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5th Grade Fraction Problems and Practice Exercises

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In 5th grade, students further their understanding of fractions by adding and subtracting fractions with unlike denominators. They also learn to multiply and divide fractions with whole numbers. If your child needs additional practice, keep reading for a fraction review and sample practice questions.

How to Solve Fraction Equations in 5th Grade

To add or subtract two fractions, both must have the same denominator. This is known as equivalent fractions. If your child is struggling with solving fraction problems with unlike denominators, follow the guidelines below.

In order to solve a problem like 3/4 + 5/6, the two fractions must have the same denominator. First, identify the common factor. For this problem, four and six are both factors of 12, so the denominator for both fractions needs to be 12. Multiply 3/4 by 3/3, so the fraction becomes 9/12. Then, multiply 5/6 by 2/2 which equals 10/12. As a result, the new addition problem should look like this: 9/12 + 10/12 = 19/12.

Practice Exercises

Addition and subtraction.

1. 1/2 - 1/4

If your child is just beginning to study fractions with unlike denominators, you may want to start out your review with easier problems to boost his or her confidence. This problem is simple because only the first fraction needs to be changed to make the fractions equivalent. Multiply 1/2 by 2/2 so that it equals 2/4. Then, solve like normal: 2/4 - 1/4 = 1/4.

2. 5/6 - 2/3

The common factor for both fractions is six. Multiply the second fraction (2/3) by 2/2, so that it becomes 4/6. Then, subtract: 5/6 - 4/6 = 1/6.

3. 6/7 + 1/8

This problem is more difficult because the only common denominator for both fractions is 56. Begin by multiplying: 6/7 x 8/8 = 48/56. Do the same for the second fraction: 1/8 x 7/7 = 7/56. Then, add: 48/56 + 7/56 = 55/56.

Multiplication and Division

Begin by turning the whole number (3) into a fraction, so the equation should look like this: 1/4 x 3/1. Then, multiply (1 x 3) / (4 x 1) = 3/4.

The answer to this problem is 8/7.

The answer for this problem is 18/8, or 9/4. Note that the answer for this problem needs to be simplified. Often, this is a step that students forget to do. Remind your child at home to always check if an answer can be simplified.

4. 5 ÷ 2/6

Because this is a division problem, remember to flip the fraction, making it a reciprocal fraction. The equation should look like this: 5 x 6/2 = 5 x 3 = 15.

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5th Grade Fractions Worksheets

In 5th Grade Fractions Worksheets we will solve how to compare two fractions, comparing mixed fractions, addition of like fractions, addition of unlike fractions , addition of mixed fractions , word problems on addition of fractions, subtraction of like fractions, subtraction of unlike fractions, word problems on subtraction of fractions, multiplications of fractions, word problems on multiplication of fractions, fraction of fraction, reciprocal of fractions, division of fractions, word problems on division of fractions.

I. Answer the following:

1. The reciprocal of 7\(\frac{1}{8}\) is ………….. .

2. 8 boys shared \(\frac{2}{5}\) of a cake equally. What fraction of the cake did each boy get?

3. Which is greater 5\(\frac{1}{7}\) or 3\(\frac{1}{7}\)?

4. What is the half of 60?

5. Find the difference between the sum and product of 2\(\frac{1}{4}\) and 1\(\frac{4}{5}\).

6. Which is greater \(\frac{23}{25}\) or 1?

7. If \(\frac{17}{19}\) of the cup is filled, then what fraction of the cup is empty?

8. A family eats 1\(\frac{2}{3}\) cakes in a meal. Will 3 cakes be enough for 2 meals?

Operations on Fractions

II. Solve the given:

(i) \(\frac{7}{10}\) + \(\frac{3}{10}\)

(ii) \(\frac{14}{25}\) - \(\frac{9}{25}\)

(iii) \(\frac{5}{7}\) + \(\frac{13}{28}\) + \(\frac{3}{4}\)

(iv) 7 - \(\frac{3}{12}\)

(v) \(\frac{8}{15}\) + \(\frac{19}{30}\) - \(\frac{4}{5}\)

(vi) \(\frac{16}{44}\) ÷ \(\frac{8}{11}\)

(vii) \(\frac{6}{31}\) × \(\frac{62}{18}\)

(viii) \(\frac{24}{50}\) ÷ \(\frac{8}{25}\)

