Word problems for adding and subtracting fractions: Add & subtract fractions word problems worksheets

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Adding and subtracting fractions grade 5 worksheets





Add and Subtract Fractions with Like and Unlike Denominators exercises

Grab amazing skills to add and subtract fractions with our remarkable addition and subtracting fractions grade 5 worksheets. Given that adding and subtracting fractions is an essential skill in many math concepts and in our daily lives, our fraction problem solving worksheets with answers will offer your kids admirable problem solving strategies to confidently solve fraction word problems. At the same time, they’ll practice thrilling add and subtract fractions with like and unlike denominators exercises.



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Important facts about addition and subtraction of fractions for grade 5


One very importance of fractions is that it helps kids understand the nature of numbers and their interactions in a special way.

To this effect, our fractions exercises have been designed in way to provide an enriching experience of basic essentials of number theory, such as finding the LCD, GCF, Prime factorization.


Free fun models — quick mastery add and subtract fractions with like and unlike denominators


Available in our addition and subtracting fractions grade 5 worksheets are free fun models helpful for kid’s quick mastery add and subtract fractions with like and unlike denominators.

To begin with, you’ll discover here that our exercises are full of exciting models such as add and subtract unlike fractions using models, add and subtract like fractions using number lines, add and subtract fractions in recipes etc.

All these fun models and word problems will greatly enrich kid’s reasoning skills as they’ll now be able to visualize and solve problems of add and subtract fractions more clearly and accurately.

Secondly, you’ll equally find in our add and subtract fractions with like and unlike denominators exercises helpful tips for easy calculations.

  • Fractions with like denominators are very easy to add or subtract. You simply need to add or subtract the numerators and write the sum over the common denominator.

  • Whereas before you add or subtract fractions with unlike denominators, you must first of all find equivalent fractions with the same denominator

    Example:

    Find the LCM of both fractions;
    5/6  +  1/3   (LCM of 6 and 3 is 6)

    Divide the LCM by the denominator of each fraction. Get the result, and then multiply by the numerator.     →     5/6 + 2/6

    When the results of the fractions have been gotten, then you can now add or subtract those results normally to obtain your final answer.

    Your new answer will now be the numerator, while the found LCM will be the denominator.

    So,    5/6  +  2/6  =  7/6

Subtracting Fractions In Word Problems

 

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All Common Core: 4th Grade Math Resources

7 Diagnostic Tests
189 Practice Tests
Question of the Day
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Common Core: 4th Grade Math Help »
Number & Operations: €”Fractions »
Build fractions from unit fractions »
Solve Word Problems Involving Addition and Subtraction of Fractions: CCSS. Math.Content.4.NF.B.3d »
Subtracting Fractions In Word Problems

A baker used  of a package of sprinkles and  of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

Possible Answers:

Correct answer:

Explanation:

The phrase, «how much more» tells as that we want to find the difference, so we subtract. 

Report an Error

A baker used  of a package of sprinkles and  of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

Possible Answers:

Correct answer:

Explanation:

The phrase, «how much more» tells as that we want to find the difference, so we subtract.  

Report an Error

A baker used  of a package of sprinkles and  of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

Possible Answers:

Correct answer:

Explanation:

The phrase, «how much more» tells as that we want to find the difference, so we subtract. 

Report an Error

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All Common Core: 4th Grade Math Resources

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Tasks of increased difficulty «Fractions» | Educational and methodical material in mathematics (Grade 4) on the topic:

2.3. ADDITION AND SUBTRACTION OF REGULAR FRACTIONS

In the real educational process, not so many tasks for adding and subtracting fractions with the same denominators are required — there will be enough tasks from the textbook. We will pay more attention to problems in which the entire quantity is taken as a unit. Moreover, at first it is better to represent it as 2/2, 3/3, etc. quantities.

163. The girl read 2/5, then another 1/5 of the book. What part of the book did she read?

164. Tourists covered 1/7, then another 3/7 of the entire route. What part of the route do they have left to go?

165. Two tractor drivers mowed 5/9 of the meadow, and the first tractor driver mowed 2/9 of the meadow. What part of the meadow was mowed by the second tractor driver?

166. The first tractor driver plowed 2/7 fields, the second — 3/7 fields. Together they plowed 10 hectares. Determine the area of ​​the field.

