
  2. Create Equivalent Fractions:
    • For \(\frac{1}{3}\): Multiply top and bottom by \(4\): \(\frac{1 \times 4}{3 \times 4} = \frac{4}{12}\).
    • For \(\frac{1}{4}\): Multiply top and bottom by \(3\): \(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\).
  3. Add the Numerators:

    \(\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}\).

  4. Simplify: \(\frac{7}{12}\) cannot be simplified further.

So, \(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\).

Example 2: Subtracting Fractions

Let's subtract \(\frac{5}{6} - \frac{1}{2}\).

  1. Find the LCM of \(6\) and \(2\):
    • Multiples of \(6\): \(6, 12, 18, ...\)
    • Multiples of \(2\): \(2, 4, 6, 8, ...\)
    The LCM is \(6\). (Notice that \(6\) is already a multiple of \(2\), so we only need to change one fraction!)
  2. Create Equivalent Fractions:
    • \(\frac{5}{6}\) already has the common denominator.
    • For \(\frac{1}{2}\): Multiply top and bottom by \(3\): \(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\).
  3. Subtract the Numerators:

    \(\frac{5}{6} - \frac{3}{6} = \frac{5 - 3}{6} = \frac{2}{6}\).

  4. Simplify: \(\frac{2}{6}\) can be simplified by dividing both top and bottom by \(2\): \(\frac{2 \div 2}{6 \div 2} = \frac{1}{3}\).

So, \(\frac{5}{6} - \frac{1}{2} = \frac{1}{3}\).

You've got this! Keep practicing, and you'll be a fraction master in no time! 🎉