(ix) \(\frac{13}{18}\) ÷ \(\frac{39}{36}\)

Fraction of a Fraction

III. Find the given:

(i) \(\frac{2}{10}\) of 40 mangoes

(ii) \(\frac{3}{15}\) of $75

(iii) \(\frac{3}{4}\) of 20 cups

(iv) \(\frac{3}{7}\) of 1 week

IV. Compare the given fractions and put the right sign <, > or =.

(i) \(\frac{3}{4}\) ……… \(\frac{5}{6}\)

(ii) \(\frac{5}{7}\) ……… \(\frac{15}{21}\)

(i) \(\frac{17}{34}\) ……… \(\frac{8}{32}\)

V. Convert the given fractions in lowest terms:

(i) \(\frac{15}{60}\)

(ii) \(\frac{22}{77}\)

(iii) \(\frac{18}{54}\)

(iv) \(\frac{36}{60}\)

(v) \(\frac{21}{63}\)

VI. Word Problems on Fractions:

1. The cost of comic is $57\(\frac{1}{2}\) and that of color book is $25\(\frac{1}{4}\). Which costs more and by how much?

2. Tom spent \(\frac{3}{5}\) of his money on bag and spent \(\frac{2}{7}\) of his money on stationary. What fraction of money is left with him?

3. Kate has $630. She wants to buy a bag that costs \(\frac{5}{9}\) of the amount she has. What should be the cost of the bag?

4. How many pieces of 2\(\frac{3}{4}\) m each can be cut from a string of 16\(\frac{1}{2}\) m length?

Answers on 5th Grade Fractions Worksheets are given below to check the exact answers of the questions. 

5th Grade Fractions Worksheets

I.   1.  \(\frac{8}{27}\)

2.  \(\frac{1}{20}\)

3.  5\(\frac{1}{7}\)

4.  30

7.  \(\frac{2}{19}\)

8.  No, 3\(\frac{1}{3}\) cakes required

II.  (i) 1

(ii) \(\frac{1}{5}\)

(iii) 1\(\frac{13}{14}\)

(iv) \(\frac{81}{12}\)

(v) \(\frac{11}{30}\)

(vi) \(\frac{1}{2}\)

(vii) \(\frac{2}{3}\)

(viii) \(\frac{3}{2}\)

(ix) \(\frac{2}{3}\)

III.  (i) 8 mangoes

(iii) 15 cups

(iv) 3 days

IV.  (i) \(\frac{3}{4}\) < \(\frac{5}{6}\)

(ii) \(\frac{5}{7}\) = \(\frac{15}{21}\)

(i) \(\frac{17}{34}\) > \(\frac{8}{32}\)

V.  (i) \(\frac{1}{4}\)

(ii) \(\frac{2}{7}\)

(iii) \(\frac{1}{3}\)

(iv) \(\frac{3}{5}\)

(v) \(\frac{1}{3}\)

VI. 1.  Comic cost more, $32\(\frac{1}{4}\)

2.  \(\frac{4}{35}\)

3.  $350

5th Grade Math Problems

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Fraction Word Problems (Grade 5)

These lessons, with videos, examples and solutions help Grade 5 students learn to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Related Pages Common Core for Grade 5 More Lessons for Grade 5

For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Common Core: 5.NF.2

Suggested Learning Targets

  • I can solve addition and subtraction word problems with fractions.
  • I can estimate fractions to make sense of my answer.

Solve Fraction Word Problems with Visual Bar Models

Example: Kayla weighed her Halloween treats. She counted 1/4 of a pound of lollipops and 2/7 of a pound of gobstoppers. She also counted 1/3 of a pound of mints. How many pounds of candy did Kayla have altogether?

Add mixed numbers word problems

Example: While gardening, Jan spend 1 3/4 hours planting and 2 1/8 hours trimming. What was the total hours worked by Jan in her garden?

Solve word problems involving addition of fractions - unlike denominators

Example: Matthew ran 1/6 of a mile then took a break before running another 3/4 of a mile. How far did Matthew run in all?

Subtracting Fractions From Whole Numbers Solve a word problem using bar models.

Example: A craft store has a 9-yard spool of ribbon. In the morning, a customer buys 1/5 yard of ribbon from the spool. In the afternoon, another customer buys 7/10 yard of ribbon from the spool. How much ribbon is left?

