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\\November 22, 2023 3:12 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Step 2: Add the numerator to the product obtained to get the numerator of the improper
fraction.
Step 3: Keep the denominator same.

Whole number × Denominator + Numerator
Mixed fraction =
Denominator
example 2: Convert the following mixed fractions into improper fractions.
3 3 2 7
(a) 1 (b) 4 (c) 5 (d) 2
8 5 7 9

Solution: We have,

Mixed fraction = (Whole number × Denominator) + Numerator
Denominator
= improper fraction
3 ( 1 × 8) + 3 83 11 3 ( 4 × 5) + 3 20 3 23
+
+
(a) 1 = = = (b) 4 = = =
8 8 8 8 5 5 5 5
2 ( 5 × 7) + 2 35 2 37 7 ( 2 × 9) + 7 18 7 25
+
+
(c) 5 = = = (d) 2 = = =
7 7 7 7 9 9 9 9

EquivalEnt Fractions

The fractions which represent the same part of a whole object or a fractional number are
called equivalent or equal fractions.

Look at the following diagrams. Here, the shaded part of each diagram is equal.

1 2 3 4
2 4 6 8
4
1 2 3
4
3
1
2
Here, = = = . Thus, , , and are all equivalent fractions.
2 4 6 8 2 4 6 8
Finding Equivalent Fractions
We can find the equivalent fraction of a given fractions by multiplying the numerator and
the denominator by the same non-zero number.
3
example 1: Write three equivalent fractions of .
4
Solution: We have,

3 = 3 × 2 = ; = 3 × 3 = 9 ; = 3 × 4 = 12
6 3
3
4 4 × 2 8 4 4 × 3 12 4 4 × 4 16
6 9 12 3
Hence, , , are three equivalent fractions of .
8 12 16 4

We can also find out the equivalent fractions by dividing the numerator and the denominator
by the same non-zero number.

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