Subtracting Fractions on a Number Line
Basics on the topic Subtracting Fractions on a Number Line
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How to Subtract 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 backward the number of parts as shown by the numerator of the second fraction to find the answer. Remember to simplify the fraction if you can.
Transcript Subtracting Fractions on a Number Line
Axel and Tank are leaving the Oyster gas station! "While I drive this thing, Tank, keep an eye on the fuel gauge!" "You got it, partner! I'll track how much gas we use!" Let's help keep track of the gas left in the submarine by subtracting fractions on a number line. We can use a number line like this to help us when subtracting fractions. To subtract fractions on a number line, first, check that the fractions have like, or common, denominators. Fivesixths and threesixths have the same denominator, so they have like denominators. Next, divide the number line into equal parts between whole numbers as shown by the denominator. Six is the denominator, so make six equal parts between whole numbers and label them, like this. Now find fivesixths on the number line, which is here. Then, identify the numerator of the fraction we are subtracting, which is three. Count three parts backwards from fivesixths. What fraction do we land on? Twosixths. Fivesixths minus threesixths is twosixths. Finally, simplify the answer if possible. To simplify fractions, find a common factor for the numerator and denominator. Twosixths can be simplified by dividing the numerator and denominator by two, making the fraction onethird. Now that we have looked at the steps needed to subtract fractions on a number line, let's help Axel and Tank calculate how much gas they have left in their submarine! Axel and Tank started their journey with seveneighths of gas in their submarine, and have used sixeighths of it. With the number line ready, what is the first step? First, check that the fractions have like, or common, denominators. Since both fractions have an eight for the denominator, they have like denominators. What is the next step? Divide the number line into equal parts between whole numbers as shown by the denominator, which is eight, and label each part on the number line. What should we do next? Find the first fraction, seveneighths, which is here. How do we find the answer? Identify the numerator of the fraction we are subtracting, which is six. Count six parts backwards from seveneighths. Seveneighths minus sixeighths is oneeighth. Can oneeighth be simplified? Oneeighth cannot be simplified. We leave the answer as oneeighth. While Axel and Tank continue their submarine adventure, let's review! Remember, when subtracting fractions on a number line, first, check that the fractions have like, or common, denominators. Next, divide the number line into equal parts as shown by the denominators. Then, locate the first fraction on the number line. Finally, count backward the number of parts as shown by the numerator of the fraction being subtracted for the answer. Remember to simplify the fraction if you can. "Oh no! I can't believe we ran out of gas!" "It's okay Tank, I will go get some more gas from the Oyster station, you wait here!" "Fine, but please hurry up, I don't know where we are!"
Subtracting Fractions on a Number Line exercise

How do we subtract fractions on a number line?
HintsWhat must be checked before you divide your number line?
Where do we start jumping back from? By what do we jump backwards?
Solution Check the fractions have the same denominator.
 Divide the number line into equal parts.
 Locate the first fraction on the number line.
 Find the numerator of the fraction being subtracted and jump backwards by this many.
 Don't forget to simplify your answer if needed.

How much gas will Axel and Tank have left?
HintsCount how many parts the number line is divided into. Use the markers on the number line, and the numbers that are already there, to help you to place the fractions in the correct places.
Some of the fractions have been filled in here, use this number line to help you fill in the rest.
Once you have a complete number line, locate the larger fraction $\frac{6}{7}$, and count back the numerator of the smaller fraction.
SolutionAxel and Tank will have $\mathbf{\frac{2}{7}}$ of a tank left after their journey.
Once we placed each fraction on the number line we needed to:
 Locate the larger fraction from our equation, $\frac{6}{7}$
 Count backwards 4 (the numerator of the smaller fraction, $\frac{4}{7}$)
 As we can see from the jumps, this takes us to $\frac{2}{7}$.

How much chocolate is left?
HintsThe number sentence we are trying to solve is $\frac{9}{10}$  $\frac{6}{10}$. Can you draw a number line to help?
A number line split into tenths like this will help.
Use the number line to locate the first fraction, $\frac{9}{10}$. What is your next step?
Find the numerator in $\frac{6}{10}$ and count that many backwards.
SolutionAxel will have $\mathbf{\frac{3}{10}}$ of the chocolate bar left.
 Locate the larger fraction, $\frac{9}{10}$, on the number line.
 Find the numerator of the smaller fraction. The numerator in $\frac{6}{10}$ is 6.
 Count 6 jumps backwards.
 We land on $\frac{3}{10}$.