Adding and subtracting unlike fractions word problems

  • Drew and Maddy were filling the class raised garden bed with soil. Drew shoveled in 1/3 of a cubic yard, and Maddy shoveled in 1/2 of a cubic yard. How much soil did they put into the garden bed altogether?
  • Caden invited Owen over to his house. Caden shared his chocolate stash from last Halloween. He still had 4/5 of a pound of chocolate. Caden asked Owen how much chocolate he would like. Owen said that he would like 1/3 of a pound of chocolate. How much chocolate does Caden have left?

Adding and subtracting mixed numbers word problems

  • Jaida went gold panning and found 1 1/5 pounds of gold. The next day she found 3 1/4 pound more. How much total gold did Jaida find?
  • Jonathan collected 4 1/2 kilograms of filberts. He gave 2 3/4 kilograms to his friend. How many kilograms of filberts does Jonathan have now?

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grade 5 fraction problem solving

Fractions - Grade 5 Maths Questions With Solutions

Grade 5 maths multiple choice questions on fractions with answers are presented. Also Solutions and explanations are included. Note that mixed numbers are written as follows: whole part followed by a proper fraction. For example: \( 5 \dfrac{1}{2} \) is a mixed number meaning \( 5 +\dfrac{1}{2} \). More resources on fractions are included.

  • \( \dfrac{1}{1} \) only
  • \( \dfrac{2}{2} \) only
  • \( \dfrac{3}{3} \) only
  • Any fraction of the form \(\dfrac{n}{n} \) where \( n \) is a whole number
  • \( \dfrac{5}{5} \)
  • \( \dfrac{1}{5} \)
  • \( \dfrac{5}{1} \)
  • \( \dfrac{1}{1} \)
  • \( \dfrac{3}{4} \)
  • \( \dfrac{3}{8} \)
  • \( \dfrac{7}{8} \)
  • \( \dfrac{2}{14} \)
  • \( \dfrac{6}{7} \)
  • \( \dfrac{2}{7} \)
  • \( \dfrac{4}{7} \)
  • \( \dfrac{2}{15} \)
  • \( \dfrac{1}{8} \)
  • \( \dfrac{13}{15} \)
  • \( 8 \dfrac{2}{5} \)
  • \( 8 \dfrac{5}{6} \)
  • \( \dfrac{2}{5} \)
  • \( \dfrac{3}{4} \) hour
  • \( \dfrac{2}{4} \) hour
  • 1 and \( \dfrac{1}{4} \) hours
  • \( \dfrac{5}{2} \) and \( \dfrac{2}{5} \)
  • \( \dfrac{4}{3} \) and \( \dfrac{8}{6} \)
  • \( \dfrac{1}{4} \) and \( \dfrac{2}{4} \)
  • \( \dfrac{2}{3} \) and \( \dfrac{1}{3} \)
  • \( 1 \dfrac{2}{5} \)
  • \( 2 \dfrac{7}{6} \)
  • \( 2 \dfrac{1}{6} \)
  • \( \dfrac{2}{3} \)
  • \( \dfrac{5}{12} \)
  • \( \dfrac{1}{4} \)
  • \( \dfrac{7}{12} \)
  • \( \dfrac{10}{3} \)
  • \( \dfrac{10}{8} \)
  • \( \dfrac{13}{4} \)
  • \( \dfrac{5}{7} \)
  • \( \dfrac{1}{35} \)
  • \( \dfrac{14}{15} \)
  • \( \dfrac{6}{35} \)
  • \( \dfrac{35}{6} \)
  • \( \dfrac{15}{14} \)
  • \( \dfrac{3}{4}\)
  • \( \dfrac{1}{2} \)

Pin it!

