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converting a Mixed Fraction to an improper Fraction

To convert a mixed fraction to an improper fraction, follow these steps:
Step 1: Multiply the whole number by the denominator.

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

Mixed fraction = (Whole number × Denominator) + Numerator = Improper fraction
Denominator
Example 2: Convert the following mixed fractions into improper fractions.
3
3
( a) 1 (b) 4 (c) 5 2 ( d) 2 7
8 5 7 9
Solution: We have:
(Whole number × Denominator) + Numerator
Mixed fraction = = Improper fraction
Denominator
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
7 (
2 (
+
+
( c) 5 = 5 × 7) + 2 = 35 2 = 37 ( d) 2 = 2 × 9) + 7 = 18 7 = 25
7 7 7 7 9 9 9 9
EquivalEnt Fractions

The fractions that represent the same part of a whole object or the same fractional value
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
1 2 3
3
4
4
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 fractions of a given fraction by multiplying the numerator and
the denominator by the same non-zero number.
3
Example 1: Write three equivalent fractions of .
4
3
6 3
3
Solution: We have: = 3 × 2 = ; = 3 × 3 = 9 ; = 3 × 4 = 12
4 4 × 2 8 4 4 × 3 12 4 4 × 4 16
6 9
3
Hence, , , 12 are three equivalent fractions of .
8 12 16 4
We can also find equivalent fractions by dividing the numerator and the denominator by
the same non-zero number.

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