Question

Layla skated x kilometers. Lamel skated
5
2
​
less than Layla. We can use the equation y=
5
3
​
x to represent this distance. Write
5
3
​
in decimal form.
You can use long division to write
5
3
​
as a decimal. Divide 30 tenths by 5 on the algorithm to find the decimal equivalent.
0 .
6

5 3 .0

.
0
.

Answer 1

To convert the fraction \( \frac{5}{3} \) to decimal form using long division, follow these steps:

1. **Set up the long division**: You want to divide 5 by 3.
2. **Determine how many times 3 goes into 5**:
- 3 goes into 5 once (1).
3. **Multiply and subtract**:
- \( 1 \times 3 = 3 \)
- \( 5 - 3 = 2 \)
4. **Add a decimal and continue the division**: For 2, add a decimal point and bring down a zero to make it 20.
5. **Determine how many times 3 goes into 20**:
- 3 goes into 20 six times (6).
6. **Multiply and subtract**:
- \( 6 \times 3 = 18 \)
- \( 20 - 18 = 2 \)
7. **Bring down another zero**: Now you have 20 again.
8. **Repeat the process**: You can see that you will keep getting 6 again and again.

Thus, \( \frac{5}{3} \) as a decimal is \( 1.666... \), often written as \( 1.67 \) when rounded to two decimal places.

So, the decimal form of \( \frac{5}{3} \) is approximately \( 1.666...\).

In your original context, using the \( y = \frac{5}{3} x \) equation implies that Lamel skated \( 1.666... \) times the distance as represented, indicating the relationship based on Layla's distance \( x \).