  • \( \dfrac{6}{4} \)
  • \( 2 \dfrac{3}{4} \)
  • \( 1 \dfrac{3}{4} \)
  • True or false \[ 2 \dfrac{1}{2} = 2 \times \dfrac{1}{2} \] Solution
  • \( \dfrac{5}{6} \)
  • \( 3 \dfrac{5}{6} \)
  • \( 2 \dfrac{5}{6} \)
  • \( \dfrac{7}{3} \)
  • \( \dfrac{1}{3} \)
  • \( \dfrac{3}{3} \)
  • \( 4 \dfrac{7}{8} \)
  • \( 3 \dfrac{1}{8} \)
  • \( 3 \dfrac{7}{8} \)
  • \( 3 \dfrac{1}{4} \)
  • \( \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} \)
  • \( 3 \times \dfrac{1}{4} \)
  • \( 3 + \dfrac{1}{4} \)
  • \( \dfrac{4}{3} \)
  • True or false \[ \dfrac{2}{5} \gt \dfrac{3}{8} \] Solution
  • \( \dfrac{1}{3} \; , \; \dfrac{4}{9} \; , \; \dfrac{3}{5} \; , \; \dfrac{7}{6} \)
  • \( \dfrac{4}{9} \; , \; \dfrac{1}{3} \; , \; \dfrac{3}{5} \; , \; \dfrac{7}{6} \)
  • \( \dfrac{1}{3} \; , \; \dfrac{4}{9} \; , \; \dfrac{7}{6} \; , \; \dfrac{3}{5} \)
  • \( \dfrac{1}{3} \; , \; \dfrac{3}{5} \; , \; \dfrac{4}{9} \; , \; \dfrac{7}{6} \)
  • \( 4 \dfrac{2}{3} \)
  • \( 1 \dfrac{2}{3} \)
  • \( 2 \dfrac{2}{3} \)
  • \( \dfrac{8}{3} \)
  • 100 minutes
  • red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \), green: \( \dfrac{3}{16} \), black: \( \dfrac{3}{16} \), yellow: \( \dfrac{3}{16} \)
  • red: \( \dfrac{4}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \) , green:\( \dfrac{3}{32} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)
  • red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{16} \) , green: \( \dfrac{3}{16} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)
  • red: \( \dfrac{1}{4} \) , blue: \( \dfrac{1}{16} \) , orange: \( \dfrac{1}{32} \) , green: \( \dfrac{3}{32} \) , black: \( \dfrac{3}{16} \) , yellow: \( \dfrac{3}{16} \)

Answers to the Above Questions

More references and links.

More resources on fractions are included. Primary Maths (grades 4 and 5) with Free Questions and Problems With Answers Middle School Maths (grades 6,7,8 and 9) with Free Questions and Problems With Answers High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers Home Page

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  • Fractions and Mixed Numbers- Grade 6 Math Questions and Problems With Answers
  • Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
  • Interactive Tutorial on Equivalent Fractions
  • High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
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Unit 1: Decimal place value

Unit 2: add decimals, unit 3: subtract decimals, unit 4: add and subtract fractions, unit 5: multi-digit multiplication and division, unit 6: multiply fractions, unit 7: divide fractions, unit 8: multiply decimals, unit 9: divide decimals, unit 10: powers of ten, unit 11: volume, unit 12: coordinate plane, unit 13: algebraic thinking, unit 14: converting units of measure, unit 15: line plots, unit 16: properties of shapes.

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  • Fractions and mixed numbers worksheet with answers grade 5

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Lesson summary

  • INTRODUCTION
  • Download worksheets
  • Related Contents
  • Strategies for quickly mastering fractions and mixed numbers...

Get more contents on Fractions And Mixed Numbers Word Problems...

Fractions and mixed numbers worksheet with answers Grade 5 are designed to offer 5 th graders simple ways of adding, subtracting, multiplying, and dividing mixed numbers. A fraction, in simple words, is part of a whole. For instance, if an orange is cut into 4 pieces to share with four kids, what quantity of orange will each child have? Each child will have ¼. This ¼ is called a fraction of a whole (I orange). Here, 1 is the numerator, while 4 is the denominator. So, for a number to be a fraction, it must consist of a numerator and a denominator.

On the other hand, a mixed number consists of a whole number and a fraction. For instance, 3 ½. From the example, you can see that a mixed number is a combination of a whole number (3) and a fractional part (½). Once you master these skills, you will enjoy solving our thrilling fractions and mixed numbers problems. Most people find it easy to work with mixed numbers, whereas others prefer to convert the mixed number to an improper fraction before working with them.

Thus, how do we convert a mixed number to an improper fraction? To convert a mixed number to an improper fraction (3 ½) ;

  • first, multiply the whole number by the denominator 3 x 2 = 6
  • add the product to the numerator 6 + 1 = 7
  • finally, the sum (7) will become the new numerator, while the denominator (2) remains the same. So, 3 ½ converted to an improper fraction will be 7/2

unlike proper fractions whose numerators are always smaller than the denominators, the numerator of an improper fraction is always greater than the denominator.

