For example:
\(\dfrac{1}{5}\) and \(\dfrac{3}{5}\) are like fractions because they have same denominators \((5)\).
A
B
C
D
Given:
Number of equal parts \(=6\)
Number of shaded parts \(=4\)
Fraction of shaded parts \(=\dfrac{4}{6}\)
Option (A):
Number of equal parts \(=6\)
Number of shaded parts \(=5\)
Fraction of shaded parts \(=\dfrac{5}{6}\)
\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{5}{6}\right)\) are same and they are also the parts of the same whole
\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{5}{6}\) are like fractions.
Hence, option (A) is incorrect.
Option (B):
Number of equal parts \(=6\)
Number of shaded parts \(=3\)
Fraction of shaded parts \(=\dfrac{3}{6}\)
\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{3}{6}\right)\) are same and they are also the parts of the same whole
\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{3}{6}\) are like fractions.
Hence, option (B) is incorrect.
Option (C):
Number of equal parts \(=4\)
Number of shaded parts \(=1\)
Fraction of shaded parts \(=\dfrac{1}{4}\)
\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{1}{4}\right)\) are different and they are also not the parts of the same whole
\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{1}{4}\) are not like fractions.
Hence, option (C) is correct.
Option (D):
Number of equal parts \(=6\)
Number of shaded parts \(=1\)
Fraction of shaded parts \(=\dfrac{1}{6}\)
\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{1}{6}\right)\) are same and they are also the parts of the same whole
\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{1}{6}\) are like fractions.
Hence, option (D) is incorrect.
Option C is Correct
For example: \(\dfrac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2},\dfrac{7}{2}\) are like fractions.
Bananas = \(7\)
Apples = \(5\)
Then,
Number of bananas sold in fraction form = \(\dfrac{7}{12}\)
Number of apples sold in fraction form = \(\dfrac{5}{12}\)
\( \dfrac{7}{12}\) and \(\dfrac{5}{12}\) have same denominators.
Thus, these are like fractions.
Note:- In the above example, bananas and apples are different wholes.
A \(3\) cars out of \(5\) and \(1\) pencil out of \(5\)
B \(4\) dusters out of \(5\) and \(4\) sharpeners out of \(7\)
C \(2\) mugs out of \(3\) and \(1\) page out of \(2\)
D \(9 \) bags out of \(20\) and \(6\) slices out of \(29\)
For example: \(\dfrac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2},\dfrac{7}{2}\) are like fractions.
Now, finding their shares in fraction form.
Monica's share:
Number of slices Monica ate = \(3\)
Total number of slices = \(5\)
\(\therefore\) Monica's share in fraction form = \(\dfrac{3}{5}\)
Tina's share:
Number of slices Tina ate \( = 4\)
Total number of slices = \(5\)
\(\therefore\) Tina's share in fraction form = \(\dfrac{4}{5}\)
Note:- If two or more fractions are parts of different wholes and each whole has same number of equal parts, then the fractions are like fractions.
A
B
C
D
In option (A),
Number of equal parts in
Figure (I) = \(2\)
Figure (II) = \(4\)
Shaded parts in
Figure (I) = \(1\)
Figure (II) = \(1\)
Fraction of the shaded parts
For Figure (I) = \(\dfrac{1}{2}\)
For Figure (II) = \(\dfrac{1}{4}\)
\( \dfrac{1}{4}\) and \(\dfrac{1}{2}\) have different denominators. Thus, these are not like fractions.
Hence, option (A) is incorrect.
In option (B),
Number of equal parts in
Figure (I) = \(5\)
Figure (II) = \(4\)
Shaded parts in
Figure (I) = \(3\)
Figure (II) = \(3\)
Fraction of the shaded parts
For Figure (I) = \(\dfrac{3}{5}\)
For Figure (II) = \(\dfrac{3}{4}\)
\( \dfrac{3}{5}\) and \(\dfrac{3}{4}\) do not have same denominators. Thus, these are not like fractions.
Hence, option (B) is incorrect.
In option (C),
Number of equal parts in
Figure (I) = \(8\)
Figure (II) = \(8\)
Shaded parts in
Figure (I) = \(3\)
Figure (II) = \(5\)
Fraction of the shaded parts
For Figure (I) = \(\dfrac{3}{8}\)
For Figure (II) = \(\dfrac{5}{8}\)
\( \dfrac{3}{8}\) and \(\dfrac{5}{8}\) have same denominators. Thus, these are like fractions.
