For example: \(1\dfrac {1}{3}\)
In \(1\dfrac {1}{3}\), whole number = 1, fraction = \(\dfrac {1}{3}\)
\(\therefore\;1\dfrac {1}{3}\) is a mixed number.
For example: \(1\dfrac {1}{3}\)
\(\because\) In \(1\dfrac {1}{3}\), whole number = 1
Fraction = \(\dfrac {1}{3}\)
\(\therefore\;1\dfrac {1}{3}\) is a mixed number.
A \(\dfrac {1}{2}\)
B \(3\)
C \(\dfrac {1}{5}\)
D \(2\dfrac {1}{3}\)
Total number of chocolates = \(3\)
Ana ate = \(\dfrac {1}{2}\)
Chocolate remaining = \(2\) and a half part
= \(2+\dfrac {1}{2}\)
\(=2\dfrac {1}{2}\)
\(2\dfrac {1}{2}\) has both, a whole number and a fraction part.
\(\therefore\) It is a mixed number.
A \(\dfrac {3}{4}\)
B \(1\dfrac {3}{4}\)
C \(2\dfrac {1}{4}\)
D \(2\dfrac {3}{4}\)
For example:
\(\dfrac {1}{2}=\dfrac {2}{4}=\dfrac {4}{8}\) are equivalent fractions.
Multiply both numerator and denominator by the same non-zero whole number, like 2 in this case.
\(\Rightarrow\dfrac {1×2}{3×2}=\dfrac {2}{6}\)
The Greatest Common Factor of 2 and 6 is 2, so we divide both the numerator and the denominator by 2.
We get \(\dfrac{1}{3}\) which is same as the original fraction.
The new fraction \(\left(\dfrac{2}{6}\right)\) is the equivalent fraction of the original fraction.
Equivalent fraction of \(\dfrac {1}{3}=\dfrac {2}{6}\)
Though, \(\dfrac {1}{3}\) and \(\dfrac {2}{6}\) look different but they have the same value.
A \(\dfrac {9}{6}\)
B \(\dfrac {6}{9}\)
C \(\dfrac {12}{4}\)
D \(\dfrac {15}{8}\)
Equivalent fractions are fractions which have the same values, even though they look different.
For example: \(\dfrac{1}{2}=\dfrac{2}{4}=\dfrac{4}{8}\) are equivalent fractions.
Pictorial representation is a better tool to understand the equivalent fractions.
Let us consider an example:
They are saying that they both have eaten the same amount of pizza.
Is it true?
To solve this problem, consider the following procedure:
By observing the figure, it is clear that both of them have eaten the same amount of pizza.
\(\therefore\) Fraction of a pizza eaten by Carl = Fraction of a pizza eaten by Kevin
Fraction of pizza eaten by Carl = 4 out of 8 \(=\dfrac{4}{8}\)
Fraction of pizza eaten by Kevin = 2 out of 4 \(=\dfrac{2}{4}\)
\(\Rightarrow\;\dfrac{4}{8}=\dfrac{2}{4}\)
So, \(\dfrac{4}{8}\) and \(\dfrac{1}{2}\) are equivalent fractions.
Thus, they are correct.
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Two fractions are equivalent or equal if they represent the same point on the number line.
For example: Consider \(\dfrac {1}{2}\) and \(\dfrac {3}{6}\).
Step 1: Define the interval from \(0\) to \(1\) and divide it into \(2\) equal segments.
Step 2: The size of each segment is \(\dfrac {1}{2}\).
Step 3: Now, if we divide each segment of length \(\dfrac {1}{2}\) into 3 equal parts, we will get:
\(\dfrac {1}{2}=\dfrac {1×3}{2×3}=\dfrac {3}{6}\)
Step 4: We can see that the fractions \(\dfrac {1}{2}\) and \(\dfrac {3}{6}\) represent the same point on the number line.
Thus, they are equivalent fractions.
A \(\dfrac {5}{8}\)
B \(\dfrac {9}{12}\)
C \(\dfrac {18}{20}\)
D \(\dfrac {6}{12}\)