2C Fraction Word Problems Study Guide

📘 Key Vocabulary — Key Words That Tell You the Operation

"of" — means multiply. Example: "1/2 of 24" means 1/2 × 24. ("de" = multiplicar)

"per" / "each" — means divide. Example: "split equally per person" means divide. ("por" / "cada" = dividir)

"total" / "altogether" / "in all" — means add. Example: "how many in all?" means add. ("total" / "en total" = sumar)

"how much more" / "how much less" / "left over" — means subtract. Example: "how much more does she need?" means subtract. ("cuánto más" / "cuánto queda" = restar)

"equally" / "shared" / "split" — means divide. ("igualmente" / "compartir" / "dividir")

🗝️ Visual Reference — Key Words to Operations

Key Word(s)	Operation	Example
of	Multiply (×)	"3/4 of 20 cups" → 3/4 × 20
per, each, equally, split, shared	Divide (÷)	"12 cookies split among 1/3 bags" → 12 ÷ 1/3
total, altogether, in all, combined	Add (+)	"ate 1/4 and 2/4, how much total?" → 1/4 + 2/4
how much more, left, remaining, difference	Subtract (−)	"had 3/4, used 1/2, how much left?" → 3/4 − 1/2

🔢 Step-by-Step — Solving Fraction Word Problems

1 Read the problem carefully. Underline the numbers and circle the key words.
2 Identify the operation using the key words table above.
3 Set up the equation with the fractions and operation.
4 Solve using the correct method (common denominator for +/−, straight across for ×, KCF for ÷).
5 Check: Does your answer make sense? Is it reasonable?

Example: Maria has 3/4 of a pizza. She eats 1/3 of it. How much pizza did she eat?

Key word: "of" → multiply
Equation: 1/3 × 3/4 = 3/12 = 1/4
Maria ate 1/4 of the whole pizza. ✓ That makes sense because she ate part of a part.

💡 Language Tip — Reading Word Problems

Read the problem 3 times: 1st for the story, 2nd for the numbers, 3rd for the question.
Draw a picture if it helps you see the problem.
Rewrite the problem in your own words using simpler English.
Look for the question mark (?) — that tells you what to solve for.

⚠️ Watch Out!

"Of" ALWAYS means multiply with fractions. This is the most important key word to remember!
Don't confuse "how many groups" (divide) with "how much total" (multiply). Read carefully!
Check if your answer is reasonable. If you multiply a fraction by a fraction, the answer should be SMALLER than both numbers.
Units matter: Make sure your answer has the right label (cups, miles, pounds, etc.).

✏️ Practice Problems

Write fractions as a/b. Write mixed numbers as: whole a/b (example: 1 1/2). Include only the number, not the unit.

1. A recipe calls for 3/4 cup of sugar. You want to make 1/2 of the recipe. How many cups of sugar do you need?

Hint: "of" means multiply. Find 1/2 × 3/4.

2. You have 6 pounds of trail mix. Each bag holds 2/3 of a pound. How many bags can you fill?

Hint: "each bag holds" means divide. Find 6 ÷ 2/3.

3. Sam ran 2/5 of a mile on Monday and 1/3 of a mile on Tuesday. How far did he run in all?

Hint: "in all" means add. Find 2/5 + 1/3.

4. A board is 5/6 of a meter long. You cut off 1/4 of a meter. How much board is left?