Fractions of a whole: modeling word problems

key notes :

🔹 What is a Fraction?

  • A fraction shows part of a whole.
  • Example: 🍎 1/4 of a cake = 1 part out of 4 equal parts.

🔹 Numerator & Denominator

  • Numerator (top number) = how many parts we have.
  • Denominator (bottom number) = total equal parts in the whole.
  • Example: 3/5 → numerator = 3, denominator = 5 🖐️

🔹 Identifying the Whole

  • First, find the whole in the problem.
  • Example: “Out of 12 chocolates, 1/3 are dark chocolate.” → Whole = 12 🍫

🔹 Finding the Fraction of a Whole

  • Multiply the whole by the fraction:

Fraction of a whole = Whole × Numerator/Denominator

  • Example: 1/3 of 12 → 12 × 1/3 = 4 🍫

🔹 Using Visual Models

  • Draw bars, circles, or grids to see the parts.
  • Example: Divide a pizza 🍕 into 8 equal slices. 3/8 = 3 slices.

🔹 Word Problems Steps 📝

  1. Read carefully 👀
  2. Identify the whole 🏠
  3. Identify the fraction 🔢
  4. Multiply to find the part ✖️
  5. Draw a model (optional but helpful) 🖍️
  6. Write the answer with units ✅

🔹 Mixed Numbers & Improper Fractions

  • Some problems have more than one whole.
  • Example: 1 1/2 pizzas → 1 whole + 1/2 of another pizza 🍕🍕

🔹 Practice Tip 💡

  • Use real-life examples: cakes 🎂, chocolates 🍫, pencils ✏️, water bottles 🥤.
  • Draw models and color the parts for better understanding 🎨

🔹 Quick Tip ⚡

Always check your answer: Does the fraction make sense for the whole? 🤔

Learn with an example

Elizabeth is selling jars of homemade jam at the Good Earth Farmers Market. Before any shoppers arrive, she uses masking tape to divide her table into 2 equal sections. She fills 1 section of the table with jars of blueberry jam.

Which model represents the fraction of the table that Elizabeth fills with jars of blueberry jam?

The table is the whole.

Elizabeth divides the table into 2 equal sections. The model should have 2 equal parts.

She fills 1 section of the table with jars of blueberry jam.

So, shade 1 part of the model.

This model shows 1/2. It represents the fraction of the table that Elizabeth fills with jars of blueberry jam.

Eliza keeps frogs and turtles as pets. Eliza’s pets live in a long tank. The tank is divided into 3 equal parts. Turtles live in 1 part.

Which model represents the fraction of the tank that turtles live in?

The tank is the whole.

The tank is divided into 3 equal parts. The model should have 3 equal parts.

turtles live in 1 part .

so, shade 1 part of the model .

This model shows 1/3 . It represents the fraction of the tank that turtles live in.

Elsie is using a long wooden board to fix a broken fence. She saws the board into 4 equal pieces. Elsie uses 1 piece to fix the front of the fence.

Which model represents the fraction of the board that Elsie uses to fix the front of the fence?


The board is the whole.

Elsie saws the board into 4 equal pieces. The model should have 4 equal parts.

elsie uses 1 plece to fix the front of the fence .

so, shade 1 part of the model .

This model shows 1/4 . It represents the fraction of the board that Elsie uses to fix the front of the fence.

Let’s practice!