Find the answers to these subtraction problems.
HintsLook at the denominators of the fractions in the equations. Can you make a number line with this many parts to help you to subtract?
For example, to solve $\frac{7}{10}$  $\frac{3}{10}$, we could divide a number line into 10 equal parts like this.
Once we have done that, we can locate the first fraction and count back by the numerator of the second fraction.
Remember, answers are simplified if needed. For example, we could simplify $\frac{2}{8}$ to $\frac{1}{4}$ by dividing both the numerator and denominator by 2.
Solution$\frac{7}{10}$  $\frac{3}{10}$ = $\frac{2}{5}$
 Counting 3 jumps backwards from $\frac{7}{10}$ on a number line gets us to $\frac{4}{10}$.
 $\frac{4}{10}$ can be simplified to $\frac{2}{5}$ by dividing both the numerator and the denominator by 2.
$\frac{5}{6}$  $\frac{3}{6}$ = $\frac{1}{3}$
 Counting 3 jumps backwards from $\frac{5}{6}$ on a number line gets us to $\frac{2}{6}$.
 $\frac{2}{6}$ can be simplified to $\frac{1}{3}$ by dividing both the numerator and the denominator by 2.
$\frac{7}{9}$  $\frac{5}{9}$ = $\frac{2}{9}$
 Counting 5 jumps backwards from $\frac{7}{9}$ on a number line gets us to $\frac{2}{9}$. This cannot be simplified further.
$\frac{8}{12}$  $\frac{2}{12}$ = $\frac{1}{2}$
 Counting 2 jumps backwards from $\frac{8}{12}$ on a number line gets us to $\frac{6}{12}$.
 $\frac{6}{12}$ can be simplified to $\frac{1}{2}$ by dividing both the numerator and the denominator by 6.

How much gas will be left?
HintsThe first step is to locate the larger fraction, $\frac{5}{8}$, on the number line.
We then need to find the numerator of the smaller fraction. What is the numerator in $\frac{3}{8}$?
We then need to jump backwards that amount.
SolutionThey will have $\mathbf{\frac{2}{8}}$ of a tank of gas left when they get home.
 Locate the larger fraction, $\frac{5}{8}$ on the number line.
 Find the numerator of the smaller fraction. The numerator of $\frac{3}{8}$ is 3.
 Count backwards 3 from $\frac{5}{8}$.
 We land on $\frac{2}{8}$.

What fraction will be left?
HintsMake sure the denominators are the same in each equation.
For example if we were subtracting $\frac{5}{12}$  $\frac{2}{6}$, we would multiply the numerator and the denominator of $\frac{2}{6}$ by 2 to make $\frac{4}{12}$. Now we can subtract $\frac{5}{12}$  $\frac{4}{12}$.
Draw your own number line to help you to solve. Divide your number line into equal parts as shown by the denominators.
Remember to simplify your answer by dividing the numerator and denominator by the same number.
Solution$\mathbf{\frac{1}{2}}$
 $\frac{9}{10}$  $\frac{2}{5}$ : first convert the fraction, $\frac{2}{5}$, by multiplying the numerator and denominator by 2 to make $\frac{4}{10}$ so both fractions in the equation have the same denominator. $\frac{9}{10}$  $\frac{4}{10}$ = $\frac{5}{10}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 5.
 $\frac{7}{8}$  $\frac{3}{8}$ = $\frac{4}{8}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 4.
 $\frac{12}{14}$  $\frac{5}{14}$ = $\frac{7}{14}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 7.
$\mathbf{\frac{2}{3}}$
 $\frac{5}{6}$  $\frac{1}{6}$ = $\frac{4}{6}$ which can be simplified to $\frac{2}{3}$ by dividing both the numerator and denominator by 2.
 $\frac{11}{12}$  $\frac{1}{4}$ : first convert the fraction, $\frac{1}{4}$, by multiplying the numerator and denominator by 3 to make $\frac{3}{12}$ so both fractions in the equation have the same denominator. $\frac{11}{12}$  $\frac{3}{12}$ = $\frac{8}{12}$ which can be simplified to $\frac{2}{3}$ by dividing both the numerator and denominator by 4.
$\mathbf{\frac{3}{5}}$
 $\frac{13}{15}$  $\frac{4}{15}$ = $\frac{9}{15}$ which can be simplified to $\frac{3}{5}$ by dividing both the numerator and denominator by 3.
 $\frac{17}{20}$  $\frac{5}{20}$ = $\frac{12}{20}$ which can be simplified to $\frac{3}{5}$ by dividing both the numerator and denominator by 4.