Maharashtra Board Class 6 Maths part 1 Chapter 4 Operations on Fractions PDF Download

Operations On Fractions

Let's Recall

Let's divide the apples equally between two children.

Let's Learn

Conversion Of An Improper Fraction Into A Mixed Number

Example: If 7 apples are divided equally between 2 people, how many will each one get?

\(\frac{7}{2}\) = 7 ÷ 2

Each will get 3 full apples and \(\frac{1}{2}\) apple.

When we divide 7 by 2, we get:

Quotient = 3

Remainder = 1

Divisor = 2

\(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Take Care!

While dividing, we take care to see that the remainder is smaller than the divisor. As a result, in the mixed number, the numerator of the fractional part is smaller than its denominator.

Teacher's Note

When we share 7 apples between 2 children, each child gets 3 whole apples and half an apple. This is like sharing 7 rupees between 2 people - each gets 3 rupees and 50 paise.

Exam Trick

Remember: Improper fraction means the top number is bigger than the bottom number. Mixed number means you have a whole number plus a fraction. Just convert by dividing!

Points To Remember

When you divide an improper fraction, the remainder must be smaller than the divisor.
The mixed number has a whole part and a fractional part.
The numerator of the fraction part is always smaller than the denominator.
You can check your answer by multiplying back: 3 × 2 + 1 = 7.

Conversion Of A Mixed Number Into An Improper Fraction

Example: 3\(\frac{2}{5}\) is a mixed number. Convert this into an improper fraction.

3\(\frac{2}{5}\) = 3 + \(\frac{2}{5}\)

= \(\frac{3}{1}\) + \(\frac{2}{5}\)

= \(\frac{3 \times 5}{1 \times 5}\) + \(\frac{2}{5}\)

= \(\frac{3 \times 5 + 2}{5}\)

= \(\frac{15 + 2}{5}\)

= \(\frac{17}{5}\)

Teacher's Note

To convert a mixed number like 3\(\frac{2}{5}\), multiply the whole number by the denominator, then add the numerator. This is like counting: 3 whole things plus 2 more parts.

Exam Trick

Remember the formula: (Whole number × Denominator + Numerator) ÷ Denominator. Write it on paper first, then solve step by step.

Points To Remember

Multiply the whole number by the bottom number.
Add the numerator to this answer.
Put this new number on top and keep the same denominator on the bottom.
Check: Your new fraction should be bigger than the mixed number.

Addition And Subtraction Of Mixed Numbers

Example 1: Add 5\(\frac{1}{2}\) + 2\(\frac{3}{4}\)

Method I

5\(\frac{1}{2}\) + 2\(\frac{3}{4}\) = 5 + 2 + \(\frac{1}{2}\) + \(\frac{3}{4}\)

= 7 + \(\frac{1 \times 2}{2 \times 2}\) + \(\frac{3}{4}\)

= 7 + \(\frac{2}{4}\) + \(\frac{3}{4}\)

= 7 + \(\frac{2 + 3}{4}\)

= 7 + \(\frac{5}{4}\)

= 7 + 1\(\frac{1}{4}\)

= 8\(\frac{1}{4}\)

Method II

5\(\frac{1}{2}\) + 2\(\frac{3}{4}\) = \(\frac{5 \times 2 + 1}{2}\) + \(\frac{2 \times 4 + 3}{4}\)

= \(\frac{11}{2}\) + \(\frac{11}{4}\)

= \(\frac{11 \times 2}{2 \times 2}\) + \(\frac{11}{4}\)

= \(\frac{22}{4}\) + \(\frac{11}{4}\)

= \(\frac{22 + 11}{4}\)

= \(\frac{33}{4}\)

= 8\(\frac{1}{4}\)

Teacher's Note

When adding mixed numbers like 5\(\frac{1}{2}\) and 2\(\frac{3}{4}\), you can add the whole numbers first, then add the fractions. It is like adding 5 rupees and 2 rupees, then adding 50 paise and 75 paise together.

Exam Trick

Use Method I if the fractions have easy denominators. Use Method II if you want to be very careful and convert everything to improper fractions first.

Points To Remember

You can add whole numbers and fractions separately.
Make sure the fractions have the same denominator before adding them.
Method I is easier and faster for most problems.
Always check if your final fraction can be made into a mixed number.

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