Fraction Word Problems — Add Then Divide

📝 Practice Worksheets

Fraction Word Problems Dividing Fraction — Word Problems Dividing Fractions — Word Problems 2 Dividing Fractions Using Visual Models

🛠️ Related Tools

Fraction Operations Practice

🔑 Key Concepts

Sometimes you must combine amounts before dividing.
Key words like total or together often mean add first.
Key words like each or per often mean divide.
Convert mixed numbers or fractions when needed before dividing.
Always read the question carefully to determine the order of operations.

✏️ Worked Examples – Add, Then Divide

Example 1 – Juice Mixture

Lena mixes \(\frac{2}{3}\) cup of juice and \(\frac{1}{6}\) cup of water. She uses \(\frac{1}{12}\) cup of the mixture for each drink. How many drinks can she make?

Step 1: The word together means add the two amounts.

\(\displaystyle \frac{2}{3}+\frac{1}{6}\)

Rewrite two-thirds using a denominator of 6.

\(\displaystyle \frac{4}{6}+\frac{1}{6}=\frac{5}{6}\)

Step 2: The word each means divide the total mixture by the amount used for one drink.

\(\displaystyle \frac{5}{6}\div\frac{1}{12}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{5}{6}\times\frac{12}{1}=\frac{60}{6}=10\)

Final Answer:

\(\boxed{10\text{ drinks}}\)

Example 2 – Baking Mixture

A cook combines \(\frac{3}{4}\) cup of flour and \(\frac{1}{8}\) cup of sugar. Each cookie uses \(\frac{1}{16}\) cup of the mixture. How many cookies can be made?

Step 1: The word combines means add the two amounts.

\(\displaystyle \frac{3}{4}+\frac{1}{8}\)

Rewrite three-fourths using a denominator of 8.

\(\displaystyle \frac{6}{8}+\frac{1}{8}=\frac{7}{8}\)

Step 2: The word each means divide the total mixture by the amount used for one cookie.

\(\displaystyle \frac{7}{8}\div\frac{1}{16}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{7}{8}\times\frac{16}{1}=\frac{112}{8}=14\)

Final Answer:

\(\boxed{14\text{ cookies}}\)

Example 3 – Paint Mixture

Sam mixes \(\frac{5}{6}\) cup of paint and \(\frac{1}{3}\) cup of water. He uses \(\frac{1}{6}\) cup of the mixture for each project. How many projects can he complete?

Step 1: Find the total amount by adding.

\(\displaystyle \frac{5}{6}+\frac{1}{3}\)

Rewrite one-third using a denominator of 6.

\(\displaystyle \frac{5}{6}+\frac{2}{6}=\frac{7}{6}\)

Step 2: The word each means divide the total mixture by the amount used for one project.

\(\displaystyle \frac{7}{6}\div\frac{1}{6}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{7}{6}\times\frac{6}{1}=\frac{42}{6}=7\)

Final Answer:

\(\boxed{7\text{ projects}}\)

💡 Main Idea

Some fraction word problems require more than one operation. First, combine quantities when the problem describes a total amount. Then divide to determine how many groups or servings can be made. Paying attention to key words helps identify the correct sequence of operations.

🚀 What Comes Next

Next, students will solve multi-step fraction problems involving mixed numbers and real-world contexts. These problems may require identifying several operations in sequence and explaining the reasoning behind each step.

Fraction Word Problems — Add Then Divide

📝 Practice Worksheets

🛠️ Related Tools

🔑 Key Concepts

✏️ Worked Examples – Add, Then Divide

💡 Main Idea

🚀 What Comes Next

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