# SSAT Middle Level Math : How to divide fractions

## Example Questions

### Example Question #161 : How To Divide Fractions

Tim has  of peanuts that he wants to divide evenly into  bags. How much will each bag of peanuts weigh?

Explanation:

We are splitting  into  equal groups, so we are dividing  by

To solve  we multiply by the reciprocal.

### Example Question #162 : How To Divide Fractions

David has  of peanuts that he wants to divide evenly into  bags. How much will each bag of peanuts weigh?

Explanation:

We are splitting  into  equal groups, so we are dividing  by

To solve  we multiply by the reciprocal.

### Example Question #163 : How To Divide Fractions

Solve the following problem.

Explanation:

When dividing fractions, you invert the second fraction and multiply.

### Example Question #164 : How To Divide Fractions

How many  servings are in  cups of chocolate chips?

Explanation:

Because we want to know how many  servings are in  cups, we are dividing  by

Remember, whenever we divide by a fraction, we multiply by the reciprocal

### Example Question #165 : How To Divide Fractions

Solve:

Explanation:

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

because  can go into  one time with  left over.

### Example Question #166 : How To Divide Fractions

Solve:

Explanation:

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

because  can go into  one time with  left over.

### Example Question #167 : How To Divide Fractions

The above rectangle is divided into squares of equal size. The shaded region has area 45. Give the area of the entire rectangle.

Explanation:

Seven of the ten squares of the rectangle -  of it - is shaded in. If we let  be the area of the rectangle, then

Divide 450 by 7 - the quotient is 64 and the remainder is 2, so the area can be written as .

### Example Question #168 : How To Divide Fractions

The above hexagon is divided into triangles of equal size. The area of the shaded region is 72. Give the area of the entire hexagon.

Explanation:

7 of the 12 triangles - that is,  of the hexagon - is shaded, so, if we let  be the area of the hexagon,

Solving:

so the area can be written as .

### Example Question #169 : How To Divide Fractions

These figures are NOT necessarily drawn to scale

The shaded portions Figure 1 and Figure 2 are of equal area. Figure 1 has area 36; what is the area of Figure 2?

Explanation:

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. Since Figure 1 has area 36, the shaded portion has area

.

Figure 2 is a triangle divided into 4 triangles of equal size; 1 is shaded, which means that  of Figure 2 is shaded. Since this shaded portion has area equal to that of Figure 1, which is 12, the area of all of Figure 2 is

.

### Example Question #170 : How To Divide Fractions

Each of the rectangles in the above diagram has the same area, and is divided into squares of the same size and shape; the area of the shaded region is 10. Give the area of one of the four rectangles.