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Watch First β€” Adding and Subtracting Fractions - Math Antics

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Fractions – Adding & Subtracting

Why This Matters for Nursing: Medication doses often come in fractions. If a patient needs Β½ tablet in the morning and ΒΌ tablet at night, you need to know the total: ΒΎ tablet per day.

What You Need to Know

A fraction represents a part of a whole. It has two parts: - Numerator (top): How many parts you have - Denominator (bottom): How many equal parts make the whole

Β½ ΒΌ ΒΎ + =

To add or subtract fractions, the denominators MUST be the same. If they're not, you need to find a common denominator first.

The Golden Rule

Same denominators? Just add/subtract the numerators. Keep the denominator the same.


🧠 Memory Trick

"Denominator = Down Below" (both start with D)

Think of the denominator as the "name" of the fractionβ€”you can only combine fractions with the same name!

Just like you can't add 3 apples + 2 oranges and call it "5 apples," you can't add β…“ + ΒΌ directly.


Step-by-Step: Same Denominators

Add: 2/5 + 1/5

2/5 + 1/5 = 3/5
  1. Check denominators: Both are 5 βœ“
  2. Add the numerators: 2 + 1 = 3
  3. Keep the denominator: 5
  4. Answer: 3/5

Subtract: 7/8 - 3/8

  1. Check denominators: Both are 8 βœ“
  2. Subtract the numerators: 7 - 3 = 4
  3. Keep the denominator: 8
  4. Simplify: 4/8 = 1/2

Step-by-Step: Different Denominators

Add: 1/3 + 1/4

  1. Find the Least Common Denominator (LCD):
  2. Multiples of 3: 3, 6, 9, 12, 15...
  3. Multiples of 4: 4, 8, 12, 16...
  4. LCD = 12

  5. Convert each fraction:

  6. 1/3 = ?/12 β†’ 1Γ—4 = 4, so 1/3 = 4/12
  7. 1/4 = ?/12 β†’ 1Γ—3 = 3, so 1/4 = 3/12

  8. Add the new fractions:

  9. 4/12 + 3/12 = 7/12

  10. Answer: 7/12


✏️ Worked Examples

Example 1: Same Denominator

Problem: 3/7 + 2/7

Step 1 β€” Check the denominators. Look at the bottom numbers of both fractions. The first fraction has 7 on the bottom. The second fraction also has 7 on the bottom. They match! That means we can add these directly without any extra work.

Step 2 β€” Add the top numbers (numerators). When the denominators are the same, you only add the tops: 3 + 2 = 5

Step 3 β€” Keep the bottom number the same. Don't touch the denominator. It stays 7.

Step 4 β€” Check if we can simplify. Can we divide both 5 and 7 by the same number? 5 is prime, and 7 is prime, so no β€” we're done.

Answer: 5/7


Example 2: Step-by-Step Solution

To solve this type of problem, start by identifying the key values given in the question. Then apply the formula we covered above...

Step 1: Convert the mixed number to an improper fraction...

Step 2: Find the common denominator between the two fractions...

Keep reading β€” there's more to this guide

The worked examples and practice problems are the part that actually prepares you for the TEAS.

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