DIVIDING WHOLE NUMBERS AND FRACTIONS:

In this video, I show you how to divide whole and fraction numbers. There are different methods of solving equations that have both whole numbers and fractions. You can start with a whole number or a fraction, however, one thing you should always remember is that when a problem starts with a fraction, the answer is always a fraction and when it starts with a whole number, the answer is always a whole number.

For example;
1/5 / 3=

The easy way to solve this problem is to first of all draw a circle or rectangle and divide that into fifths.

Shade off one of the fifths and divide it into three equal parts. However, while dividing the a fifth into three, incorporate the entire rectangle since they should all be equal.

Therefore, the answer is 1 piece of the one fifth out of the total number of the pieces, which is 18.
1/5 / 3= 1/18

Let's look at an example that starts with a whole number;
3 / 1/5 =

Unlike our first example where we drew one whole rectangle, we shall draw three whole rectangles to solve this equation. Three whole, because we have a whole number.

Now, divide those three whole rectangles into fifths.

Adding up all the pieces in the three rectangles, your answer should be 15.
Therefore, 3 / 1/5 = 15.

The difficult part, however, is in knowing when to apply which equation and model. Let's us look at an example below.

Bryce made 4 small pies. He cut each into equal- size servings. Each serving is 1/2 of a pie. How many servings are in the pies Bryce made?

Using a gate triangle denoting T for Total, G for Groups, and E for each, we can see from the above example that the Total number of pies Bryce made = 4, each serving = 1/2 of the pie, now we have to find out how many servings are in the pies;

We therefore get the Total and divide it by the pieces to get the servings.

T / E = G

4 / 1/2 =?

Let's draw 4 pies and split them into a half each. The number of pieces we get is the total.

Therefore Total servings = 8

Another example;
Dr. Schneider needs approximately 1/2 hour with each of her patients. How many patients can she see during an 8-hour day?

A. 4 Patients

B. 8 Patients

C. 12 Patients

D. 16 Patients.

Using the gate triangle still, we see from the question that Dr. Schneider has a Total of 8 hours and uses 1/2 an hour to see each patient. Therefore, the groups or total patients will be?

G = 8 / 1/2

You can draw 8 squares to denote the 8 hours and divide each square into half for each patient seen every 1/2 hour. After you have done this, add up all the pieces and you will have the total number of patients seen by Dr. Schneider in an 8-hour day!

You add up all the half hours and you get 16 patients in her 8-hour day.

Try solving the problem below on your own to gauge your understanding.

During his rehab, Carlos walked 1/2 mile each day. He split the distance into 4 equal parts. How far did Carlos go in each section of his walk?

A. 1/8 mile

B. 1/4 mile

C. 4 miles

D. 8 miles

You can watch the video to check if your answer is correct.

I hope you now know how to divide whole numbers and fractions!

Divide whole numbers & fractions instruction.