Exercise on Addition of Similar Fractions

Here are some exercises on addition of similar fractions. Do your best before reading the solutions and answers below. You can download the printable version below.

Add the following fractions.

1.) \dfrac {1}{5} +  \dfrac {2}{5}

2.) \dfrac {3}{8} +  \dfrac {1}{8}

3.) \dfrac {1}{7} +  \dfrac {2}{7} + \dfrac {3}{7}

4.) \dfrac {5}{6} +  \dfrac {1}{6}

5.) \dfrac {5}{12} +  \dfrac {11}{12}

6.) \dfrac {7}{3} +  \dfrac {2}{3}

7.) \dfrac {2}{15} +  \dfrac {5}{15}

8.) \dfrac {2}{9} +  \dfrac {3}{9} + \dfrac {1}{9}

9.) \dfrac {5}{6} +  \dfrac {3}{6}

10.) 4 \dfrac {1}{4} + 2 \dfrac {3}{4}

Solutions/Answer key:

1.) \dfrac {1}{5} +  \dfrac {2}{5} = \dfrac {3}{5}

2.) \dfrac {3}{8} +  \dfrac {1}{8} = \dfrac {4}{8} =  \dfrac {1}{2}

3.) \dfrac {1}{7} +  \dfrac {2}{7} + \dfrac {3}{7} = \dfrac {6}{7}

4.) \dfrac {5}{6} +  \dfrac {1}{6} = \dfrac {6}{6} = 1

5.) \dfrac {5}{12} +  \dfrac {11}{12} = \dfrac {16}{12} = 1 \dfrac {4}{12}  = 1 \dfrac {1}{4}

6.) \dfrac {7}{3} +  \dfrac {2}{3} = \dfrac {9}{3} = 3

7.) \dfrac {2}{15} +  \dfrac {5}{15} = \dfrac {7}{15}

8.) \dfrac {2}{9} +  \dfrac {3}{9} + \dfrac {1}{9} = \dfrac {6}{9} = \dfrac {2}{3}

9.) \dfrac {5}{6} +  \dfrac {3}{6} = \dfrac {8}{6} = 2 \dfrac {2}{6} =  2 \dfrac {1}{3}

10.) 4 \dfrac {1}{4} + 2 \dfrac {3}{4} = 6 \dfrac {3}{4}

Exercise on Addition of Similar Fractions (110 downloads)

Factoring Tutorial Series

Below are the tutorials on Factoring. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Basic Concepts of Factoring
Lesson 2: Factoring Polynomials with Common Monomial Factor
Lesson 3: Factoring Polynomials by Grouping Part 1
Lesson 4: Factoring Polynomials by Grouping Part 2
Lesson 5: Factoring Perfect Square Trinomials
Lesson 6: Factoring General Trinomials Part 1
Lesson 7: Factoring General Trinomials Part 2
Lesson 8: Factoring General Trinomials Part 3
Lesson 9: Factoring Difference of Two Squares
Lesson 10: Factoring Sum and Difference of Two Cubes
Lesson 11: Factoring Polynomials with More than 2 Factors

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Clock Word Problem Solving Series

Below are the tutorials on Clock Word Problem Series. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Introduction to the Clock Problems Tutorial Series
Lesson 2: Clock Problems: Formula for the Amount of Rotation of the Hour Hand
Lesson 3: DERIVATION of the Amount of Rotation of the Hour Hand Given the Time
Lesson 4: Derivation of the Formula for the Amount of Rotation of the Minute Hand
Lesson 5: Derivation of the Formula for Calculating the Angle Between the Hands of the Clock
Lesson 6: Applying the Clock Angle Problem Formulas

to be continued…

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Angle Sum Tutorial Series

Below are the tutorials on Angle Sum Theorem. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: A Brief Review of the Concept of Angles
Lesson 2: Proof that The Sum of the Interior Angles of Triangles is 180 degrees
Lesson 3: Proof that The Sum of the Interior Angles of a Quadrilateral is 360 degrees
Lesson 4: Proof that The Sum of the Interior Angles of a Pentagon is 540 degrees
Lesson 5: Sum of the Interior Angles of Any Polygon (Derivation)

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Time Calculation Tutorial Series

Below are the tutorials on solving problems involving time calculation. All links point videos on the Sipnayan Youtube channel. The link to the complete Playlist can be found here.

