T.3 Multiply fractions by whole numbers: word problems
Multiply a fraction by a whole number
Multiplying a fraction by a whole number means taking a part of something (a fraction) and repeating that part a certain number of times (the whole number). The answer can be a whole number, a fraction, or a mixed number.
- If you eat 14 of a pizza and you do that for 3 days, how much pizza did you eat in total? → 14 × 3 = 34
- If you jog 23 of a mile each day for 5 days, you jog 23 × 5 = 103 miles, which is the same as 313 miles.
A whole number can be written as a fraction with a denominator of 1. For example, 4 = 41. This makes multiplication easier to understand.
The rule for multiplying fractions by whole numbers
Rule: Multiply the numerator (top number) of the fraction by the whole number. Keep the denominator (bottom number) the same. Then simplify if needed.
- 38 × 5 = 3×58 = 158 = 178
- 25 × 4 = 2×45 = 85 = 135
- 710 × 2 = 1410 = 75 = 125
Always check if your answer can be simplified. For example, 46 simplifies to 23. An answer is in simplest form when the numerator and denominator have no common factors other than 1.
What is a word problem?
A word problem is a math question written as a short story or real-life situation. You have to read carefully to find the numbers and what operation to use. For this topic, you look for a fraction, a whole number, and clue words like “each,” “every,” “total,” or “in all.”
- Maya uses 34 cup of flour for one batch of cookies. She makes 6 batches. How much flour does she use in total?
- Step 1: Find the fraction: 34 cup.
- Step 2: Find the whole number: 6 batches.
- Step 3: Multiply: 34 × 6 = 184 = 424 = 412 cups.
Not every word problem gives the whole number directly. Sometimes you must find it by reading carefully (for example, “one week” = 7 days).
How to turn a word problem into a multiplication equation
Step 1: Identify the fraction (the part for one unit). Step 2: Identify the whole number (how many times that part repeats). Step 3: Write the equation: fraction × whole number = ? Step 4: Multiply the numerator by the whole number. Step 5: Simplify or convert to a mixed number.
- Each student drinks 23 liter of juice at a party. There are 9 students. How many liters of juice do they drink in total?
- Equation: 23 × 9 = 2×93 = 183 = 6 liters.
If the whole number is large, you can multiply first and then divide by the denominator. This is often faster than drawing pictures.
Writing answers as mixed numbers
When the numerator becomes larger than the denominator (an improper fraction), you can rewrite it as a mixed number. A mixed number has a whole number part and a fraction part. This is often easier to understand in word problems (e.g., “312 pizzas” instead of “72 pizzas”).
- 114 = 234 because 11 ÷ 4 = 2 remainder 3.
- 92 = 412 because 9 ÷ 2 = 4 remainder 1.
- 155 = 3 because 15 ÷ 5 = 3 exactly.
In 4th grade, teachers often want answers as mixed numbers in simplest form unless the problem asks for an improper fraction.
Real-world word problems step by step
Let’s practice reading a longer word problem, finding the fraction and whole number, multiplying, and writing the final answer with the correct unit.
- A recipe calls for 35 teaspoon of salt for one loaf of bread. Levi wants to make 8 loaves. How much salt does he need?
- Step 1: Fraction = 35 teaspoon.
- Step 2: Whole number = 8 loaves.
- Step 3: Multiply: 35 × 8 = 245.
- Step 4: Convert: 24 ÷ 5 = 4 remainder 4 → 445 teaspoons.
- Answer: Levi needs 445 teaspoons of salt.
Always include the unit (teaspoons, cups, miles, hours, etc.) in your final answer. Without the unit, the answer is incomplete.
Common mistakes to avoid
Many 4th graders make these mistakes when multiplying fractions by whole numbers. Knowing them ahead of time will help you get the right answer.
- Mistake: Multiplying the denominator by the whole number.
❌ 13 × 4 = 112 (wrong).
✅ Correct: 13 × 4 = 43 = 113. - Mistake: Forgetting to simplify.
❌ 26 × 3 = 66 = 66 (not simplified).
✅ Correct: 66 = 1. - Mistake: Misreading the word problem (using the wrong whole number).
✅ Fix: Read twice. Circle the fraction. Underline the whole number. Write the equation before solving.
Estimate before you multiply. For example, 12 × 7 is about 3.5. If your answer is very different (like 14), you probably multiplied incorrectly.
Practice word problems with guided steps
Try these four word problems. Follow the steps: fraction × whole number = ? → simplify → write as mixed number if needed.
- 1. A turtle moves 34 foot per minute. How far does it move in 8 minutes? → 34 × 8 = 244 = 6 feet.
- 2. One serving of cereal has 23 gram of sugar. If you eat 5 servings, how much sugar do you eat? → 23 × 5 = 103 = 313 grams.
- 3. A flashlight beam covers 56 of a yard. How many yards does it cover after 9 flashes? → 56 × 9 = 456 = 152 = 712 yards.
- 4. Kendra paints 78 of a wall in one hour. How much can she paint in 4 hours? → 78 × 4 = 288 = 72 = 312 walls.
If your answer is an improper fraction, check whether the problem wants it left that way or converted to a mixed number. In 4th grade word problems, mixed numbers are preferred.
Common Core alignment: CCSS.MATH.CONTENT.4.NF.B.4.C – Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NF.B.4.C. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.