As earlier said, we will provide plenty of fractions and mixed numbers worksheets wherein the exercises for each concept (adding, subtracting, multiplying, dividing, scaling fractions) will be formulated in its worksheet. This is so that kids should have accurate mastery of each exercise before moving on to the next. The exercises are short and easy for kids to solve in just one sitting.

Most importantly, our fractions and mixed numbers practice resource is given with a solution and answer sheet to help kids check their answers and do corrections in case of a mistake.

Adding, subtracting, multiplying, and dividing mixed numbers worksheet Grade 5

Our adding, subtracting, multiplying, and dividing mixed numbers worksheet Grade 5 offers an effective way with fun strategies of solving math operations on fractions efficiently. We will formulate a variety of simple exercises and real-life problem-solving on fractions and mixed operations for kids to practice how to add, subtract, multiply, and divide fractions in math class and real life. We have realized how challenging it usually is when we need to solve fraction problems in real life. To solve this problem, we designed an exceptional fractions and mixed numbers worksheet with answers Grade 5 for kids to learn and know how to add, subtract, multiply, and divide fractions problems effortlessly.

Adding and subtracting fractions and mixed numbers is as simple as adding and subtraction whole numbers. With fractions, you must ensure the denominators are the same before adding or subtracting. If the denominators are different, you'll need to find the least common denominator (LCD) and rewrite the fractions with equivalent denominators before adding or subtracting. As earlier said, you can convert mixed fractions to improper fractions before adding or subtracting.

Now, let's consider adding/subtracting mixed fractions with equal denominators, like 2 3/5 + 6 1/5

  • Before we begin solving, you can see that we have a common denominator, 5
  • Now, we will add the whole numbers separately, i.e., 2 + 6 = 8
  • Secondly, we add the numerators, i.e., 3 + 1 = 4.
  • So, our new numerator will be 4, while our denominator (5) remains the same.
  • 2 3/5 + 6 1/5 = 8 4/5.

Subtracting mixed fractions follows the same procedure as above.

When multiplying mixed numbers, we must convert them to improper fractions first. If you are multiplying a mixed fraction by a whole number, rewrite the whole number as a fraction with the denominator 1. There, you'll have two fractions. This goes the same with multiplying fractions of a whole. Here, you simply need to change the "of" into a multiplication sign and multiply. For instance

When multiplying a fraction by a fraction (proper or improper), first multiply the two numerators and then multiply the two denominators. Finally, simplify the new fractions (answer) or convert it back to a mixed number if necessary.

When dividing mixed numbers, we must also convert the mixed numbers to improper fractions. If you are dividing a mixed fraction by a whole number, rewrite the whole number as a fraction with the denominator 1. There, you'll have two fractions. From here, you can follow the keep-change-flip method below:

  • KEEP = Keep the first fraction as it is and leave it alone.
  • CHANGE = Change the division sign to a multiplication sign.
  • FLIP = Flip the second fraction (swap the numerator and the denominator)

Finally, solve the problem by multiplying the fractions and simplifying the answer or converting it back to a mixed number if necessary.

From the above methods of solving mixed fractions problems, you will bear with me that your kids will feel comfortable and confident in solving all fractions and mixed numbers problems, whether in math class or real life.

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Strategies for quickly mastering fractions and mixed numbers worksheet with answers grade 5

Are you in need of fun strategies for quickly mastering fractions and mixed numbers worksheet with answers grade 5? If yes! Then you are just at the right place. We will provide you with the best strategies to determine how big or small a fraction is. Unlike whole numbers, which, when we multiply, become bigger, fractions can become smaller, bigger, or even remain the same when we multiply them. As such, scaling is the best strategy to determine if a fraction is greater or less than a whole. In line with this, we will formulate easy-to-solve scaling whole numbers by fractions exercise by using the comparative signs ( , = ) to determine if an expression is smaller, bigger, or equal to a given whole.

Note the rules of scaling, which state that when you multiply by a fraction that is less than one whole, the size will be scaled down. Also, when you multiply by a fraction that is greater than one whole, the size will be scaled up. This rule will help kids determine the reasonableness of their answers when solving fraction problems.

grade 5 fraction problem solving

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grade 5 fraction problem solving

  • What is fraction? A fraction is a numerical quantity that is not a whole number. For example, ½ is a fraction of 1 as numerator and 2 as a denominator

Fractions having the same denominator are called like fractions. For example, ½,3/2, 5/2, 7/2, are all like fractions.

