Each pan of this 3/4 bar has been split into 2 equal parts. There are now 8 part

Question

Each pan of this 3/4 bar has been split into 2 equal parts. There are now 8 parts, and 6 of these are shaded. Because this splitting has neither increased nor decreased the total shaded amount of the bar, both 3/4 and 6/8 are fractions for the same amount. a. Split each pan of these bars into 2 equal parts, and complete the equations. 4/9 = 3/10 = 1/5 = b. Split each part of these bars into 3 equal parts, and complete the equations. 6/7 = 5/8 = 1/6 = c. Split each part of these bars into 4 equal parts, and complete the equations. 0/3 = 3/4 = 1/2 = d. Suppose that each part of the Fraction Bar for a/b is split into 3 equal parts. How many of the parts will be shaded? ___How many parts will there be in all?___ Write the fraction for this bar.___

Explanation / Answer

a) Split into 2 equal parts

4/9 = 4 * 2 / 9 * 2 = 8 / 18

3/10 = 3 *2 / 10 *2 = 6 /20

1/5 = 1 *2 / 5 * 2 = 2 / 10

b) split into 3 equal parts

6/7 = 6 * 3 / 7 * 3 = 18 /21

5/8 = 5 * 3 / 8 * 3 = 15 /24

1/6 = 1 * 3 / 6 * 3 = 3 / 18

c) Split into 4 equal parts

0/3 = 0 * 4 / 3 * 4 = 0 / 12

3/4 = 3 * 4 / 4 * 4 = 12 /16

1/2 = 1 * 4/ 2 * 4 = 4 /8

d) a / b = a * 3 / b * 3 = 3a/ 3b

There are now 3b parts and 3a of these are shaded.

The total shaded amount of the bar , both a/b and 3a/3b are the fractions for the same amount

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