Question

spiral review

1. solve each equation. write each solution as a fraction and as a decimal.

equation	solution (fraction)	solution (decimal)
$5y = 3$
$0.3z = 0.09$

problems 7–10: each lap around a track is 400 meters. how many meters will someone run in

1. 2 laps?
2. 5 laps?
3. $x$ laps?
4. if sol ran 7,600 meters, how many laps did they run? explain your thinking.

Explanation:

Problem 6: Solve each equation, write solution as fraction and decimal

Equation \( 2x = 3 \)

Step 1: Isolate \( x \)

Divide both sides by 2: \( x = \frac{3}{2} \)

Step 2: Convert to decimal

\( \frac{3}{2} = 1.5 \)

Solution (Fraction): \( \frac{3}{2} \)

Solution (Decimal): \( 1.5 \)

Equation \( 5y = 3 \)

Step 1: Isolate \( y \)

Divide both sides by 5: \( y = \frac{3}{5} \)

Step 2: Convert to decimal

\( \frac{3}{5} = 0.6 \)

Solution (Fraction): \( \frac{3}{5} \)

Solution (Decimal): \( 0.6 \)

Equation \( 0.3z = 0.09 \)

Step 1: Isolate \( z \)

Divide both sides by 0.3: \( z = \frac{0.09}{0.3} \)
Simplify: \( z = \frac{9}{30} = \frac{3}{10} \) (multiply numerator/denominator by 100 to eliminate decimals: \( \frac{0.09 \times 100}{0.3 \times 100} = \frac{9}{30} \), then reduce)

Step 2: Convert to decimal

\( \frac{3}{10} = 0.3 \)

Solution (Fraction): \( \frac{3}{10} \)

Solution (Decimal): \( 0.3 \)

Problem 7: 2 laps

Answer:

800 meters

Problem 8: 5 laps