Subtracting Fractions with Like Denominators

Subtracting Fractions with Like Denominators exercise

• What are the steps to subtract like fractions?

  Hints

  The numerator is the top number in the fraction and the denominator is the bottom number.

  To subtract fractions, they need to have the same denominator.

  As long as fractions have the same denominator, their top numbers can be subtracted.

  Solution

  First, check that the denominators are the same and write it in the total.

  • $\frac{5}{\textbf{8}} - \frac{3}{\textbf{8}} = \frac{}{\textbf{8}}$

  Then, subtract the numerators.

  • $5 - 3 = 2$

  Finally, write the numerator above the denominator.

  • * $\frac{5}{8} - \frac{3}{8} = \frac{\textbf{2}}{8}$

• Which subtraction problems have like fractions?

  Hints

  Like fractions have the same number in the denominator.

  The denominator is the bottom number in the fraction.

  Solution

  Like fractions are fractions that have the same denominator, or bottom number. These problems have like fractions:

  • $\frac{3}{4} - \frac{1}{4}$
  • $\frac{2}{2} - \frac{1}{2}$
  • $\frac{7}{8} - \frac{3}{8}$

  These problems do not have like fractions:

  • $\frac{3}{8} - \frac{3}{4}$
  • $\frac{5}{6} - \frac{2}{3}$
  • $\frac{2}{6} - \frac{2}{4}$

• Which images model the subtraction problems?

  Hints

  The denominator is the total number of equal parts.

  Count the number of shaded parts. This is the numerator.

  Solution

  First, look at the common denominator. That is the number of total pieces each rectangle is divided into.

  Then, look at the numerators. That is the number of shaded parts of the rectangles.

  2/3 - 1/3: each rectangle will have 3 parts. The first rectangle will have 2 shaded parts and the second will have 1 shaded part.

  3/4 - 1/4: each rectangle will have 4 parts. The first rectangle will have 3 shaded parts and the second will have 1 shaded part.

  5/6 - 2/6: each rectangle will have 6 parts. The first rectangle will have 5 shaded parts and the second will have 2 shaded parts.

  5/8 - 2/8: each rectangle will have 8 parts. The first rectangle will have 5 shaded parts and the second will have 2 shaded parts.

• Solve the subtraction problems.

  Hints

  When subtracting like fractions, the denominator stays the same.

  Subtract the numerators to find the new numerator.

  Solution

  When subtracting like fractions, find the solution by:

  • Keeping the denominator the same
  • Subtracting the numerators

  $\frac{3}{3}$ - $\frac{2}{3}$ = $\frac{1}{3}$

  $\frac{5}{6}$ - $\frac{3}{6}$ = $\frac{2}{6}$

  $\frac{5}{8}$ - $\frac{1}{8}$ = $\frac{4}{8}$

  $\frac{3}{4}$ - $\frac{2}{4}$ = $\frac{1}{4}$

• Solve the subtraction problem using the model.

  Hints

  First, check that the denominators are the same. Then, subtract the numerators.

  • The numerator is the top number.
  • The denominator is the bottom number.

  Solution

  First, check that the denominators are the same. They are both 8, so these fractions are like fractions.

  Write 8 in the denominator of the total.

  $\frac{7}{8} - \frac{5}{8} = \frac{?}{\textbf{8}}$

  Next, subtract the numerators: 7 - 5 = 2.

  Write 2 in the numerator of the total.

  So, $\frac{7}{8} - \frac{5}{8} = \frac{\textbf{2}}{8}$.

• Solve the subtraction problems and simplify.

  Hints

  To simplify, find a common factor of both the numerator and denominator. Then, divide both numbers by the common factor.

  To subtract fractions with like denominators, keep the denominator the same and subtract the numerators.

  Solution

  First subtract the numerators and keep the denominators.

  • For example, $\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$.

  Then if needed, simplify by dividing the numerator and denominator by a common factor.

  • For example, both 3 and 6 are divisible by 3. So, $\frac{3}{6} = \frac{1}{2}$.

  Continue this for each problem:

  • $\frac{7}{8} - \frac{3}{8} = \frac{4}{8} \rightarrow \frac{4}{8} = \frac{\textbf{1}}{\textbf{2}}$
  • $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} \rightarrow \frac{2}{4} = \frac{\textbf{1}}{\textbf{2}}$
  • $\frac{3}{3} - \frac{1}{3} = \frac{\textbf{2}}{\textbf{3}}$
  • $\frac{5}{6} - \frac{1}{6} = \frac{4}{6} \rightarrow \frac{4}{6} = \frac{\textbf{2}}{\textbf{3}}$
  • $\frac{3}{4} - \frac{2}{4} = \frac{\textbf{1}}{\textbf{4}}$
  • $\frac{5}{8} - \frac{3}{8} = \frac{2}{8} \rightarrow \frac{2}{8} = \frac{\textbf{1}}{\textbf{4}}$
  • $\frac{7}{8} - \frac{5}{8} = \frac{2}{8} \rightarrow \frac{2}{8} = \frac{\textbf{1}}{\textbf{4}}$