  • Fractions having different denominators are called, unlike fractions. For example, ½, 2/3, ¾, 4/5, are all unlike fractions
  • A fraction whose numerator is less than the denominator is called proper fraction. For example, 8/9, 7/8, 6/7, 5/6 are all proper fractions.
  • A fraction whose numerator is greater than the denominator is called improper fraction. For example, 3/2, 4/3, 5/4, 6/5 are all improper fractions.

Maths class 5 Fraction

EXAMPLE 1: Find the fraction of shaded and unshaded part.

Maths class 5 Fraction

EXAMPLE 2: Find the fraction of red balls, green balls and blue balls.

Maths class 5 Fraction

SOLUTION: Total number of balls= 10 Number of red balls= 4

Fraction of red balls= 4/10= 2/5

Fraction of green balls= 5/10= ½

Fraction of blue balls= 1/10

Fraction as a division

  • Any fraction can be expressed as a division by writing its numerator as dividend and denominator as divisor

Numerator/Denominator

= Dividend ÷ Divisor

=Dividend/Divisor

EXAMPLE 1: Write 1÷2 as a fraction.

SOLUTION: ½

EXAMPLE 2: Write 2/3 as division.

SOLUTION: 2÷3

To convert a mixed no. into an improper fraction & vice versa

  • To convert a mixed number into an improper fraction multiply the quotient with the divisor and add the product with remainder in the numerator. The denominator will contain the divisor.

Maths class 5 Fraction

  • To convert an improper fraction into a mixed number, divide the numerator of the fraction by the denominator. Write the quotient as the whole number. The remainder in the numerator and the divisor in the denominator.

Maths class 5 Fraction

Finding and checking equivalent fraction

  • To find the equivalent fraction to a given fraction, divide or multiply the numerator or denominator by the same number. (other than zero)

Maths class 5 Fraction

  • To check for equivalent fractions, we need two equivalent fraction.

Maths class 5 Fraction

SOLUTION: 2x4=8 3X3=9 8≠9

Hence, the fractions are not equal.

Maths class 5 Fraction

To find a fraction in its lowest term

  • A fraction is in its lowest term when the numerator and the denominator don’t have a common factor, except 1.
  • There are two methods of finding a fraction in its lowest term. They are: Method 1: Divide the numerator and denominator with their common factor till we are left with only the common factor 1

Method 2: Divide the numerator and denominator of the given fraction with their HCF.

Maths class 5 Fraction

To find the fraction of a number or quantity

  • Divide the number by the denominator. Then, multiply the quotient so obtained by the numerator.

EXAMPLE 1: A group has 120 children. 4/5 of them are girls. Find the number of boys.

Maths class 5 Fraction

No. of boys= (120-96) = 24

EXAMPLE 2: Find 1/4 of a year in months.

SOLUTION: A year has 12 months. ¼ X 12 = 3 months [ANS]

To compare unlike fractions

  • First find the LCM of the denominators of the given fractions.
  • Then convert the unlike fractions into equivalent like fraction with LCM as their common denominator.
  • Compare the like fractions.

Convert mixed fractions into improper fractions to compare them.

Maths class 5 Fraction

To add/subtract unlike fractions

  • Find the LCM of the denominator of unlike fraction.
  • Then convert the unlike fraction into equivalent like fraction with LCM as common denominator.
  • Add/subtract the like fraction so obtained.

EXAMPLE 1: Add/subtract ½ and/from 1/6.

SOLUTION: LCM of 2 and 6 is = 2x3=6 2| 2,6 1,3

Maths class 5 Fraction

Reciprocal of a fractional number

  • When the product of two fraction is 1, we say that each of the fraction is the reciprocal or multiplicative inverse of the other.

Maths class 5 Fraction

Division of fractions

  • Division is repeated subtraction.
  • Division by a fraction is same as multiplication by its reciprocal. 0 has no reciprocal. The reciprocal of 1 is 1. 0 divided by any non-zero number = 0

Maths class 5 Fraction

Practice these questions

Maths class 5 Fraction

  • LCM of denominators is to be found only while performing addition or subtraction of unlike fractions.
  • While multiplying fractions we can change their order, but the product remains the same. (commutative property)
  • If a fraction is multiplied by 0, the product is always zero.
  • If a fraction is multiplied by 1, the product is the same fraction.
  • A fraction is in the lowest term when the only common factor between the numerator and the denominator is 1
  • If any of the fraction is a mixed number or a whole number, change it to an improper function and then multiply.

