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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

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mathsFractionsTypes of fractions

### Equivalent Fractions and Simplest form of a fraction

Fractions that specify the same amount with different place values are equivalent fractions. In the set of equivalent fractions, the fractions without a common factor between numerator and denominator is the simplest form.

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What is the fraction represented by the colored portion in the picture?

• 2/4
• 2/4
• 4/2

The answer is '2/4'

What is the fraction represented by the colored portion in the picture?

• 1/2
• 1/2
• 2/1

The answer is '1/2'

The picture shows three parts in three different colors.

•  The gray part shows the whole

•  The orange part shows the fraction 2/4

•  The purple part shows the fraction 1/2 The fraction 2/4 and 1/2 represent the same amount and the same number.

The numerator and denominator of one fraction is a multiple of numerator and denominator of another fraction respectively. Such fractions are called equivalent fractions.

What does the word 'equivalent' mean?

• enlarge and expand
• equal in value or amount
• equal in value or amount

The answer is 'equal in value or amount'.The equivalent fractions are fraction of equal amount.

What are the fractions 3/4 and (12)/(16) called?

• Pronunciation : Say the answer once

The picture shows four fractions , 1/2, 2/4, 3/6, and 4/8. These are equivalent fractions.

The fractions 2/4, 3/6, and 4/8 have numerator and denominator with common factors 2, 3 and 4 respectively.

Only the fraction 1/2 has no common factor between numerator and denominator. A fraction without a common factor between the numerator and the denominator is the simplest form of the equivalent fractions.

What does the word 'simplest' mean?

• without complexity; plain and elementary
• without complexity; plain and elementary
• not often and remarkable

The answer is 'without complexity; plain and elementary'.

What is the form of fraction that has no common factor between numerator and denominator?

• Pronunciation : Say the answer once

The answer is 'simplest form of a fraction'.

Fractions that specify the same amount with different place values are equivalent fractions.

The fraction that specifies the same amount with lowest denominator possible is the simplest form of equivalent fractions.

Equivalent Fraction: Two fractions p/q and l/m are equivalent if the numerators l, p and the denominators m, q have a common factor a. That is l = a xx p and m = a xx q. a is an integer. Note that, l/m and p/q specify the same amount with different place values.

Simplest Form of a fraction: A fraction p/q without a common factor between the numerator and the denominator is the simplest form of the equivalent fractions. That is, p != a xx q for any integer a.

Solved Exercise Problem:

Given fractions 1/2and 2/4. Which one is the simplest form of the given equivalent fractions?

• The given fractions are not equivalent
• 1/4
• 1/2
• 1/2
• 2/4

The answer is '1/2'.

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