Like denominators
Two or more fractions are said to have like denominators if they have same denominators.
For example: \(\dfrac{3}{5},\;\dfrac{2}{5}\)
Here, like denominator \(=5\)
Here, both the fractions have the same denominator = \(10\)
Step 1: Find the difference of the numerators.
\(7-3=4\)
Step 2: Difference of numerators becomes the new numerator.
Numerator \(=4\)
Step 3: Denominator remains the same.
Denominator \(=10\)
Step 4: Write the resulting fraction.
Fraction \(=\dfrac{4}{10}\)
Step 5: Simplify the result.
\(2\) and \(5\) do not have any common factor other than \(1\).
\(\therefore\;\dfrac{2}{5}\) is in its simplest form.
Thus, \(\dfrac{2}{5}\) is our final answer.
A \(\dfrac{6}{9}\)
B \(-\dfrac{1}{3}\)
C \(\dfrac{1}{3}\)
D \(-\dfrac{2}{9}\)
Step 1: Subtract the fraction part first.
\(\dfrac{4}{5}-\dfrac{1}{4}\)
The least common multiple of \(5\) and \(4\):
Multiples of \(5=5,\;10,\;15,\;20\,...\)
Multiples of \(4=4,\,8,\;12,\;16,\;20\,...\)
Least common multiple (L.C.M) \(=20\)
L.C.M becomes the lowest common denominator (L.C.D).
L.C.D \(=20\)
Convert each fraction into equivalent fraction with L.C.D as the denominator.
Equivalent fraction of \(\dfrac{4}{5}=\dfrac{4×4}{5×4}=\dfrac{16}{20}\)
Equivalent fraction of \(\dfrac{1}{4}=\dfrac{1×5}{4×5}=\dfrac{5}{20}\)
Subtract the equivalent fractions of \(\dfrac{4}{5}\) and \(\dfrac{1}{4}\).
\(\dfrac{16}{20}-\dfrac{5}{20}=\dfrac{16-5}{20}=\dfrac{11}{20}\)
Simplify the resulting fraction.
\(11\) and \(20\) do not have any common factor other than \(1\).
\(\therefore\;\dfrac{11}{20}\) is in its simplest form.
Step 2: Subtract the whole numbers.
\(5-3=2\)
Step 3: Write the difference of whole numbers and fractions together as a mixed number, i.e.
\(2\dfrac{11}{20}\)
Thus, \(2\dfrac{11}{20}\) is our final answer.
A \(3\dfrac{1}{3}\)
B \(4\dfrac{2}{9}\)
C \(5\dfrac{1}{9}\)
D \(2\dfrac{1}{9}\)
So, when she subtracts these two squares, she gets:
Thus, figure (E) shows the subtraction of the shaded part of figure (D) from the shaded part of figure (C) and represents the fraction equals \(\dfrac{3}{6}\).
Thus, figure (G) shows the subtraction of the shaded part of figure (F) from the shaded part of figure (E) and the fraction represented equals \(\dfrac{1}{6}\).
In order to perform subtraction of fractions having different denominators, we first need to convert them into fractions with like denominators.
To understand it easily, let us consider the following example: \(\dfrac{3}{2}-\dfrac{7}{8}\)
Step 1: Find the least common multiple of denominators.
The least common multiple (L.C.M) of \(2\) and \(8\):
Multiples of \(2=2,\;4,\;6,\;8\;...\)
Multiples of \(8=8,\;16\,...\)
L.C.M of \(2\) and \(8=8\)
Step 2: L.C.M becomes the lowest common denominator (L.C.D).
L.C.D \(=8\)
Step 3: Convert the fractions into equivalent fractions with L.C.D as the denominator.
\(\dfrac{7}{8}\) already has \(8\) as its denominator.
\(\therefore\) It does not need to be converted.
Step 4: Rewrite the expression with fractions having same denominators.
\(\dfrac{12}{8}-\dfrac{7}{8}\)
Step 5: Find the difference of numerators and it becomes the new numerator.
\(12-7=5\)
Numerator \(=5\)
Step 6: Denominator remains the same.
Denominator \(=8\)
Step 7: Write the resulting fraction.
Resulting fraction \(=\dfrac{5}{8}\)
Step 8: Simplify the result.
\(5\) and \(8\) do not have any common factor other than \(1\).
\(\therefore\;\dfrac{5}{8}\) is in its simplest form.
Thus, \(\dfrac{5}{8}\) is our final answer.
