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Solve fraction word problems

Fraction word problems are interpreted by identifying the whole, the fractional unit, and the relationship between quantities, then representing that relationship with a visual model such as a number line or bar model and an equation. The understanding includes adding and subtracting fractions and mixed numbers with like denominators and finding a whole-number multiple of a fraction, while recognizing that denominators name equal-sized parts and are not combined; unlike-denominator operations, fraction-by-fraction multiplication, and fraction division are beyond this scope.

Detailed Explanation: Solve fraction word problems

A fraction word problem tells you how quantities are related. To solve one:

  1. Identify the whole.
  2. Identify the fractional unit.
  3. Decide whether to add or subtract.
  4. Draw a bar model or number line.
  5. Write and solve an equation.

Example:
Mia walked (238)(2\frac{3}{8}) miles in the morning and (128)(1\frac{2}{8}) miles in the afternoon. How many miles did she walk altogether?

Step 1: Identify the whole and the fractional unit.

The whole is 11 mile. Each mile is divided into 88 equal parts, so the fractional unit is 18\frac{1}{8} mile.

Step 2: Identify the relationship.

The word “altogether” means we should add:

238+1282\frac{3}{8}+1\frac{2}{8}

Step 3: Use a bar model.

Think of the distances as:

  • Morning: 22 whole miles and 33 eighths
  • Afternoon: 11 whole mile and 22 eighths

Together, there are 33 whole miles and 55 eighths:

2 wholes +3 eighths+1 whole +2 eighths=3 wholes +5 eighths\boxed{2\text{ wholes }+3\text{ eighths}} + \boxed{1\text{ whole }+2\text{ eighths}} = \boxed{3\text{ wholes }+5\text{ eighths}}

Step 4: Solve.

Add the whole numbers and then add the fractions:

2+1=32+1=3 38+28=58\frac{3}{8}+\frac{2}{8}=\frac{5}{8}

So,

238+128=3582\frac{3}{8}+1\frac{2}{8}=3\frac{5}{8}

Mia walked (358)(3\frac{5}{8}) miles altogether. The denominators stay 88 because they name the same-sized parts; we do not add the denominators.

Learn by doing: Solve fraction word problems

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    Fraction Addition - To Next Whole (Simple) - No Changed Denominator

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