Hence, option (C) is correct.
In option (D),
Number of equal parts in
Figure (I) = \(2\)
Figure (II) = \(4\)
Shaded parts
Figure (I) = \(1\)
Figure (II) = \(3\)
Fraction of the shaded parts
For Figure (I) = \(\dfrac{1}{2}\)
For Figure (II) = \(\dfrac{3}{4}\)
\(\dfrac{1}{2}\) and \(\dfrac{3}{4}\) do not have same denominators. Thus, these are not like fractions.
Hence, option (D) is incorrect.
Option C is Correct
For example:- \(\dfrac{1}{2},\;\dfrac{1}{3},\; \dfrac{5}{6}\) are unlike fractions.
Cherri buys \(21\) colored pens out of which \(10\) are red.
Fraction of red colored pens (In case of Cherri) = \(\dfrac{10}{21}\)
Tina buys \(23\) colored pens out of which \(11\) are red.
Fraction of red colored pens (In case of Tina) = \(\dfrac{11}{23}\)
\( \dfrac{10}{21}\) and \(\dfrac{11}{23}\) have different denominators. Thus, these are unlike fractions.
A \(\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}\)
B \(\dfrac{2}{13},\dfrac{4}{13},\dfrac{1}{13},\dfrac{6}{13}\)
C \(\dfrac{2}{15},\dfrac{7}{15},\dfrac{6}{15},\dfrac{1}{15}\)
D \(\dfrac{11}{13},\dfrac{7}{13},\dfrac{6}{13},\dfrac{4}{13}\)
For example:- \(\dfrac{1}{2},\;\dfrac{1}{3},\; \dfrac{5}{6}\) are unlike fractions.
Strawberry cake = \(8\)
Chocolate cake = \(4\)
Fraction for strawberry cake = \(\dfrac{3}{8}\)
Fraction for chocolate cake = \(\dfrac{1}{4}\)
\( \dfrac{3}{8}\) and \(\dfrac{1}{4}\) do not have common denominators. Thus, they are unlike fractions.
A
B
C
D
In option (A),
Number of equal parts in
Figure (I) = \(4\)
Figure (II) = \(4\)
Shaded parts in
Figure (I) = \(1\)
Figure (II) = \(3\)
Fraction of the shaded part
For Figure (I) = \(\dfrac{1}{4}\)
For Figure (II) = \(\dfrac{3}{4}\)
\( \dfrac{1}{4}\) and \(\dfrac{3}{4}\) have common denominators. Thus, they do not represent unlike fractions.
Hence, option (A) is incorrect.
In option (B),
Number of equal parts in
Figure (I) = \(8\)
Figure (II) = \(8\)
Shaded parts in
Figure (I) = \(3\)
Figure (II) = \(5\)
Fraction of the shaded part
For Figure (I) = \(\dfrac{3}{8}\)
For Figure (II) = \(\dfrac{5}{8}\)
\( \dfrac{3}{8}\) and \(\dfrac{5}{8}\) have common denominators. Thus, they do not represent unlike fractions.
Hence, option (B) is incorrect.
In option (C),
Number of equal parts in
Figure (I) = \(8\)
Figure (II) = \(4\)
Shaded parts in
Figure (I) = \(3\)
Figure (II) = \(3\)
Fraction of the shaded part
For Figure (I) = \(\dfrac{3}{8}\)
For Figure (II) = \(\dfrac{3}{4}\)
\(\dfrac{3}{8}\) and \(\dfrac{3}{4}\) have different denominators. Thus, they represent unlike fractions.
Hence, option (C) is correct.
In option (D),
Number of equal parts in
Figure (I) = \(6\)
Figure (II) = \(6\)
Shaded parts in
Figure (I) = \(1\)
Figure (II) = \(5\)
Fraction of the shaded part
For Figure (I) = \(\dfrac{1}{6}\)
For Figure (II) = \(\dfrac{5}{6}\)
\( \dfrac{1}{6}\) and \(\dfrac{5}{6}\) have common denominators. Thus, they do not represent unlike fractions.
Hence, option (D) is incorrect.
Option C is Correct