  1. How to Convert Time in Minutes to Hours-and-Minutes
  2. How to Convert Time in Hours-Minutes to Minutes
  3. How to Add Time in Hours and Minutes Part 1
  4. How to Add Time in Hours and Minutes Part 2
  5. How to Subtract Time in Hours and Minutes Part 1
  6. How to Subtract Time in Hours and Minutes Part 2

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Downloadable PDF Worksheet on Adding Similar Fractions

The video below is a tutorial on addition of similar fractions. If you are not familiar with the topic yet, you can watch it first before answering the practice exercises below. 

Add the following fractions. If the answer is in improper fraction, convert to mixed number. All answers must be in lowest terms.

Questions

1.) \displaystyle \frac{1}{7} + \frac{2}{7}

2.) \displaystyle\frac{2}{9} + \frac{5}{9}

3.) \displaystyle\frac{1}{15} + \frac{2}{15} + \frac{4}{15}

4.) \displaystyle\frac{5}{16} + \frac{7}{16} + \frac{3}{16}

5.) \displaystyle\frac{1}{12} + \frac{5}{12}

6.) \displaystyle\frac{3}{8} + \frac{5}{8}

7.) \displaystyle\frac{5}{9} + \frac{8}{9}

8.) 3 \displaystyle\frac{4}{13} + \frac{5}{13}

9.) 7 \displaystyle\frac{3}{20} + 2 \frac{7}{20}

10.) 5 \displaystyle\frac{2}{20} + \frac{3}{10}

Answers

1.) \frac{3}{7}

2.) \frac{7}{9}

3.) \frac{7}{15}

4.) \frac{15}{16}

5.) \frac{1}{2}

6.) 1

7.) 1 \frac{4}{9}

8.) 3 \frac{9}{13}

9.) 9 \frac{1}{2}

10._ 5\frac{2}{5}

You may download the pdf file of the questions above here: Addition of Similar Fractions (133 downloads)  

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Addition of Similar Fractions (133 downloads)

LCM and GCF Word Problems Set 1

1.) What is the LCM of 12, 8, and 5?

a.) 120                        b.) 72                          c.) 60                           d.) 40

2.) Fe has 12 apples, 16 oranges, and 24 chicos. She wants to put all of them into baskets with each basket having the same number of each kind of fruit and none is left over. What is the largest number of baskets that Fe need?

a.) 2                             b.) 4                            c.) 6                             d.) 12

3.) In a terminal, green buses leave every 15 minutes and blue buses leave every 20 minutes. If a green bus left at 9:00 am, what time will a green and a blue bus leave at the same time?

a.) 9:30 am                 b.) 9:40 am                 c.) 9:45 am                 d.) 10:00 am

4.) A charity organization will be giving out 450 packs of noodles, 600 cans of sardines and 300 bags of rice. What is the most number of families that can receive the items if each family will receive the same number of each item and no item is left over?

a.) 150                        b.) 300                        c.) 450                        d.) 600

5.) Consider the following sequence of numbers:

5, 10, 15, 20, 25, 30,…
8, 16, 24, 32, 40, 48,…
9, 18, 27, 36, 45, 54,…

What is the first common number that will appear in the three sequences?

a.) 240                        b.) 320                        c.) 360                        d.) 420

6.) James has two types of wires. One wire is 72 inches and the other wire is 84 inches. He wants to cut both pieces so that all of the pieces have the same length. If he wants the pieces to be as long as possible and no wire is to be left over, how long should each piece be?

a.) 6 in                        b.) 8 in                        c.) 12 in                      d.) 13 in

7.) One clock chimes every 20 minutes and other clock chimes every 50 minutes. if the clock chimes at the same time at 10:00 am, what time will the two clocks chimes again at the same time?