A \(\dfrac{1}{12}\)
B \(\dfrac{2}{6}\)
C \(\dfrac{7}{12}\)
D \(\dfrac{3}{6}\)
For example: \(\dfrac{3}{3}\) or \(\dfrac{5}{5}\) or \(\dfrac{2}{2}\) are equivalent to \(1.\)
Case I: If we subtract a mixed number from a whole number:
For example: \(5-3\dfrac{1}{2}\)
Step 1: Borrow \(1\) from \(5\) to make it four, i.e.
\(5=4+1\)
Step 2: Take \(1\) and change it into a fraction having \(2\) as the denominator.
\(1=\dfrac{2}{2}\)
[In \(3\dfrac{1}{2}\), the denominator is \(2]\)
\([\,\therefore\) We take \(1=\dfrac{2}{2}]\)
Step 3: Rewrite the problem.
\(5=4+1\)
\(=4+\dfrac{2}{2}\)
\(=4\dfrac{2}{2}\)
Step 4: Subtract the mixed numbers having same denominators.
\(\underline{\;\;\;\;4\dfrac{2}{2}\\-3\dfrac{1}{2}}\)
Subtract the fraction part, i.e.
\(\dfrac{2}{2}-\dfrac{1}{2}=\dfrac{1}{2}\)
Simplify the resulting fraction.
\(1\) and \(2\) do not have any common factor other than \(1\).
\(\therefore\;\dfrac{1}{2}\) is in its simplest form.
Subtract the whole numbers, i.e.
\(4-3=1\)
Put the difference of whole numbers and fractions together as a mixed number, i.e.
\(1\dfrac{1}{2}\)
Thus, \(1\dfrac{1}{2}\) is our final answer.
Case II: If fraction part of the subtrahend is greater than the fraction part of minuend:
For example: \(\underline{\;\;\;\;7\dfrac{1}{8}\;\;(\text{minuend})\\-4\dfrac{5}{8}\;\;\text{(subtrahend)}}\)
Step 1: First rename the top mixed number, i.e.
\(7\dfrac{1}{8}=7+\dfrac{1}{8}\)
Borrow \(1\) from \(7\) to make it \(6,\) i.e.
\(7=6+1\)
Take \(1\) and change it into a fraction having \(8\) as the denominator, i.e.
\(1=\dfrac{8}{8}\)
[ In \(7\dfrac{1}{8}\) and \(4\dfrac{5}{8}\), the denominators are \(8]\)
\([\,\therefore\) We take \(1=\dfrac{8}{8}]\)
Thus, \(7\dfrac{1}{8}=6+\dfrac{8}{8}+\dfrac{1}{8}\)
\(=6+\dfrac{8+1}{8}\)
\(=6+\dfrac{9}{8}\)
\(=6\dfrac{9}{8}\)
Step 2: Rewrite the problem and subtract the mixed numbers with same denominators.
\(\underline{\;\;\;\;6\dfrac{9}{8}\\-4\dfrac{5}{8}}\)
Subtract the fraction part, i.e.
\(\dfrac{9}{8}-\dfrac{5}{8}=\dfrac{9-5}{8}=\dfrac{4}{8}\)
Simplify the resulting fraction, i.e. \(\dfrac{4}{8}\)
The greatest common factor of \(4\) and \(8=4\)
Divide by \(4\), \(\dfrac{4\div4}{8\div4}=\dfrac{1}{2}\)
\(1\) and \(2\) do not have any common factor other than \(1\).
\(\therefore\;\dfrac{1}{2}\) is in its simplest form.
Subtract the whole numbers, i.e.
\(6-4=2\)
Put the difference of whole numbers and fractions together as a mixed number, i.e.
\(2\dfrac{1}{2}\)
Thus, \(2\dfrac{1}{2}\) is our final answer.
A \(6\dfrac{1}{3}\)
B \(5\dfrac{2}{3}\)
C \(4\dfrac{2}{3}\)
D \(4\dfrac{1}{3}\)
Subtraction of fractions on a number line is represented by taking away the part which we want to subtract.
Before performing subtraction on the number line, we have to make sure that each fraction has the same denominator.
For example: Represent \(\dfrac {7}{5}-\dfrac {3}{5}\) on a number line.
Step 1: Represent \(\dfrac {7}{5}\) on the number line.
Step 2 : Represent \(\dfrac {3}{5}\) on the number line.
Step 3 : Subtraction means moving 3 units in backward direction, each of length \(\dfrac {1}{5}\), from \(\dfrac {7}{5}\).
\(\dfrac {7}{5}-\dfrac {3}{5}=\dfrac {4}{5}\)
Hence, the result is \(\dfrac {4}{5}\).