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Solve multi-step fraction problems

Multistep fraction problem solving involves interpreting relationships among positive fractions, mixed numbers, and whole numbers, then selecting and sequencing addition, subtraction, multiplication, and division—including division as sharing or determining how many groups—to preserve the meaning and units of each quantity. Equations, bar models, and estimation support reasoning about the solution, including recognizing that unlike denominators cannot be added directly and checking whether an answer is reasonable; the scope excludes negative rational numbers, variable-based generalizations, and more advanced fraction expressions.

Detailed Explanation: Solve multi-step fraction problems

Read the problem carefully and identify what each fraction means. Then solve one step at a time, keeping the units the same.

Example:
A baker has 34\frac{3}{4} kilogram of flour. She adds 1121\frac{1}{2} kilograms more. She uses 23\frac{2}{3} of the total flour. She packs the remaining flour into bags that each hold 16\frac{1}{6} kilogram. How many bags can she fill?

1. Find the total amount of flour.

Add the two amounts:

34+112\frac{3}{4}+1\frac{1}{2}

Rewrite the mixed number and use a common denominator:

112=32=641\frac{1}{2}=\frac{3}{2}=\frac{6}{4}

So,

34+64=94=214\frac{3}{4}+\frac{6}{4}=\frac{9}{4}=2\frac{1}{4}

The baker has 2142\frac{1}{4} kilograms of flour.

2. Find how much flour she uses.

“23\frac{2}{3} of the total” means multiply:

23×94\frac{2}{3}\times\frac{9}{4}

Multiply the numerators and denominators, then simplify:

2×93×4=1812=32=112\frac{2\times9}{3\times4}=\frac{18}{12}=\frac{3}{2}=1\frac{1}{2}

She uses 1121\frac{1}{2} kilograms.

3. Find the amount left.

Subtract the amount used from the total:

94−32\frac{9}{4}-\frac{3}{2}

Rewrite 32\frac{3}{2} with denominator 44:

32=64\frac{3}{2}=\frac{6}{4}

Then subtract:

94−64=34\frac{9}{4}-\frac{6}{4}=\frac{3}{4}

There are 34\frac{3}{4} kilogram left.

4. Find how many bags she can fill.

Each bag holds 16\frac{1}{6} kilogram, so divide to find how many groups of 16\frac{1}{6} are in 34\frac{3}{4}:

34÷16\frac{3}{4}\div\frac{1}{6}

Multiply by the reciprocal of 16\frac{1}{6}:

34×61=184=92=412\frac{3}{4}\times\frac{6}{1}=\frac{18}{4}=\frac{9}{2}=4\frac{1}{2}

She can completely fill 44 bags, with 12\frac{1}{2} kilogram-bag’s worth left over.

Check your answer:
Since 34\frac{3}{4} is close to 11 and each bag holds about 16\frac{1}{6}, there should be about 66 bags. An answer of 4124\frac{1}{2} is reasonable because 34\frac{3}{4} is less than 11 kilogram.

Answer: The baker can fill 44 complete bags, with 112\frac{1}{12} kilogram of flour left over.

Learn by doing: Solve multi-step fraction problems

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    Fraction Addition - Mixed (No Simplifying Answers) - One Changed Denominator

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