167. Solve problems 150 (a-c) using fraction subtraction.

168. Solve problems 154 (1-2) using fraction subtraction.

169. 1) Sparrows were sitting on a branch. When the third part of the sparrows flew away, there were 6 of them left. How many sparrows were on the branch initially?

2) Someone has spent 3/4 of his money and has 200 rubles left. How much money did he have?

3) On the first day, the tourists covered 2/5 of the planned route, and on the second day, the remaining 15 km. What is the length of the route?

4) Vasya has 200 stamps in his collection. Over the past year, the number of stamps in the collection has increased by 1/4. How many stamps were in the collection a year ago?

170. Before lunch, the turner completed 2/8 of the task, after lunch — 3/8 of the task, after which he had 24 parts to turn. How many parts did he have to grind?

171. From «Arithmetic» by L.N. Tolstoy. Husband and wife took money from the same chest, and nothing was left. The husband took 7/10 of all the money, and the wife 690 rubles. How much was all the money?

We advise you to pay attention to problems 172–173, which allow several ways of solving. The necessary recommendations are given in the «Answers and Tips» section.

172. Solve problems from Egyptian papyri in two ways.

1) The quantity and its fourth part give together 15. Find
quantity.

2) The number and half of it is 9. Find the number.

173. Write a problem similar to the Egyptian problems and solve it in two ways.

Starting from the next problem, addition and subtraction of fractions with different denominators occur in the solutions. If this material was not studied in the 5th grade, then the remaining tasks related to fractions should be postponed until the 6th grade.

174. a) Every hour the first pipe fills 1/2 of the pool and the second 1/3 of the pool. What part of the pool is filled by both pipes in 1 hour of joint work?

b) The first brigade can complete 1/12 of the task per day, and the second — 1/8 of the task. What part of the task will two teams complete in 1 day of joint work?

c) A passenger car travels 1/10 of the distance between cities per hour, and a truck 1/12 of this distance. What part of this distance do the cars approach each other in 1 hour when moving towards each other?

175. a) Two tractor drivers plowed 2/3 fields in 1 day of joint work. The first tractor driver plowed 1/2 of the field. What part of the field was plowed by the second tractor driver?

b) Two cars traveling towards each other approached 1/3 of the distance between two cities in 1 hour. The first car covered 1/8 of this distance. What fraction of the total distance was traveled by the second car?

c) After two pipes, 1/3 of the pool is filled every hour. Through the first pipe, 1/10 of the pool is filled in 1 hour. What part of the pool is filled in 1 hour through the second pipe?

176. First, 1/2 of the water in it was poured out of the barrel, then 1/3, 1/15 and 1/10. What part of the water was poured out?

177.* I drank half a cup of black coffee and refilled it with milk. Then I drank 1/3 cup and topped it up with milk. Then I drank 1/6 cup and topped it up with milk. Finally, I drank the contents of the cup to the end. What did I drink more: coffee or milk?

178. Ancient problems. 1) Two pedestrians came out at the same time towards each other from two villages. The first one can cover the distance between two villages in 8 hours, and the second one in 6 hours. What part of the distance do they approach in 1 hour?

2) Three carpenters were hired to build the bath; the first did on day 2/33 of all the work, the second on 1/11, the third on 7/55. What fraction of the total work did they all do in a day?

3) 4 scribes were hired to copy the essay; the first one could rewrite the essay alone in 24 days, the second in 36 days, the third in 20 and the fourth in 18 days. What part of the essay will they rewrite in one day if they work together?

179. 1) The typist retyped the third part of the manuscript, then another 10 pages. As a result, she retyped half of the entire manuscript. How many pages are in the manuscript?

2) Old problem. A passer-by who caught up with another asked: “How far is it to the village we have ahead of us?” Another passer-by answered: “The distance from the village from which you are walking is equal to a third of the entire distance between the villages, and if you walk another 2 versts, then you will be exactly in the middle between the villages.” How many versts are left for the first passer-by to walk?

180. Adam Rize’s task (XVI century). Three won some amount of money. The first accounted for 1/4 of this sum, the second 1/7, and the third 17 florins. How big is all the winnings?

