Equivalent Fractions

[ggfrac]1/2[/ggfrac], [ggfrac]1/5[/ggfrac], [ggfrac]1/10[/ggfrac]. A smaller denominator means that the whole is cut into fewer pieces, which means that each piece is bigger.

[ggfrac]2/3[/ggfrac], [ggfrac]4/5[/ggfrac], [ggfrac]10/10[/ggfrac]. If the denominator is the same, the numerator tells us how many equal-sized pieces there are.

The fraction means that there are 3 wholes. 1 means that there is only one piece, so the whole has not been divided into smaller pieces. 3 means that there are 3 wholes.

[ggfrac]5/8[/ggfrac]and [ggfrac]3/8[/ggfrac]. [ggfrac]5/8[/ggfrac] is greater because more of the pie is shaded and because we know that more pieces of the same size of slices are greater.

[ggfrac]4/10[/ggfrac] and [ggfrac]3/4[/ggfrac]. [ggfrac]3/4[/ggfrac] is greater because more of the pie is shaded in.

We should cut each slice in half. Now there are twice as many slices and they are twice as small. The amount of pie is the same.

[ggfrac]4/6[/ggfrac], [ggfrac]6/9[/ggfrac], [ggfrac]8/12[/ggfrac], [ggfrac]10/15[/ggfrac], [ggfrac]12/18[/ggfrac], ...

If we multiply 5 by 3, we get 15. If we multiply 6 by 3 we get 18. Both the numerator and denominator are multiplied by 3, so the fractions are equivalent.

When we cut more slices out of the same amount of a pie, we make more slices (the numerator grows) and at the same time, each slice gets smaller (the denominator grows). Notice that when the numerator and denominator are the same in a fraction, that is the same as 1 whole. Whenever we multiply something by 1, that means we do not change the amount, we just express it in a different way.

We can see that 5 × 3 = 15. Then if these are equivalent fractions, we multiply 2 by 3 as well. But 2 × 3 = 6, so [ggfrac]2/5[/ggfrac] and [ggfrac]12/15[/ggfrac] are not equivalent. Or we can see that 2 × 6 = 12. Then we multiply 5 by 6 as well. But 5 × 6 = 30, so [ggfrac]12/15[/ggfrac] is not equivalent to [ggfrac]2/5[/ggfrac]. We could also check using division.