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T.2 Add, subtract, multiply, and divide fractions and mixed numbers: word problems

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Understanding Fractions and Mixed Numbers

Fractions show parts of a whole. A mixed number has a whole number and a fraction together.

Examples:
  • 34 means 3 parts out of 4 equal parts.
  • 212 means 2 whole parts and 12 of another part.
Note

The top number is called the numerator and the bottom number is the denominator. They show how many equal parts a whole is divided into and how many parts are being used.

Adding Fractions and Mixed Numbers in Word Problems

To add fractions, make sure the denominators (bottom numbers) are the same. Then add the numerators and keep the denominator the same. When adding mixed numbers, add the whole numbers first, then the fractions.

Example Problem:
  • Emma ran 34 mile on Monday and 14 mile on Tuesday. How far did she run in all?
  • Step 1: Denominators are the same (4), so add the numerators → 3 + 1 = 4.
  • Step 2: The sum is 44 = 1 whole mile.
Note

Always check that fractions have the same denominator before adding. Simplify your final answer if possible.

Subtracting Fractions and Mixed Numbers in Word Problems

To subtract fractions, make sure the denominators are the same. Subtract the numerators and keep the denominator. For mixed numbers, subtract the whole numbers and fractions separately. You may need to regroup if the top fraction is smaller.

Example Problem:
  • Liam baked 234 pizzas. He ate 12 of a pizza. How much pizza is left?
  • Step 1: Change 234 to an improper fraction → 114.
  • Step 2: Subtract 24 from 11494.
  • Step 3: Simplify → 214 pizzas left.
Note

If needed, regroup from the whole number when the top fraction is smaller. Always simplify your result to the lowest terms.

Multiplying Fractions and Mixed Numbers in Word Problems

To multiply fractions, multiply the numerators together and the denominators together. When multiplying mixed numbers, change them to improper fractions first, multiply, and then simplify.

Example Problem:
  • A recipe uses 23 cup of sugar. If you make 3 batches, how much sugar do you need?
  • Step 1: Multiply 23 × 3.
  • Step 2: Write 3 as 31. Multiply → 63.
  • Step 3: Simplify → 2 cups of sugar.
Note

Always simplify your answer and change improper fractions back into mixed numbers when needed.

Dividing Fractions and Mixed Numbers in Word Problems

To divide fractions, multiply by the reciprocal of the second fraction. For mixed numbers, change them to improper fractions first, then multiply by the reciprocal.

Example Problem:
  • A piece of ribbon is 34 yard long. You want to cut it into pieces that are 18 yard each. How many pieces can you make?
  • Step 1: Divide 34 ÷ 18.
  • Step 2: Multiply by the reciprocal of 1834 × 81.
  • Step 3: Multiply → 244 = 6 pieces.
Note

Remember: “Keep, Change, Flip.” Keep the first fraction, change the division to multiplication, and flip the second fraction.

Solving Multi-Step Fraction Word Problems

Some problems use more than one operation. Read carefully to decide what to do first. Use parentheses or step-by-step reasoning to solve correctly.

Example Problem:
  • A baker used 12 bag of flour for bread and 34 bag for cakes. Then she bought 2 more bags. How many bags does she have now?
  • Step 1: Add the fractions → 12 + 34 = 54 = 114.
  • Step 2: Add 2 more bags → 114 + 2 = 314 bags total.
Note

Write out each step clearly. Decide whether to add, subtract, multiply, or divide based on what the problem is asking.