Quiz for Fractions

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grade 5 fraction problem solving

Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions

Problem Solving using Fractions

Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less

Table of Contents

grade 5 fraction problem solving

What are Fractions?

Types of fractions.

  • Fractions with like and unlike denominators
  • Operations on fractions
  • Fractions can be multiplied by using
  • Let’s take a look at a few examples

Solved Examples

  • Frequently Asked Questions

Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.

For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction  \(\frac{1}{2}\) . 

Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .

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Proper fractions

A fraction in which the numerator is less than the denominator value is called a  proper fraction.

For example ,  \(\frac{3}{4}\) ,  \(\frac{5}{7}\) ,  \(\frac{3}{8}\)   are proper fractions.

Improper fractions 

A fraction with the numerator higher than or equal to the denominator is called an improper fraction .

Eg \(\frac{9}{4}\) ,  \(\frac{8}{8}\) ,  \(\frac{9}{4}\)   are examples of improper fractions.

Mixed fractions

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.

We express improper fractions as mixed numbers.

For example ,  5\(\frac{1}{3}\) ,  1\(\frac{4}{9}\) ,  13\(\frac{7}{8}\)   are mixed fractions.

Unit fraction

A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .

new2

Fractions with Like and Unlike Denominators

Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.

For example,  

\(\frac{1}{4}\)  and  \(\frac{3}{4}\)  are like fractions as they both have the same denominator, that is, 4.

\(\frac{1}{3}\)  and  \(\frac{1}{4}\)   are unlike fractions as they both have a different denominator.

Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.

There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.

Fractions can be Multiplied by Using:

Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor. 

Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

= \(\frac{5~+~12}{30}\)  

=  \(\frac{17}{30}\) 

( \(\frac{5}{2}~-~\frac{1}{6}\) )

= \(\frac{12~-~5}{30}\)

= \(\frac{7}{30}\)

Examples of Multiplication and Division

Multiplication:

(\(\frac{1}{6}~\times~\frac{2}{5}\))

= (\(\frac{1~\times~2}{6~\times~5}\))                                       [Multiplying numerator of fractions and multiplying denominator of fractions]

=  \(\frac{2}{30}\)

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\))                                     [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

= \(\frac{12}{5}\)

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

Let’s add \(\frac{7}{8}\)  and  \(\frac{2}{3}\)   using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.

\(\frac{7}{8}\) + \(\frac{2}{3}\)

= \(\frac{21~+~16}{24}\)    

= \(\frac{37}{24}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

Solution:  

Let’s subtract  \(\frac{12}{17}\) from \(\frac{11}{13}\)   using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.

\(\frac{11}{13}\) – \(\frac{12}{17}\)

= \(\frac{187~-~156}{221}\)

= \(\frac{31}{221}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

= \(\frac{270}{221}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25}{33}~\times~\frac{41}{45}\)                            [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\)  ]

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{1125}{1353}\)

Example 5: 

Sam was left with   \(\frac{7}{8}\)  slices of chocolate cake and    \(\frac{3}{7}\)  slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared   \(\frac{10}{11}\)  slices from the total number he had with his parents. What is the number of slices he has remaining?

To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,

=   \(\frac{7}{8}\) +   \(\frac{3}{7}\)   

=   \(\frac{49~+~24}{56}\)

=   \(\frac{73}{56}\)

To find out the remaining number of slices Sam has   \(\frac{10}{11}\)  slices need to be deducted from the total number,

= \(\frac{73}{56}~-~\frac{10}{11}\)

=   \(\frac{803~-~560}{616}\)

=   \(\frac{243}{616}\)

Hence, after sharing the cake with his friends, Sam has  \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had  \(\frac{243}{616}\)  slices of cake left with him.

Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of   \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?

First  \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters =  \(\frac{15}{8}\) x 1000 = 1875 ml

To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.

The number of oranges required for 1875 m l of juice =  \(\frac{1875}{25}\) ml = 75 oranges

To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has

=  \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups,   \(\frac{3}{8}\) th  of a cup cannot be sold alone.

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

What is a mixed fraction?

A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.

How will you add fractions with unlike denominators?

When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions. 

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