Are the lengths 1⁄2 and 2⁄4 equal? Are the lengths 2⁄4 and 4⁄8 equal?
Answer
Yes to both. Place the three shaded strips one below the other — all three shaded portions end at exactly the same place.
1/2 = 2/4 = 4/8
Why: when you cut every part into two, you get twice as many parts but each is half as long. Two effects cancel, so the total length does not change.
Q2.
Now, check whether 1⁄3 and 2⁄6 are equivalent fractions or not, using paper strips.
Answer
Take two identical strips. Fold one into 3 equal parts and shade one part; fold the other into 6 equal parts and shade two parts. Put them side by side — the shaded lengths match.
1/3 = (1 × 2)/(3 × 2) = 2/6
Yes, 1⁄3 and 2⁄6 are equivalent fractions.
Q3.
Are the lengths 1⁄2 and 3⁄6 equal?
Answer
Yes. On the fraction wall the strip of one half and the three strips of one sixth end at the same line.
The fraction wall up to sixths. The red dashed line shows that 1⁄2, 2⁄4 and 3⁄6 all end at the same place.
3/6 = (3 ÷ 3)/(6 ÷ 3) = 1/2
Q4.
Are 2⁄3 and 4⁄6 equivalent fractions? Why?
Answer
Yes, they are equivalent.
2/3 = (2 × 2)/(3 × 2) = 4/6
On the fraction wall, two strips of 1⁄3 cover exactly the same length as four strips of 1⁄6, because each third is made of two sixths.
Q5.
How many pieces of length 1⁄6 will make a length of 1⁄2?
Answer
1/2 = 3/6 = 1/6 + 1/6 + 1/6
Answer: 3 pieces.
Q6.
How many pieces of length 1⁄6 will make a length of 1⁄3?
Answer
1/3 = 2/6 = 1/6 + 1/6
Answer: 2 pieces.
Tip: a sixth is half of a third, so it always takes two sixths to make one third.