Are 2/3 and 4/6 equivalent fractions? Why?
Yes, 2/3 and 4/6 are equivalent fractions.
Explanation: When we divide a whole into 3 equal parts and take 2 parts, we get 2/3. When we divide the same whole into 6 equal parts and take 4 parts, we get 4/6. Both represent the same amount.
Verification: 4/6 can be simplified to 2/3 by dividing both numerator and denominator by 2. 4/6 = (4 ÷ 2)/(6 ÷ 2) = 2/3
∴ 2/3 and 4/6 are equivalent fractions.
Explanation
The chapter demonstrates using the fraction wall that 2/3 and 4/6 have the same length. Equivalent fractions represent the same quantity but are expressed using different fractional units. The fraction wall visually shows that 2 parts out of 3 equals 4 parts out of 6.
Solution Steps
Compare the two fractions: 2/3 and 4/6
Simplify 4/6 by dividing both numerator and denominator by their common factor 2
Verify: (4 ÷ 2)/(6 ÷ 2) = 2/3
Conclude that both fractions represent the same quantity, so they are equivalent