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Adding Fractions on a Number Line

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Adding Fractions on a Number Line
CCSS.MATH.CONTENT.4.NF.B.3.A

Basics on the topic Adding Fractions on a Number Line

Content

How to Add Fractions on a Number Line

  • First, check that the fractions have like, or common, denominators.
  • Next, divide the number line into equal parts between whole numbers as shown by the denominators.
  • Then, locate the first fraction on the number line.
  • Finally, jump forward the number of parts as shown by the numerator of the second fraction to find the sum.

Remember to simplify the fraction if you can.

Transcript Adding Fractions on a Number Line

"While I fill the tank, keep your eye on the fuel gauge!" "You got it partner, I'll calculate the total fuel we have!" Let's help Tank calculate the total amount of fuel in the submarine by adding fractions on a number line. We can use a number line like this to help us when adding fractions. To add fractions on a number line, first, check that the fractions have LIKE, or common, denominators. One-eighth and five-eighths have the same number on the bottom, so they have like denominators. Next, use the number in the denominator to divide the number line into equal parts between the whole numbers. Eight is the denominator, so make eight equal parts between zero and one, and label them like this. Now find one-eighth on the number line, which is here. Then identify the numerator of the fraction we are adding, which is five. Jump five parts forward from one-eighth. We land on six-eighths. One-eighth plus five-eighths is six-eighths. Finally, simplify the sum if possible. To simplify fractions, find a common factor for the numerator and denominator. Six-eighths can be simplified by dividing the numerator and denominator by two, making the fraction three-fourths. Now we have looked at the steps needed to add fractions on a number line, let's help calculate how much gas Axel and Tank now have in their submarine! The submarine had two-sixths of gas left, and Axel added three-sixths to the submarine. With the number line ready, what is the first step? First, check that the fractions have like, or common, denominators. Since both fractions have a six for the denominator, they have like denominators. What is the next step? Divide the number line into equal parts between zero and one as shown by the denominator, which is six, and label each part on the number line. What should we do next? Find the first fraction, two-sixths, which is here. How do we find the sum? We identify the numerator of the fraction we are adding, which is three, and jump three parts forward from two-sixths. The sum of two-sixths plus three-sixths is five-sixths. Can five-sixths be simplified? Five-sixths cannot be simplified since no factor below six goes into five and six, except for one, so we leave the sum as five-sixths. While Axel finishes up and pays for the gas, let's review! Remember, when adding fractions on a number line, first, check that the fractions have like, or common, denominators. Next, divide the number line into equal parts between whole numbers as shown by the denominators. Then, locate the first fraction on the number line. Finally, jump forward the number of parts as shown by the numerator of the second fraction to find the sum. Remember to simplify the fraction if you can. "Alright, are you ready to hit the road, Tank?" "I was born ready, partner!"

Adding Fractions on a Number Line exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Adding Fractions on a Number Line.
  • What are the steps to add fractions?

    Hints

    Before you start adding the fractions, what do you need to check is the same?

    Once you have divided your number line into equal parts, what do you need to locate?

    Solution

    First, check that the fractions you are adding have the same denominator.

    Next, divide the number line into equal parts as shown by the denominators.

    Then, locate the first fraction on the number line.

    Finally, count forward the number of parts shown by the numerator on the second fraction.

  • How much gas is in the the tank?

    Hints

    Each interval on the number line goes up in steps of $\frac1 6$. How many jumps will be needed to add $\frac3 6$?

    There was already $\frac1 6$ in the tank so start your jumps from there.

    Solution
    • We are adding $\frac1 6$ + $\frac3 6$, so we start at $\frac1 6$.
    • Next, look at the numerator of the fraction we are adding; in $\frac3 6$ the numerator is 3, so we make 3 jumps.
    • This gets us to $\frac4 6$.
    • So $\frac1 6$ + $\frac3 6$ = $\frac4 6$
  • Which number lines show the correct way of adding the fractions?

    Hints

    The number line should be divided into equal parts based on the denominator. What is the denominator in the fractions that Axel and Tank are adding here?

    The friends added $\frac1 9$ and $\frac6 9$. There are two ways to add these fractions, depending on which order they are added.

