Two landscapers are working on the front garden of a hotel. In one day, the first landscaper finished 
2/5of the job and the second finished 1/3 of the job. How much of the job is not yet done?

Let's solve this step by step.

### Step 1: Determine how much of the job has been completed.
- The first landscaper completed \(\frac{2}{5}\) of the job.
- The second landscaper completed \(\frac{1}{3}\) of the job.

### Step 2: Add the fractions of the job completed by both landscapers.
To add \(\frac{2}{5}\) and \(\frac{1}{3}\), we first need to find a common denominator.

The least common denominator (LCD) of 5 and 3 is 15.

\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]

Now, add the two fractions:

\[
\frac{6}{15} + \frac{5}{15} = \frac{11}{15}
\]

### Step 3: Subtract the total completed work from 1 (the whole job).
The entire job is 1, or \(\frac{15}{15}\).

\[
\text{Job not yet done} = 1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}
\]

### Final Answer:
\(\frac{4}{15}\) of the job is not yet done.

Would you like to explore this further or have any questions?

---

**Here are 8 related questions to consider:**
1. What if the first landscaper had completed \(\frac{3}{5}\) of the job? How much would remain?
2. If a third landscaper completed \(\frac{2}{15}\) of the remaining work, how much would be left?
3. How would the work division change if both landscapers worked at the same rate?
4. What fraction of the job would remain if the second landscaper completed \(\frac{2}{3}\) of the job?
5. How much would each landscaper need to complete to finish the job in half a day?
6. How would the calculation change if we used decimal values instead of fractions?
7. How long would it take to complete the remaining \(\frac{4}{15}\) of the job if both landscapers worked together again?
8. What is the total fraction of the job completed after 2 days if each landscaper works at the same rate every day?

**Tip:** Always double-check your fractions by ensuring they have a common denominator before adding or subtracting!

Learn how to calculate the fraction of a landscaping job that remains unfinished, solved step-by-step. This problem involves fractions and requires adding fractions with a common denominator. Suitable for students in Grades 4-6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation