Skill: 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 $(2\frac{3}{8})$ miles in the morning and $(1\frac{2}{8})$ miles in the afternoon. How many miles did she walk altogether?

Step 1: Identify the whole and the fractional unit.

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

Step 2: Identify the relationship.

The word “altogether” means we should add:

$$2\frac{3}{8}+1\frac{2}{8}$$

Step 3: Use a bar model.

Think of the distances as:

• Morning: $2$ whole miles and $3$ eighths
• Afternoon: $1$ whole mile and $2$ eighths

Together, there are $3$ whole miles and $5$ 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:

$$2+1=3$$ $$\frac{3}{8}+\frac{2}{8}=\frac{5}{8}$$

So,

$$2\frac{3}{8}+1\frac{2}{8}=3\frac{5}{8}$$

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