$\displaystyle b \div a = 4.5 \div 1.5 = 3$

$\displaystyle b - a = 4.5 - 1.5 = 3$

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.

$\displaystyle \frac{2}{5} \times \frac{2}{2}\rightarrow\frac{4}{10}$

$\displaystyle \frac{1}{2}\times\frac{5}{5} \rightarrow \frac{5}{10}$

The problem now looks like this:

$\displaystyle \frac{4}{10} + \frac{5}{10} =$

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

$\displaystyle \frac{4}{10} + \frac{5}{10} = \frac{4+5}{10}=\frac{9}{10}$

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. $\displaystyle \tfrac{1}{10}$ already has a denominator of 10, so there is no need to change it. 

$\displaystyle \frac{2}{5}\times\frac{2}{2}\rightarrow\frac{4}{10}$

The problem now looks like this:

$\displaystyle \frac{1}{10}+\frac{4}{10}=$

Add the fractions by finding the sum of the numerators.

$\displaystyle \frac{1}{10}+\frac{4}{10}=\frac{1+4}{10}=\frac{5}{10}$

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

$\displaystyle \frac{5}{10}\rightarrow\frac{1}{2}$

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. $\displaystyle \tfrac{2}{9}$ already has a denominator of 9, so there is no need to change it. 

$\displaystyle \frac{1}{3}\times\frac{3}{3}\rightarrow\frac{3}{9}$

The problem now looks like this:

$\displaystyle \frac{2}{9}+\frac{3}{9}=$

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

$\displaystyle \frac{2}{9}+\frac{3}{9}=\frac{2+3}{9}=\frac{5}{9}$

$\displaystyle \frac{3}{4} < 1$ and $\displaystyle A$ is positive, so by the multiplication property of inequality,

$\displaystyle \frac{3}{4} \cdot A < 1 \cdot A$

$\displaystyle \frac{3}{4} A < A$

Also,

$\displaystyle A < A + \frac{3}{4 }$,

so

$\displaystyle \frac{3}{4} A < A+ \frac{3}{4 }$

1 of the 4 circles in the diagram - $\displaystyle \frac{1}{4}$ of the circles - are shaded, as are 2 of the 8 squares - $\displaystyle \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$ of them.

The circle is divided into sixteen regions of equal size, eleven of which are white; this is $\displaystyle \frac{11}{16}$ of the circle. The square is divided into three regions of equal size, two of which are white; this is $\displaystyle \frac{2}{3}$ of the circle. $\displaystyle LCM (16, 3) = 48$, so we can compare the fractions by rewriting them with this denominator:

$\displaystyle \frac{11}{16} = \frac{11 \times 3 }{16 \times 3} = \frac{33}{48}$

and 

$\displaystyle \frac{2}{3} = \frac{2 \times 16}{3\times 16 } = \frac{32}{48}$

$\displaystyle \frac{11}{16} > \frac{2}{3}$, 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 $\displaystyle \frac{3}{24} = \frac{3 \div 3}{24\div 3 } = \frac{1}{8}$ of Figure 1 is shaded.

Figure 2 is a circle  divided into 8 sectors of equal size; 1 is shaded, which means that $\displaystyle \frac{1}{8}$ 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 $\displaystyle \frac{8}{24}$ of Figure 1 is shaded.

Figure 2 is a triangle divided into 4 triangles of equal size; 1 is shaded, which means that $\displaystyle \frac{1}{4} = \frac{1 \times 6 }{4 \times 6} =\frac{6}{24 }$ 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 

$\displaystyle \frac{9}{18} = \frac{9 \div 9 }{18\div 9 } = \frac{1}{2}$

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 

$\displaystyle \frac{8}{16} = \frac{8 \div 8 }{16 \div 8 } = \frac{1}{2}$.

The fractions are equal.