M3L5 Application problem

Question

A farmer uses 3/4 of his field to plant corn, 1/6 of his field to plant beans, and the rest to plant wheat. What fraction of his field is used for wheat? 

At times, simply remind students of their RDW process in order to solve a problem independently. It is desired that students internalize the simple set of questions as well as the systematic approach of read, draw, write an equation, and write a statement:  

1. What do I see?  
2. What can I draw?  
3. What conclusions can I make from my drawing

Answer 1

Consider the whole field is 1, so we can get the answer by writing down:

wheat field = 1 - 3/4 - 1/6

find the LCD is 12

wheat field = 1 - 9/12 - 2/12 = 1/12

So the wheat field is 1/12 of the whole field.

Answer 2

Hi Sam F

1/12 of this field is used for Wheat

You have 1 whole field for planting

Corn will cover = 3/4

Beans will cover = 1/6

Wheat will cover whatever is left over = x

So the combination of Corn + Beans + x = 1

OR

3/4 + 1/6 + x = 1

To add you need a Least Common Denominator for the fractions then just solve for x

LCD = 12

3/4 = 9/12

1/6 = 2/12

1= 12/12

9/12 + 2/12 + x = 12/12

Combine like terms

11/12 + x = 12/12

Subtract 11/12 from both sides of the equation to solve for x

x = 12/12 - 11/12

x = 1/12

You see 1 whole field divided into areas for corn, beans, and wheat

You can draw a picture such as a rectangle to represent the field, according to the divisions given in the problem; 3/4 of your rectangle is for corn, 1/6 is for beans and the left over x is for wheat

You can conclude based on your diagram the size of the space for wheat relative to the size of the other portions in your diagram and the answer you got for x

A comparison of the given fractions 3/4 and 1/6 marked off in your drawing should easily show;

3/4 is the largest part of the field

1/6 is smaller and that there is very little left over for wheat

So your answer will be a small fraction

I hope this helps.