a.) 11:20 am               b.) 11:40 am              c.) 11:50 am               d.) 12:00 pm

8.) Lara baked 16 chocolate cookies and 32 oatmeal cookies. She wants to put it on plates. If she wants all the plates to be identical, with no cookies left over, what is the greatest number of plates that can she prepare?

a.) 4                             b.) 8                            c.) 12                           d.) 16

9.) Red, green, blue light blink every 200 milliseconds, 300 milliseconds, and 400 milliseconds respectively. If the three lights blink at the same time, in how many milliseconds will they blink at the same time, again?

a.) 500 ms.                 b.) 600 ms.                 c.) 700 ms.                  d.) 1200 ms.

10.) A rectangle is to be covered with squares with the same size with no gaps, overlaps, or excess. If its dimension is 36 by 42 inches, what is the largest possible side length of each square?

a.) 7                             b.) 6                            c.) 3                             d.) 2

Answers:
1.) a
2.) b
3.) d
4.) c
5.) c
6.) c
7.) b
8.) d
9.) d
10.) b

Factoring Tutorial Series

Below are the tutorials on solving problems involving discounts. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Basic Concepts of Factoring
Lesson 2: Factoring Polynomials with Common Monomial Factor
Lesson 3: Factoring Polynomials by Grouping Part 1
Lesson 4: Factoring Polynomials by Grouping Part 2
Lesson 5: Factoring Perfect Square Trinomials
Lesson 6: Factoring General Trinomials Part 1
Lesson 7: Factoring General Trinomials Part 2
Lesson 8: Factoring General Trinomials Part 3
Lesson 9: Factoring Difference of Two Squares
Lesson 10: Factoring Sum and Difference of Two Cubes
Lesson 11: Factoring Polynomials with More than Two Factors

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Factorial Notation Tutorial Series

Below are the tutorials on solving problems involving discounts. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: How to Use the Factorial Notation Part 1
Lesson 2: How to Use the Factorial Notation Part 2
Lesson 3: Practice Exercises on Writing Expressions in Factorial Form

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Discount Tutorial Series

Below are the tutorials on solving problems involving discounts. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Discount Sample Problem 1
Lesson 2: Discount Sample Problem 2
Lesson 3: Discount Sample Problem 3
Lesson 4: Discount Sample Problem 4
Lesson 5: Discount Sample Problem 5
Lesson 6: Discount Problems and Rate, Base, and Percentage

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Circles Tutorial Series

Below are the tutorials on Circles. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Introduction to Circles Part 1 – Basic Terms
Lesson 2: Introduction to Circles Part 2 – More Basic Terms
Lesson 3: Proof: If the Radius is Perpendicular to the Chord, it Bisects the Chord
Lesson 4: Proof: If the Radius Bisects the Chord, It is Perpendicular to the Chord
Lesson 5: Radius Perpendicular to a Chord – Exercises

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Linear Inequalities Tutorial Series

Below are the tutorials on Linear Inequalities. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Introduction to Linear Inequalities in One Variable
Lesson 2: Practice Exercises about Inequality Signs
Lesson 3: Interval Notation and Graphs Part 1
Lesson 4: Interval Notation and Graphs Part 2
Lesson 5: Interval Notation and Graphs Exercises
Lesson 6: Compound Inequalities – Using AND
Lesson 7: Graphing Compound Inequalities
Lesson 8: Solving Linear Inequalities in One Variable
Lesson 9: Solving Compound Inequalities with AND
Lesson 10: Compound Inequalities – Using OR
Lesson 11: Solving and Graphing Compound Inequalities with OR
Lesson 12: Checking Inequalities
Lesson 13: Linear Inequalities in One Variable (Summary)

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Venn Diagrams Tutorial Series

Below are the tutorials on operations on Venn Diagrams. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Tutorial Series 1

