Julian and Suz ordered a pizza that was cut into 10 slices. Suz ate 3 slices and Julian ate 4 slices. What fraction of the pizza did each person eat? What fraction of the pizza is left?
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Khan Academy Adding and Subtracting Fractions
Guidance
The problem above can be represented with fraction strips:
To subtract fractions, the fractions must have the same bottom numbers (denominators). In this case, both fractions have a denominator of 7. The answer is the result of subtracting the top numbers (numerators).
In order to subtract fractions that have different denominators, the fractions must be expressed as equivalent fractions with a least common denominator (LCD). The difference of the numerators can be written over the common denominator.
Example A
Solution:
Example B
Bessie is measuring the amount of soda in the two coolers in the cafeteria. She estimates that the first cooler is
Solution: Use fraction strips to represent each fraction.
The two green pieces will be replaced with eight purple pieces and the one blue piece will be replaced with three purple pieces.
The denominator of 12 is the LCD (least common denominator) of
Therefore, there is
Example C
Solution: The number line is labeled in intervals of 4. This indicates that each interval represents
The difference of
Concept Problem Revisited
Julian and Suz ordered a pizza that was cut into 10 slices. Suz ate 3 slices and Julian ate 4 slices. What fraction of the pizza did each person eat? What fraction of the pizza is left?
Suz ate
Vocabulary
 Denominator

The denominator of a fraction is the number on the bottom that indicates the total number of equal parts in the whole or the group.
58 has denominator 8.
 Fraction
 A fraction is any rational number that is not an integer.
 LCD

The least common denominator is the lowest common multiple of the denominators of two or more fractions. The least common denominator of
34 and15 is 20.
 LCM
 The least common multiple is the lowest common multiple that two or more numbers share. The least common multiple of 6 and 5 is 30.
 Numerator

The numerator of a fraction is the number on top that is the number of equal parts being considered in the whole or the group.
58 has 'numerator 5.
Guided Practice
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Answers:
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Practice
Complete the following subtraction problems using any method.

34−58 
45−23 
59−23 
67−23 
710−15 
23−12 
35−310 
79−13  \begin{align*}\frac{5}{8}\frac{1}{4}\end{align*}
 \begin{align*}\frac{2}{5}\frac{2}{10}\end{align*}
 \begin{align*}\frac{7}{11}\frac{1}{2}\end{align*}
 \begin{align*}\frac{5}{8}\frac{5}{12}\end{align*}
 \begin{align*}\frac{5}{6}\frac{3}{4}\end{align*}
 \begin{align*}\frac{5}{6}\frac{2}{5}\end{align*}
 \begin{align*}\frac{4}{5}\frac{3}{4}\end{align*}
For each of the following questions, write a subtraction statement and find the result.
 Sally used \begin{align*}\frac{2}{3} \ cups\end{align*} of flour to make cookies. Terri used \begin{align*}\frac{1}{2} \ cups\end{align*} of flour to make a cake. Who used more flour? How much more flour did she use?
 Lauren used \begin{align*}\frac{3}{4} \ cup\end{align*} of milk, \begin{align*}1 \frac{1}{3} \ cups\end{align*} of flour and \begin{align*}\frac{3}{8} \ cup\end{align*} of oil to make pancakes. Alyssa used \begin{align*}\frac{3}{8} \ cup\end{align*} of milk, \begin{align*}2 \frac{1}{4} \ cups\end{align*} of flour and \begin{align*}\frac{1}{3} \ cup\end{align*} of melted butter to make waffles. Who used more cups of ingredients? How many more cups of ingredients did she use?
 Write two fractions with different denominators whose difference is \begin{align*}\frac{3}{8}\end{align*}.
 Jake’s dog ate \begin{align*}12 \frac{2}{3} \ cans\end{align*} of food in one week and \begin{align*}9 \frac{1}{4} \ cans\end{align*} the next week. How many more cans of dog food did Jake’s dog eat in week one?
 Sierra and Clark each solved the same problem.

 Sierra’s Solution



\begin{align*}& \frac{3}{4}\frac{1}{6}\\
& \frac{9}{12}\frac{2}{12}\\
& =\frac{7}{12}\end{align*}

\begin{align*}& \frac{3}{4}\frac{1}{6}\\
& \frac{9}{12}\frac{2}{12}\\
& =\frac{7}{12}\end{align*}


 Clark’s Solution



\begin{align*}& \frac{3}{4}\frac{1}{6}\\
& \frac{9}{12}\frac{2}{12}\\
& =\frac{7}{0}\end{align*}

\begin{align*}& \frac{3}{4}\frac{1}{6}\\
& \frac{9}{12}\frac{2}{12}\\
& =\frac{7}{0}\end{align*}


 Who is correct? What would you tell the person who has the wrong answer?