The two quantities are equal.

When adding fractions with different denominators, you must first find a common denominator. Some multiples of 2 and 5 are:

2: 2, 4, 6, 8, 10...

5: 5, 10, 15, 20...

The first multiple 2 and 5 have in common is 10. Change each fraction accordingly so that the denominator of each is 10.

The problem now looks like this:

Add the numerators once the denominators are equal. The result is your answer.

When adding fractions with different denominators, first change the fractions so that the denominators are equal. To do this, find the least common multiple of 5 and 10. Some multiples of 5 and 10 are:

5: 5, 10, 15, 20...

10: 10, 20, 30, 40...

Since the first multiple shared by 5 and 10 is 10, change the fractions so that their denominators equal 10.  already has a denominator of 10, so there is no need to change it. 

The problem now looks like this:

Add the fractions by finding the sum of the numerators.

When possible, always reduce your fraction. In this case, both 5 and 10 are divisible by 5.

The result is your answer.

When adding fractions with different denominators, first change the fractions so that the denominators are equal. To do this, find the least common multiple of 3 and 9. Some multiples of 3 and 9 are:

3: 3, 6, 9, 12...

9: 9, 18, 27, 36...

Since the first multiple shared by 3 and 9 is 9, change the fractions so that their denominators equal 9.  already has a denominator of 9, so there is no need to change it. 

The problem now looks like this:

Solve by adding the numerators. The result is your answer.

 and  is positive, so by the multiplication property of inequality,

Also,

,

so

1 of the 4 circles in the diagram -  of the circles - are shaded, as are 2 of the 8 squares -  of them.

The circle is divided into sixteen regions of equal size, eleven of which are white; this is  of the circle. The square is divided into three regions of equal size, two of which are white; this is  of the circle. , so we can compare the fractions by rewriting them with this denominator:

and 

, making the fraction of the circle that is white the greater fraction.

Figure 1 is a rectangle divided into 24 squares of equal size; 3 of the squares are shaded, which means that  of Figure 1 is shaded.

Figure 2 is a circle  divided into 8 sectors of equal size; 1 is shaded, which means that  of Figure 2 is shaded. 

The fractions are equal.

Figure 1 is a rectangle divided into 24 squares of equal size; 8 of the squares are shaded, which means that  of Figure 1 is shaded.

Figure 2 is a triangle divided into 4 triangles of equal size; 1 is shaded, which means that  of Figure 2 is shaded.

The fraction of Figure 1 that is shaded is the greater quantity.

The square is divided into eighteen triangles of equal size and shape; nine are shaded, so the fraction of the square that is shaded is 

The triangle is divided into sixteen triangles of equal size and shape; eight are shaded, so the fraction of the square that is shaded is 

.

The fractions are equal.