The Science of Fractions.

This lesson will help you understand the difference between mixed numbers and improper fractions, how to convert between them, and how to add or subtract mixed numbers using two different methods.

🎯 Learning Objectives

• Understand what improper fractions and mixed numbers are

• Convert between improper fractions and mixed number

• Add and subtract mixed numbers using two clear methods
  

➗ What is a Mixed Number? A mixed number is a number made of a whole number and a proper fraction.

Example:
2 3/5 means 2 wholes and 3 out of 5 parts more.

➕ What is an Improper Fraction? An improper fraction has a numerator that is greater than or equal to the denominator. It represents more than one whole.

Example:
11/4 means you have more than 1 whole (because 11 is bigger than 4).

To help you visualize use the interactive diagram below:

🔄How to Convert a Mixed Number to Improper Fraction
Steps:

1. Multiply the whole number by the denominator.

2. Add the numerator to the result.

3. Write that total as the new numerator.

4. Keep the same denominator.

Example 1:
Convert 3 2/5:

• Step 1: Multiply the whole number: 3 × 5 = 15

• Step 2: Add the numerator: 15 + 2 = 17

• Step 3: Write it over the same denominator: 17/5
  ✅ Final Answer: 17/5

🔁 How to Convert Improper Fraction to Mixed Number
Steps:

1. Divide the numerator by the denominator.

2. The quotient becomes the whole number.

3. The remainder becomes the new numerator.

4. Keep the same denominator.

Example 1:
Convert 23/4:

• Step 1: 23 ÷ 4 = 5 with a remainder of 3

• Step 2: Whole number = 5

• Step 3: Remainder becomes numerator: 3

Step 4: Denominator stays 4
✅ Final Answer: 5 3/4

Adding and Subtracting Fractions:

62 + 30 = 92

92 − 51 = 41

🔬 Science Application: Measuring Liquid Volume in an Experiment

In a science lab, a student pours 2 1/4 liters of water into a beaker. Then they add another 1 2/3 liters of water. Later, 3/4 liter of water evaporates.

Question: How much water is left in the beaker?

✅ Step 1: Add the water poured in

We need to add:

2 1/4 + 1 2/3

Convert to improper fractions:

2 1/4 = (2 × 4 + 1) / 4 = 9/4  
1 2/3 = (1 × 3 + 2) / 3 = 5/3

Find a common denominator (LCM of 4 and 3 = 12):

9/4 = 27/12  
5/3 = 20/12

Add:

27/12 + 20/12 = 47/12

Convert to a mixed number:

47 ÷ 12 = 3 remainder 11 → 3 11/12

✅ Total before evaporation: 3 11/12 liters

---

✅ Step 2: Subtract evaporated water

We now subtract:

3 11/12 − 3/4

Convert to improper fractions:

3 11/12 = (3 × 12 + 11) / 12 = 47/12  
3/4 = 9/12

Subtract:

47/12 − 9/12 = 38/12

Simplify:

38 ÷ 2 = 19, 12 ÷ 2 = 6 → 19/6 = 3 1/6

✅ Final Answer: 3 1/6 liters of water remain

🧮 Convert the Final Answer to a Decimal

Our final answer was: 3 1/6

Step 1: Keep the whole number → 3

Step 2: Convert the fraction to decimal → 1 ÷ 6 = 0.1666…

🔢 Long Division: 1 ÷ 6

    0.1 6 6...
    ---------
6 | 1.0
   -  0
    ------
     10   ← 6 goes into 10 once (6 × 1 = 6)
    - 6
    ------
      40  ← bring down 0, 6 goes into 40 six times (6 × 6 = 36)
    - 36
    ------
       40 ← repeat

So, 1 ÷ 6 = 0.1666… (a repeating decimal).

When you round to two decimal places, the final answer is: 0.17

Step 3: Add the decimal to the whole number:

3 + 0.1666… = 3.1666…

✅ Final Answer (rounded to 2 decimal places): 3.17

Tip: Some students may prefer decimals when working with calculators or scientific measurements.