Lesson on the topic «Addition and subtraction of ordinary fractions». Grade 5 — UchMet

Synopsis
lesson on the topic

“Addition
and subtraction of ordinary fractions”

5
class

Soldatova
Svetlana Anatolyevna

teacher
mathematics of the first category

MOU
Uglich Physics and Mathematics Lyceum

2017
year

Basic Tutorial:
 N.Ya.
Vilenkin and others. “Mathematics. Grade 5″

Lesson type: Lesson
learning new material

Goals and objectives:

  1. Train
    addition
    and subtraction of fractions with the same
    denominators

  2. Educate
    respect for each other, ability to work
    in pairs.

  3. Develop
    skills
    organization of educational work, culture
    mathematical speech.

Lesson progress:

.
Organizing time.

— We began to study
large and significant topic «Ordinary
fractions”, got acquainted with the comparison
fractions with the same denominators,
concept of «right» and «wrong»
fractions, and today we learn that fractional
numbers, just like natural numbers,
add and subtract. But first
recall the main questions of the previous
topics.

.
Oral exercise:

1)

;

;

;
;
;

;

;

;
;

.

—
Name fractions with the same denominators.

,

—
Compare fractions
.

—
How to compare fractions with the same
denominators?

—
Name the fractions with the same numerators.

,

.

—
Compare fractions
.

.

—
How to compare fractions with the same
numerators?

—
Which of these points

and

lies to the left and why?

—
Name those fractions that are less than 1. How
they’re called?

—
Name those fractions that are equal to 1. How
they’re called?

—
Name those fractions that are greater than 1. How
they’re called?

—
What is an improper fraction?

2)
— 40 swans swam on the pond. Of them 30
were white. What fraction of all swans
were white swans?

3)
What fraction of a kilometer is 15 meters?
137 m?

— What part of the day
are 7 hours? 30 minutes?

— What fraction of an hour
are 11 minutes? 1 sec? 5 sec?

Learning new things
material.

  • Draw
    segment AB
    equal to 7 cm.

  • Designate
    segment AO equal

    segment AB.

  • How
    It can be done?

  • Designate
    another segment OD
    equal

    segment AB.

Conclusion:
At
adding fractions with the same denominators
numerators are added, and the denominator
leave the same.

  • I
    I will change the condition, and you try to solve
    inverse problem: How, knowing segments AD
    and OD
    find segment AO?

Output :
subtracting fractions with the same
denominators from the numerator of the reduced
subtract the numerator of the subtrahend, and
the denominator remains the same.

Fastening
studied material

  1. Commented
    exercises.

a)

;
b)

;
with)

;
e)

.

  1. Independent
    Job.

1
variant

2
variant

№1011

a)
;
in);

e)
;
and).

№1011

b)
;
G);

e)

;
h).

Mutual verification.

  1. Problem solving.

1) Orally. (#1007) B
the first day the potatoes were planted on

site, and on the second day — on

site. What part of the plot was
planted with potatoes in these 2 days?

2) Orally. (#1009) For
planted for two days

fields. AT
first day sown

fields. What
part of the field was sown on the second day?

3) (No. 1014) For planting
forests allocated a plot of 300 hectares.
Spruce landed on

plot,
and pine — on

site.
How many hectares are occupied by spruce and pine
together?

Solution:

1
way.

1)


— occupied by spruce.

2)


— occupied by pine.

3)


— occupied by pine and spruce.

Answer: 210
ha.

2
way:

1)

(h)
— The entire area is occupied by pine and spruce.

2)


— occupied by pine and spruce.

Answer: 210 ha.

If the children offer
different ways of solving
consider both and then suggest
compare and conclude that
the second way is more rational.

Repeat earlier
studied material.

  1. Problem solving
    to find the part of a number and a number
    on his part.

1) Igor scored 48
mushrooms, of which

boletus.
How many boletus did Igor score?

2) Igor scored 48
white mushrooms, which is

all mushrooms.
How many mushrooms did Igor collect in total?

  • Tasks have
    the same numeric data. What can
    say about their solutions?

  • In what task
    you need to find out what the part is equal to, knowing
    whole?

  • Choose a scheme
    corresponding to the condition of the first task.

  • How do you define
    type of the second task? (Finding a number
    for his part)

Solving the problem by
options: option 1 — task 1), option 2
– task 2).

  1. Equation solution :

  1. Problem solving
    using equations:

Area of ​​the first
plot is 5 times larger than the area of ​​the second
site.

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