Let's solve each of the three subtraction problems step by step.
---
1. What is $\frac{6}{7} - \frac{6}{17}$?
We are subtracting two fractions with different denominators: 7 and 17.
#### Step 1: Find a common denominator.
The least common denominator (LCD) of 7 and 17 is $7 \times 17 = 119$, since they are both prime numbers.
#### Step 2: Convert each fraction to have denominator 119.
$$
\frac{6}{7} = \frac{6 \times 17}{7 \times 17} = \frac{102}{119}
$$
$$
\frac{6}{17} = \frac{6 \times 7}{17 \times 7} = \frac{42}{119}
$$
#### Step 3: Subtract the numerators.
$$
\frac{102}{119} - \frac{42}{119} = \frac{60}{119}
$$
#### Step 4: Simplify (if possible).
Check if 60 and 119 have common factors.
- Factors of 60: $2^2 \times 3 \times 5$
- 119 = $7 \times 17$
No common factors, so the fraction is already in simplest form.
✔ Answer: $\boxed{\frac{60}{119}}$
---
2. What is $\frac{4}{5} - \frac{2}{5}$?
These fractions have the same denominator (5), so we can subtract directly.
$$
\frac{4}{5} - \frac{2}{5} = \frac{4 - 2}{5} = \frac{2}{5}
$$
✔ Answer: $\boxed{\frac{2}{5}}$
---
3. What is $\frac{6}{13} - \frac{1}{4}$?
Different denominators: 13 and 4.
#### Step 1: Find LCD of 13 and 4.
Since both are prime, LCD = $13 \times 4 = 52$
#### Step 2: Convert each fraction.
$$
\frac{6}{13} = \frac{6 \times 4}{13 \times 4} = \frac{24}{52}
$$
$$
\frac{1}{4} = \frac{1 \times 13}{4 \times 13} = \frac{13}{52}
$$
#### Step 3: Subtract.
$$
\frac{24}{52} - \frac{13}{52} = \frac{11}{52}
$$
#### Step 4: Simplify.
11 is prime, and 52 is not divisible by 11 → no simplification needed.
✔ Answer: $\boxed{\frac{11}{52}}$
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✔ Final Answers:
1. $\frac{6}{7} - \frac{6}{17} = \boxed{\frac{60}{119}}$
2. $\frac{4}{5} - \frac{2}{5} = \boxed{\frac{2}{5}}$
3. $\frac{6}{13} - \frac{1}{4} = \boxed{\frac{11}{52}}$
Parent Tip: Review the logic above to help your child master the concept of subtracting fractions sheet.