    To add $\frac1 9$ and $\frac6 9$, the friends could start at $\frac1 9$ and make 6 jumps, or they could start at $\frac6 9$ and make 1 jump.

    Solution
    • There are two correct options to add $\frac1 9$ + $\frac6 9$.
    • Both correct options have the number line divided into 9 equal parts because the denominators in $\frac1 9$ + $\frac6 9$ are 9.
    • To solve starting with the smaller fraction: $\frac1 9$ + $\frac6 9$, start at $\frac1 9$ and jump forward 6.
    • To solve starting with the larger fraction: $\frac6 9$ + $\frac1 9$, start at $\frac6 9$ and jump forward 1.
  • Practice adding fractions.

    Hints

    To add the fractions on a number line, first partition the number line to the number of parts that is in the denominator.

    Find the first fraction on the number line, then count forward by the numerator of the second fraction.

    Can you simplify your answer by dividing the numerator and denominator by the same factor?

    Solution
    • $\frac2 8$ + $\frac2 8$ = $\frac1 2$.
    Start on $\frac2 8$, count forward by two, which takes you to $\frac4 8$. $\frac4 8$ can be simplified to $\frac1 2$ by dividing both the numerator (4) and the denominator (8) by 4.
    • $\frac3 6$ + $\frac1 6$ = $\frac2 3$.
    Start on $\frac3 6$, count forward by one, which takes you to $\frac4 6$. $\frac4 6$ can be simplified to $\frac2 3$ by dividing both the numerator (4) and the denominator (6) by 2.
    • $\frac1 7$ + $\frac3 7$ = $\frac4 7$.
    Start on $\frac1 7$, count forward by three, which takes you to $\frac4 7$. This cannot be simplified any further.
    • $\frac3 5$ + $\frac2 5$ = 1.
    Start on $\frac3 5$, count forward by two, which takes you to $\frac5 5$. $\frac5 5$ can be simplified to 1 by dividing both the numerator (5) and the denominator (5) by 5.
  • Add the fractions on the number line.

    Hints

    Start by locating the first fraction in the equation on the number line.

    How many parts do you need to jump forward?

    The numerator in the second fraction ($\frac4 7$) is 4, so jump forward 4 parts.

    Solution
    • Start at $\frac2 7$
    • As we are adding $\frac4 7$, look at the numerator of that fraction.
    • The numerator of $\frac4 7$ is 4, so we make 4 jumps forward.
    • This gets us to $\frac6 7$.
    • So $\frac2 7$ + $\frac4 7$ = $\frac6 7$.
  • Adding and simplifying fractions.

    Hints

    To simplify a fraction, divide the numerator and denominator by the same factor, in this example $\frac{4}{10}$ is simplified to $\frac2 5$ by dividing both by 2.

    Sometimes it may be a fraction in the question that has already been simplified and needs expanding. For example, $\frac1 3$ can be expanded by multiplying both the numerator and denominator by 2 to get $\frac2 6$.

    Solution

    1) This answer is correct. $\frac3 8$ + $\frac3 8$ = $\frac6 8$. Divide numerator and denominator by 2 to get $\frac3 4$.

    2) This answer is correct. $\frac4 9$ + $\frac1 3$ = $\frac7 9$. First expand $\frac1 3$ by multiplying the numerator and denominator by 3 to get $\frac3 9$. $\frac4 9$ + $\frac3 9$ = $\frac7 9$.

    3) This answer is incorrect. $\frac2 6$ + $\frac2 6$ = $\frac4 6$. Divide numerator and denominator by 2 to get $\frac2 3$.

    4) This answer is incorrect. $\frac{4}{10}$ + $\frac{4}{10}$ = $\frac{8}{10}$. Divide numerator and denominator by 2 to get $\frac4 5$.

    5) This answer is correct. $\frac{3}{12}$ + $\frac{5}{12}$ = $\frac{8}{12}$. Divide numerator and denominator by 4 to get $\frac2 3$.

    6) This answer is correct. $\frac{1}{16}$ + $\frac{1}{16}$ + $\frac{2}{16}$ = $\frac{4}{16}$. Divide numerator and denominator by 4 to get $\frac1 4$.