WORD PROBLEMS ON MIXED FRACTIONS
Problem 1 :
Linda walked 2 1/3 miles on the first day and 3 2/5 miles on the next day. How many miles did she walk in all ?
Solution :
Total no. of miles she walked is
= 2 1/3 + 3 2/5
In the above mixed fractions, we have the denominators 3 and 5.
LCM of (3, 5) = 15
To simplify the above expression, we have to make the denominators of both the mixed fractions to be 15.
Then, we have
2 1/3 + 3 2/5 = 2 5/15 + 3 6/15
By regrouping, we have
2 1/3 + 3 2/5 = (2 + 3) + (5/15 + 6/15)
2 1/3 + 3 2/5 = (5) + (11/15)
2 1/3 + 3 2/5 = 5 11/15
So, Linda walked 5 11/15 miles in all.
Problem 2 :
David ate 2 1/7 pizzas and he gave 1 3/14 pizzas to his mother. How many pizzas did David have initially ?
Solution :
No. of pizzas he had initially is
= 2 1/7 + 1 3/14
= 2 2/14 + 1 3/14
By regrouping, we have
= (2 + 1) + (2/14 + 3/14)
= (3) + (5/14)
= 3 5/14
So, initially David had 3 5/14 pizzas.
Problem 3 :
Mr. A has 3 2/3 acres of land. He gave 1 1/4 acres of land to his friend. How many acres of land does Mr. A have now ?
Solution :
Now, no. of acres of land that Mr. A has
= 3 2/3 - 1 1/4
In the above mixed fractions, we have the denominators 3 and 4.
LCM of (3, 4) = 12
To simplify the above expression, we have to make the denominators of both the mixed fractions to be 12.
Then, we have
3 2/3 - 1 1/4 = 3 8/12 - 1 3/12
By regrouping, we have
3 2/3 - 1 1/4 = (3 - 1) + (8/12 - 3/12)
3 2/3 - 1 1/4 = (2) + (5/12)
3 2/3 - 1 1/4 = 2 5/12
Now, Mr. A has 2 5/12 acres of land.
Problem 4 :
Lily added 3 1/3 cups of walnuts to a batch of trail mix. Later she added 1 1/3 cups of almonds. How many cups of nuts did Lily put in the trail mix in all?
Solution :
No. of cups of nuts that Lily put in all is
= 3 1/3 + 1 1/3
By regrouping, we have
= (3 + 1) + (1/3 + 1/3)
= (4) + (2/3)
= 4 2/3
So, Lily put 4 2/3 cups of nuts in all.
Problem 5 :
In the first hockey games of the year, Rodayo played 1 1/2 periods and 1 3/4 periods. How many periods in all did he play ?
Solution :
No. of periods in all he played is
= 1 1/2 + 1 3/4
= 1 2/4 + 1 3/4
By regrouping, we have
= (1 + 1) + (2/4 + 3/4)
= (2) + (5/4)
= (2) + (1 1/4)
= (2) + (1 + 1/4)
= 3 1/4
So, Rodayo played 3 1/4 periods in all.
Problem 6 :
A bag can hold 1 1/2 pounds of flour. If Mimi has 7 1/2 pounds of flour, then how many bags of flour can Mimi make ?
Solution :
No. of bags = (Total no. of lbs) / (No of lbs per bag)
Because, we use division, we have to convert the given mixed numbers into improper fractions.
Total no. of pounds of flour is
= 7 1/2
= 15/2
No. of pounds per bag is
= 1 1/2
= 3/2
Then, we have
Number of bags = (15/2) / (3/2)
Number of bags = (15/2) ⋅ (2/3)
Number of bags = 5
So, the number of bags that Mimi can make is 5.
Problem 7 :
Jack and John went fishing Jack caught 3 3/4 kg of fish and while John caught 2 1/5 kg of fish. What is the total weight of the fish they caught?
Solution :
Total weight of the fish they caught is
= 3 3/4 + 2 1/5
In the above mixed fractions, we have the denominators 4 and 5.
L.C.M of (4, 5) = 20
To simplify the above expression, we have to make the denominators of both the mixed fractions to be 20.
