Using models to add and subtract fractions

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Intros
Lessons
  1. What are fractions?
    • What is a proper fraction?
    • What is an improper fraction?
    • What is a mixed number or mixed fraction?
    • How to represent fractions on a number line?
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Examples
Lessons
  1. Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.
    Using models to add and subtract fractions

    1. Using models to add and subtract fractions

    2. Using models to add fractions

    3. Using models to subtract fractions

    4. Using models to perform fraction additions
  2. Use a number line to calculate. Write the answer in lowest terms.
    1. 57+17\frac{5}{7}+\frac{1}{7}
    2. 2818\frac{2}{8}-\frac{1}{8}
  3. Each act in a play was 12\frac{1}{2} hour long. There were 3 acts. How long was the play? Include a number line with your answer.
    1. The diagram shows the layout of an aquatic centre. The pool took up 28\frac{2}{8} of the aquatic centre and the stands took up 38\frac{3}{8} of the aquatic centre. What is the difference between the amount of space taken up by the pool versus the stands?
      adding and subtracting fractions using model
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      Practice
      Topic Notes
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      In this section, we will write addition or subtraction statements involving fractions for given diagrams. We were introduced to addition and subtraction statements in previous sections. In this section, we will also be asked to use diagrams to solve word problems involving the addition and subtraction of fractions.

      How to add fractions

      Before we begin this chapter, make sure you've got a good grip on prime factorization and divisibility rules.

      When adding fractions, the first thing you'll have to do is make sure you have common denominators. This means that the number at the bottom of your fractions have to be the same. If your denominators aren't the same, you'll have to convert them so that they are.

      You can get common denominators by taking the LCM (least common multiple) of the numbers in your denominator. Then you'll be able to add the numerators as you would with regular numbers when you carry out addition.

      How to subtract fractions

      When subtracting fractions, you'll also have to make sure that the denominators are the same. After you've found the common factors for the denominators, you can once again carry out subtraction.

      Let's try out practice problems to see how this works. We'll demonstrate the concept using models to add fractions and using models to subtract fractions. This means you'll learn how to visually add and subtract fractions.

      Example problems

      Question 1:

      Use a number line to calculate. Write the answer in lowest terms.

      57+17\frac{5}{7} + \frac{1}{7}

      Solution:

      So let's first draw the number line. Look at it and you see the number line from 0 to 1 is divided into 7 sections. This is because we are dealing with a denominator of 7

      Divide 0 to 1 into 7 intervals becuase of a denominator of 7
      Divide 1 into 7 intervals (denominator = 7)

      If the denominator is 7, one way to represent 1 in fraction form is 77\frac{7}{7} = 1. With the number line in 7 sections, we can calculate 57+17\frac{5}{7} + \frac{1}{7} on the number line:

      Look at 57\frac{5}{7}, it is on this location of the number line

      Locate the position of 5/7 in the area of 1 divided into 7 small segments.
      Locate five seventh on the seven small segments

      And we are adding 17\frac{1}{7}, and that's the result

      Add one seventh into the previous fraction of five seventh.
      Add one seventh to the previous fraction

      And our final answer is 67\frac{6}{7}

      Question 2:

      Use a number line to calculate. Write the answer in lowest terms.

      2818\frac{2}{8} - \frac{1}{8}

      Solution:

      So, let's draw the number line again. Look at it and you'll see the number line from 0 to 1 is divided into 8 sections. This is because we are dealing with a denominator of 8

      Divide one into 8 small segments because of a denominator of 8.
      Divide 1 into 8 segments (denominator = 8)

      If the denominator is 8, one way to represent 1 in fraction form is 88\frac{8}{8} = 1. With the number line in 8 sections, we can calculate 2818\frac{2}{8} - \frac{1}{8} on the number line:

      Look at 28\frac{2}{8}, it is on this location of the number line

      Look at the location of two eighth on the intervals between 0 and 1.
      Locate two eighth

      And we are subtracting 18\frac{1}{8}, and that's the result

      Subtract one eighth from the previous fraction.
      Subtract one eighth

      And our answer is 18\frac{1}{8}

      Question 3:

      Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.

      A diagram with areas divided into small segments
      Diagram provided for statement

      Solution:

      We see the plus sign. So we are dealing with an addition. Each of the large rectangles represents a fraction. Each rectangle is divided into 20 sections. So 20 is the denominator. The shaded area represents the nominator.

      So the first box:

      Representation of fractions according to the diagram provided
      Representation in fraction form

      It represents 1020\frac{10}{20}

      And the second box:

      Another representation in fractions according the the diagram provided
      Fraction representation

      It represents 220\frac{2}{20}

      So,

      1020+220=1220\frac{10}{20} + \frac{2}{20} = \frac{12}{20}

      Addition of two fractions
      Addition of two fractions

      The question asks us to write the answer in the lowest terms. So, we need to look for the common factor of 12 and 20 in order to simplify the answer. Turns out 4 is the common factor. So, we'll divide 4 to the answer,

      12÷420÷4=35\frac{12 \div 4}{20 \div 4} = \frac{3}{5}

      So

      35\frac{3}{5}

      is the final answer.

      Question 4:

      Write the addition or subtraction statement for the diagram. Write the answer in the lowest terms.

      Addition or subtraction statement for the diagram.
      Statement for diagram of addition or subtraction

      Solution:

      We see the minus sign. So we are dealing with a subtraction. Each of the rectangles represents a fraction. Each box is divided into 6 sections. So 6 is the denominator. The shaded area represents the nominator

      So the first box:

      The fraction of the first box provided in the diagram
      Fraction of the first box

      It represents 46\frac{4}{6}

      And the second box:

      The fraction of the first box provided in the diagram
      Fraction of the second box

      It represents 26\frac{2}{6}

      So,

      4626=26\frac{4}{6} - \frac{2}{6} = \frac{2}{6}

      Subtraction of two fractions provided in the diagram
      Subtraction of two fractions

      The question asks us to write the answer in the lowest terms. So, we need to look for the common factor of 2 and 6 in order to simplify the answer. Turns out 2 is the common factor. So, we divide 2 to the answer,

      2÷26÷2=13\frac{2 \div 2}{6 \div 2} = \frac{1}{3}

      So

      13\frac{1}{3}

      is the final answer.

      Want to see an interactive diagram to see more of how to subtract fractions using a number line? Try this one out!

      Next up, learn how to multiply whole numbers and fractions, and divide fractions with whole numbers. You can also learn how to multiply proper fractions.