Solving Word Problems with Fraction Addition and Subtraction

5.NF.A.2

In this lesson:

• Translate word problems into fraction equations
• Use visual models and benchmark estimation
• Check every answer for reasonableness

Learning Objectives for This Lesson

By the end of this lesson, you will:

1. Write an equation from a fraction word problem
2. Use visual fraction models to represent and solve problems
3. Estimate answers using benchmark fractions
4. Assess reasonableness by comparing to an estimate
5. Solve joining, separating, comparing, and part-part-whole problems

You Can Compute — Can You Solve?

You already know how to calculate:

• But what if this calculation is hidden inside a story?
• "Maria ran 2/3 mile in the morning and 3/4 mile in the afternoon."
• Today's challenge: Find the math inside the words

Four Types of Fraction Word Problems

Joining Example: Setting Up the Equation

"Maria ran mile in the morning and mile in the afternoon. How far did she run in total?"

• Step 1: Identify the quantities — and
• Step 2: "In total" signals addition
• Step 3: Write the equation

Separating Example: Setting Up the Subtraction

"A recipe needs cup of flour. Tomás already added cup. How much more does he need?"

• Step 1: Quantities — cup and cup
• Step 2: "How much more...need" signals subtraction
• Step 3: Write the equation

Both Fractions Must Share the Same Whole

• Sara ate of a small pizza and of a large pizza
• Can we add ? No — the wholes differ
• Fraction addition only works when both fractions refer to the same whole

Your Turn: Write the Equation

"Li ran mile. Nora ran mile. How much farther did Li run than Nora?"

• What are the quantities?
• What operation does "how much farther" signal?
• Write the equation — don't solve yet

Think, then advance for the answer...

Answer: The Comparing Problem Equation

"How much farther did Li run than Nora?"

• Type: Comparing — we want the difference
• "How much farther" means subtract the smaller from the larger
• Both distances are in miles — same whole ✓

Why Visual Models Help You Solve

Visual models are thinking tools, not decorations:

• They show the structure of the problem
• They make the operation visible
• They help you verify your computed answer
• Joining → bars end to end
• Comparing → bars side by side

Fraction Bar Model: Adding Two-Thirds and Three-Fourths

Re-partition both bars into twelfths to add:

Number Line Model: Subtracting Three-Fourths Minus One-Third

• Start at on the number line
• Hop backward by
• Landing point =

Comparing Model: Seven-Eighths Versus One-Half

• Top bar: shaded (Li's run)
• Bottom bar: shaded (Nora's run)
• Difference: mile

Your Turn: Draw a Model

"Ava ate of a pizza and then more. How much did she eat?"

• This is a joining problem — draw bars end to end
• Find a common denominator for your bars
• Sketch your model, then advance

Try it before you look...

Answer: Adding One-Fourth and Two-Thirds

• Common denominator: 12
• and
• Total: of a pizza
• Your model should show 3 + 8 = 11 twelfths shaded

Benchmark Fractions: Your Estimation Ruler

These benchmarks help you estimate any fraction answer quickly

Classifying Fractions by Nearest Benchmark

Estimate the Sum Before You Compute

"Estimate "

• is close to
• is exactly
• Estimate: about

Now compute:

is close to 1 ✓ — estimate confirmed

Catching Errors with Benchmark Estimation

A student says:

• Estimate says the answer should be close to 1
• But is less than
• Adding to must give more than
• The answer is impossible

Your Turn: Estimate This Difference

"Estimate "

• What benchmark is near?
• What benchmark is near?
• Write your estimate, then advance

Try it before you look...

Answer: Estimating Seven-Eighths Minus Two-Fifths

• is close to 1
• is close to
• Estimate: about

Exact answer:

is close to ✓ — estimate confirmed

Three Steps to Check Your Answer

After every computation, run this checklist:

1. Compare to estimate — right ballpark?
2. Check direction — addition: answer > each addend; subtraction: answer < start
3. Check context — does the answer make sense in the story?

Full Workflow: From Words to Verified Answer

"Maria ran mile in the morning and mile in the afternoon. How far did she run in total?"

• Equation: (joining → add)
• Model: Fraction bars partitioned into twelfths
• Estimate: , so about

Full Workflow Continued: Compute and Check

Compute:

Reasonableness check:

1. Estimate was about — answer is close ✓
2. and ✓
3. Running about miles total makes sense ✓

Spot the Error: Is This Answer Reasonable?

"A baker used cup sugar and cup butter. A student says the total is cups."

• Estimate: and , so total
• But — way too small!
• What went wrong?

Think about the error, then advance...

Answer: The Common Fraction Mistake

The student added tops and bottoms: ✗

Correct computation:

• is close to our estimate of ✓
• Never add numerators and denominators separately

Practice: Solve These Two Word Problems

Problem 1: "Jake had gallon of paint. He used gallon. How much is left?"

Problem 2: "A trail is miles. Sam hiked mile. How far to go?"

For each: equation, estimate, compute, check.

Work both, then advance for answers...

Answers: Both Practice Problems Solved

Problem 1: gallon

• Estimate: about ; answer — close ✓

Problem 2: mile

• Estimate: about ; answer — close ✓

Key Takeaways From This Lesson

✓ Write the equation first — before computing
✓ Draw a model — bars or number lines
✓ Estimate with benchmarks before calculating
✓ Check every answer: estimate, direction, context

Never add tops and bottoms separately
Both fractions must share the same whole

What Comes Next in Fractions

• Practice the full workflow: equation → model → estimate → compute → check
• Next lesson: Multiplying fractions and whole numbers (5.NF.B.3)
• Remember: estimation is a habit, not an extra step