MODELING FRACTION DIVISION
About "Modeling fraction division"
Modeling fraction division :
For some real-world problems, we may need to divide a fraction by a fraction.Sometimes, we may need to divide a fraction by a whole number.
Let us see how fraction division can be modeled through some examples.
Modeling fraction division - Examples
Example 1 :
David has 3/4 cup of salsa for making burritos. Each burrito requires 1/8 cup of salsa. How many burritos can David make ?
Solution :
To find the number of burritos that can be made, you need to determine how many 1/8 -cup servings are in 3/4 cup.
In the diagram given below, 3/4 of a whole is divided into quarters and into eighths.
In the whole cup, there are eight 1/8 cups.
But, David has 3/4 cup of salsa.
So, we have to count the number of 1/8 cups in 3/4 cup in the above diagram.
And there are six 1/8 cups in 3/4 cup of salsa.
Hence, David can make 6 burritos from 3/4 cup of salsa.
Example 2 :
Five people share 1/2 pound of cheese equally. How much cheese does each person receive?
Solution :
To find how much cheese each person receives, you can divide 1/2 pound into 5 equal parts. Use the diagram to determine what fraction of a whole pound each person receives.
In the diagram given below, 1/2 of a whole is divided into halves and into tenths.
In one pound of cheese, there are ten 1/10s.
But, there is 1/2 pound of cheese.
So, we have to count the number of 1/10s in 1/2 pound of cheese.
And there are five 1/10s in 1/2 pound of cheese.
Hence, Each person will receive 1/10 pound of cheese.
Using reciprocal to divide fractions - Steps
Step 1 :
When we divide a fraction by another fraction, first we have to change the division sign as multiplication.
Step 2 :
Take reciprocal of the second fraction.
Step 3 :
Multiply the two fractions. (Numerator times numerator and denominator times denominator).
Using reciprocal to divide fractions - Examples
Example 1 :
Divide 2/5 by 6/7
Solution :
Using the method explained above, we have
2/5 ÷ 6/7 = 2/5 x 7/6
2/5 ÷ 6/7 = (2x7) / (5x6)
2/5 ÷ 6/7 = 7/15
Example 2 :
Divide 7/5 by 3/2
Solution :
Using the method explained above, we have
7/5 ÷ 3/2 = 7/5 x 2/3
7/5 ÷ 3/2 = (7x2) / (5x3)
7/5 ÷ 3/2 = 14/15
Example 3 :
Divide 5/12 by 20/13
Solution :
Using the method explained above, we have
5/12 ÷ 20/13 = 5/12 ÷ 20/13
5/12 ÷ 20/13 = 5/12 x 13/20
5/12 ÷ 20/13 = (5x13) / (12x20)
5/12 ÷ 20/13 = 13/48
Example 4 :
Divide 2/19 by 6 1/2
Solution :
First, let us convert the mixed number 6 1/2 in to improper fraction.
6 1/2 = 13/2
Now,m we have 2/19 ÷ 6 1/2 = 2/19 ÷ 13/2
Using the method explained above, we have
2/19 ÷ 13/2 = 2/19 x 13//2
2/19 ÷ 13/2 = (2x13) / (19x2)
2/19 ÷ 13/2 = 13 / 19
Example 5 :
One pizza can be made in 1/2 hour. How many pizzas can be made in 5/2 hours ?
Solution :
Time taken to make one pizza = 1/2 hour
No. of pizzas made in 5/2 hours = 5/2 ÷ 1/2
No. of pizzas made in 5/2 hours = 5/2 x 2/1
No. of pizzas made in 5/2 hours = (5x2) / (2x1)
No. of pizzas made in 5/2 hours = 5
Dividing fractions by whole numbers - Methods
Method 1 :
Step 1 :
When we divide a fraction by a whole number, first we have to write the whole number as fraction with denominator 1.
Step 2 :
Change the division sign as multiplication.
Step 3 :
Take reciprocal of the second fraction (Whole number with denominator 1).
Step 4 :
Multiply the two fractions. (Numerator times numerator and denominator times denominator).
Method 2
To divide a fraction by a whole number,
multiply the denominator of the fraction by the whole number and simplify, if possible.
Dividing fractions by whole numbers - Examples
Example 1 :
Simplify : 2/5 ÷ 6
Solution :
Using method 1, we have
2/5 ÷ 6 = 2/5 ÷ 6/1
2/5 ÷ 6 = 2/5 x 1/6
2/5 ÷ 6 = (2x1) / (5x6)
2/5 ÷ 6 = 1/15
Example 2 :
Simplify : 5/12 ÷ 20
Solution :
Using method 2, we have
5/12 ÷ 20 = 5 / (12x20)
5/12 ÷ 20 = 1/48
Example 3 :
David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?
Solution :
Part of the pizza eaten by David = 1/4
Remaining pizza = 3/4
Given : Remaining pizza is divided in to equal parts for his two kids.
So, part of the pizza received by each kid is
= 3/4 ÷ 2
= 3/(4x2)
= 3/8
Hence, each kid will receive 3/8 part of the pizza.
After having gone through the stuff given above, we hope that the students would have understood "Modeling fraction division".
Apart from the stuff given above, if you want to know more about "Modeling fraction division", please click here
Apart from "Modeling fraction division", if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
