Learn on PengiPengi Math (Grade 5)Chapter 5: Add & Subtract Fractions and Mixed Numbers

Lesson 6: Solve Multi-step Fraction Problems

Property To solve multi step word problems involving fractions and mixed numbers, follow these steps: 1. Identify: Read the problem carefully to determine what is being asked and identify the necessary operations (addition, subtraction). 2. Set up: Write mathematical expressions that represent the steps in the problem. 3. Calculate: Solve the expressions, finding common denominators and regrouping as needed. 4. Answer: State your final answer clearly, including units.

Section 1

Solving Multi-Step Fraction Word Problems

Property

To solve multi-step word problems involving fractions and mixed numbers, follow these steps:

  1. Identify: Read the problem carefully to determine what is being asked and identify the necessary operations (addition, subtraction).
  2. Set up: Write mathematical expressions that represent the steps in the problem.
  3. Calculate: Solve the expressions, finding common denominators and regrouping as needed.
  4. Answer: State your final answer clearly, including units.

Examples

Maria started with 4124\frac{1}{2} cups of flour. She used 34\frac{3}{4} cups for baking cookies. Then she added 2132\frac{1}{3} cups of flour to the bowl for another recipe. How much flour is in the bowl now?

  • Step 1: Calculate flour left after using some
412−34=424−34=364−34=3344\frac{1}{2}-\frac{3}{4}=4\frac{2}{4}-\frac{3}{4}=3\frac{6}{4}-\frac{3}{4}=3\frac{3}{4}
  • Step 2: Add the new flour to the remainder
334+213=3912+2412=51312=61123\frac{3}{4}+2\frac{1}{3}=3\frac{9}{12}+2\frac{4}{12}=5\frac{13}{12} = 6\frac{1}{12}

Section 2

Multi-Step Problems with Mixed Numbers and Fractions

Property

To solve multi-step word problems involving both mixed numbers and fractions, you can use one of two main strategies:

  1. Convert to Improper Fractions: Change all mixed numbers into improper fractions, find a common denominator, then perform the required addition and subtraction.
  2. Operate on Parts: Add or subtract the whole numbers and the fractional parts separately. You may need to regroup (borrow from a whole number) when subtracting a larger fraction from a smaller one.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Solving Multi-Step Fraction Word Problems

Property

To solve multi-step word problems involving fractions and mixed numbers, follow these steps:

  1. Identify: Read the problem carefully to determine what is being asked and identify the necessary operations (addition, subtraction).
  2. Set up: Write mathematical expressions that represent the steps in the problem.
  3. Calculate: Solve the expressions, finding common denominators and regrouping as needed.
  4. Answer: State your final answer clearly, including units.

Examples

Maria started with 4124\frac{1}{2} cups of flour. She used 34\frac{3}{4} cups for baking cookies. Then she added 2132\frac{1}{3} cups of flour to the bowl for another recipe. How much flour is in the bowl now?

  • Step 1: Calculate flour left after using some
412−34=424−34=364−34=3344\frac{1}{2}-\frac{3}{4}=4\frac{2}{4}-\frac{3}{4}=3\frac{6}{4}-\frac{3}{4}=3\frac{3}{4}
  • Step 2: Add the new flour to the remainder
334+213=3912+2412=51312=61123\frac{3}{4}+2\frac{1}{3}=3\frac{9}{12}+2\frac{4}{12}=5\frac{13}{12} = 6\frac{1}{12}

Section 2

Multi-Step Problems with Mixed Numbers and Fractions

Property

To solve multi-step word problems involving both mixed numbers and fractions, you can use one of two main strategies:

  1. Convert to Improper Fractions: Change all mixed numbers into improper fractions, find a common denominator, then perform the required addition and subtraction.
  2. Operate on Parts: Add or subtract the whole numbers and the fractional parts separately. You may need to regroup (borrow from a whole number) when subtracting a larger fraction from a smaller one.

Examples