Then, we have
3 3/4 + 2 1/5 = 3 15/20 + 2 4/20
By regrouping, we have
3 3/4 + 2 1/5 = (3 + 2) + (15/20 + 4/20)
3 3/4 + 2 1/5 = (5) + (19/20)
3 3/4 + 2 1/5 = 5 19/20
So, the total weight of the fish they caught is 5 19/20 kg.
Problem 8 :
Amy has 3 1/2 bottles in her refrigerator. She used 3/5 bottle in the morning 1 1/4 bottle in the afternoon. How many bottles of milk does Amy have left over ?
Solution :
No. of bottles of milk used is
= 3/5 + 1 1/4
In the above mixed fractions, we have the denominators 5 and 4.
L.C.M of (5, 4) = 20
To simplify the above expression, we have to make the denominators of both the mixed fractions to be 20.
Then, we have
3/5 + 1 1/4 = 12/20 + 1 5/20
By regrouping, we have
3/5 + 1 1/4 = 1 + (12/20 + 5/20)
3/5 + 1 1/4 = 1 + (17/20)
3/5 + 1 1/4 = 1 17/20
So, no. of bottles of milk used is 1 17/20.
No. of bottles remaining is
= 3 1/2 - 1 17/20
= 3 10/20 - 1 17/20
(Numerator of the first fraction is smaller than the second. In subtraction of mixed numbers, always the numerator of the first fraction to be greater)
Then, we have
= (3 + 10/20) - 1 17/20
= (2 + 1 + 10/20) - 1 17/20
= (2 + 20/20 + 10/20) - 1 17/20
= (2 + 30/20) - 1 17/20
= 2 30/20 - 1 17/20
By regrouping, we have
= (2 - 1) + (30/20 - 17/20)
= (1) + (13/20)
= 1 13/20
So, 1 13/20 bottles of milk Amy has left over.
Problem 9 :
A tank has 82 3/4 liters of water. 24 4/5 liters of water were used and the tank was filled with another 18 3/4 liters. What is the final volume of the water in the tank ?
Solution :
Initially, the tank has 82 3/4 liters.
24 4/5 liters were used -----> Subtract
The tank was filled with another 18 3/4 liters -----> Add
Then, the final volume of the water in tank is
= 82 3/4 - 24 4/5 + 18 3/4
In the above mixed fractions, we have the denominators 4 and 5.
L.C.M of (5, 4) = 20
To simplify the above expression, we have to make the denominators of both the mixed fractions to be 20.
Then, we have
= 82 15/20 - 24 16/20 + 18 15/20
By regrouping, we have
= (82 - 24 + 18) + (15/20 - 16/20 + 15/20)
= (76) + (14/20)
= (76) + (7/10)
= 76 7/10
So, the final volume of water in the tank is 76 7/10 liters.
Problem 10 :
A trader prepared 21 1/2 liters of lemonade. At the end of the day he had 2 5/8 liters left over. How many liters of lemonade was sold by the Trader?
Solution :
Initial stock of lemonade is 21 1/2 liters.
Closing stock is 2 5/8 liters.
No. of liters sold = Initial stock - closing stock
No. of liters sold = 21 1/2 - 2 5/8
No. of liters sold = 21 4/8 - 2 5/8
(Numerator of the first fraction is smaller than the second. In subtraction of mixed numbers, always the numerator of the fraction to be greater)
Then, we have
No. of liters sold = (21 + 4/8) - 2 5/8
No. of liters sold = (20 + 1 + 4/8) - 2 5/8
No. of liters sold = (20 + 8/8 + 4/8) - 2 5/8
No. of liters sold = (20 + 12/8) - 2 5/8
No. of liters sold = 20 12/8 - 2 5/8
By regrouping, we have
No. of liters sold = (20 - 2) + (12/8 - 5/8)
No. of liters sold = (18) + (7/8)
No. of liters sold = 18 7/8
So, 18 7/8 liters of lemonade was sold by the Trader.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
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
Trigonometry 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
Recent Articles
-
Model Polynomial Multiplication
Oct 25, 20 05:39 AM
Model Polynomial Multiplication
-
Properties of Quadratic Equations
Oct 25, 20 03:45 AM
Properties of Quadratic Equations
-
Properties of Equality
Oct 25, 20 03:22 AM
Properties of Equality - Concept - Solved Problems