Lesson 1: How to Read and Interpret Venn Diagrams with 2 Categories
Lesson 2: Solving Problems Using Venn Diagrams Part 1 (2 categories)
Lesson 3: Solving Problems Using Venn Diagrams Part 2 (2 categories)
Lesson 4: Solving Problems Using Venn Diagrams Part 3 (2 categories)
Lesson 5: Solving Problems Using Venn Diagrams Part 4 (2 categories)
Lesson 6: Understanding Either and Neither in Venn Diagram Problems
Lesson 7: Venn Diagrams of Not, Only, And, Either or, Neither Nor
Lesson 8: How to Read and Interpret Venn Diagrams with 3 Categories
Lesson 9: Solving Problems Using Venn Diagrams Part 1 (3 categories)
Lesson 10: Solving Problems Using Venn Diagrams Part 2 (3 categories)
Lesson 11: Solving Problems Using Venn Diagrams Part 3 (3 categories)

Tutorial Series 2

Lesson 1: Venn Diagrams in solving Word Problems Part 1
Lesson 2: Venn Diagrams in solving Word Problems Part 2
Lesson 3: Venn Diagrams in solving Word Problems Part 3

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Piecewise Functions Tutorial Series

Below are the tutorials on piecewise functions. All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: How to Write Equations of Piecewise Functions Part 1
Lesson 2: How to Write Equations of Piecewise Functions Part 2
Lesson 3: How to Write Equations of Piecewise Functions Part 3
Lesson 4: How to Write Equations of Piecewise Functions Part 4
Lesson 5: How to Graph Piecewise Functions Part 1
Lesson 6: How to Graph Piecewise Functions Part 2
Lesson 7: How to Graph Piecewise Functions Part 3
Lesson 8: How to Graph Piecewise Functions Part 4

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Polynomial Expressions Tutorial Series

Below are the tutorials on operations on polynomial expressions All links point videos on the Sipnayan Youtube channel.  The link to the complete Playlist can be found here.

Lesson 1: Introduction to Polynomial Expressions
Lesson 2: Like and Unlike Terms
Lesson 3: Addition of Polynomial Expressions Part 1
Lesson 4: Addition of Polynomial Expressions Part 2
Lesson 5: Addition of Polynomial Expressions Part 3
Lesson 6: Subtraction of Polynomial Expressions Part 1
Lesson 7: Subtraction of Polynomial Expressions Part 2
Lesson 8: Multiplication of Polynomial Expressions Part 1
Lesson 9: Multiplication of Polynomial Expressions Part 2
Lesson 10: Multiplication of Polynomial Expressions Part 3
Lesson 11: Multiplication of Polynomial Expressions Part 4
Lesson 12: Division of Polynomial Expressions Part 1
Lesson 13: Division of Polynomial Expressions Part 2
Lesson 14: Division of Polynomial Expressions Part 3
Lesson 15: Division of Polynomial Expressions Part 4
Lesson 16: Division of Polynomial Expressions Part 5
Lesson 17: Division of Polynomial Expressions Part 6

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Absolute Value Equations and Inequalities

Below are the tutorials on absolute value equations and inequalities. All links point videos on the Sipnayan Youtube channel

Lesson 1: Meaning of Absolute Value of a Number Part 1
Lesson 2: Meaning of Absolute Value of a Number Part 2
Lesson 3: Solving Absolute Value Equations Part 1
Lesson 4: Solving Absolute Value Equations Part 2
Lesson 5: Solving Absolute Value Equations Part 3
Lesson 6: Solving Absolute Value Equations Part 4
Lesson 7: Solving Absolute Value Equations Part 5
Lesson 8: Solving Absolute Value Equations Part 6
Lesson 9: Absolute Value Equation Summary
Lesson 10: Solving Absolute Value Inequalities Part 1
Lesson 11: Solving Absolute Value Inequalities Part 2
Lesson 12: Solving Absolute Value Inequalities Part 3
Lesson 13: Solving Absolute Value Inequalities Part 4
Lesson 14: Solving Absolute Value Inequalities Part 5
Lesson 15: Absolute Value Inequalities Summary

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