Fractions Exercise 7.5 - CBSE Class 6 Maths NCERT Solutions & Concepts

Visualizing Addition and Subtraction of Like Fractions

To add or subtract like fractions, we must look at them as shaded parts of a single shape. Suppose a rectangle is divided into 5 equal parts. If we shade 2 parts, we represent it as \(\frac{2}{5}\). If we shade 1 more part, we represent it as \(\frac{1}{5}\).

Looking at the rectangle, we now have a total of 3 shaded parts out of 5, which represents \(\frac{3}{5}\). Visually, you can see that the size of the total slices (the denominator) did not change; only the number of shaded slices (the numerators) were added together. This is why when adding or subtracting like fractions, we only operate on the numerators and keep the common denominator exactly as it is!

How to Solve Like Fractions: Step-by-Step

1. Check the Denominators — Ensure that the denominators of the fractions you want to add or subtract are identical. For example, in \(\frac{5}{12} + frac{4}{12}\), both fractions have 12 as their denominator.
2. Operate on the Numerators — Add or subtract only the top numbers (numerators) based on the operator sign. If it is addition, add them (5 + 4 = 9). If it is subtraction, subtract them.
3. Retain the Denominator — Write the sum or difference over the common denominator. Do NOT add or subtract the bottom numbers. The result becomes \(\frac{9}{12}\).
4. Simplify (If Required) — Reduce the resulting fraction to its simplest form by dividing the numerator and denominator by their highest common factor (HCF). Here, \(\frac{9}{12}\) simplifies to \(\frac{3}{4}\).

Avoid the 'Denominator Trap'!

A very common mistake students make during their CBSE term exams is adding the denominators.

• Incorrect: \(\frac{2}{7} + \frac{3}{7} = \frac{5}{14}\)
• Correct: \(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\)

Remember, the denominator represents the total number of equal parts a whole is divided into. Adding the denominators would mean you are changing the size of the pieces, which is incorrect. Always keep the denominator unchanged!

Examples on Fractions Ex 7 5 Class 6 NCERT

• Example 1 (Addition): Find the sum of \(\frac{1}{18}\) and \(\frac{1}{18}\). Step 1: Check denominators. Both are 18. Step 2: Add the numerators: \(1 + 1 = 2\). Step 3: Write over the common denominator: \(\frac{2}{18}\). Step 4: Simplify by dividing both by 2: \(\frac{1}{9}\).
• Example 2 (Subtraction): Subtract \(\frac{3}{7}\) from \(\frac{5}{7}\). Step 1: Write the equation: \(\frac{5}{7} - \frac{3}{7}\). Step 2: Subtract the numerators: \(5 - 3 = 2\). Step 3: Keep the same denominator: \(\frac{2}{7}\).
• Example 3 (Missing Box): Find the missing fraction in: \([ ] - \frac{3}{6} = \frac{3}{6}\). Step 1: Treat the empty box as a variable. To find it, add \(\frac{3}{6}\) to both sides. Step 2: \([ ] = \frac{3}{6} + \frac{3}{6} = \frac{6}{6}\). Step 3: Since \(\frac{6}{6} = 1\), the missing value is 1 (or \(\frac{6}{6}\)).

Practice Questions with Solutions

• Q: Solve: \(\frac{7}{12} - \frac{5}{12}\) A: Step 1: Identify that the fractions are like fractions with a common denominator of 12. Step 2: Subtract the numerators: \(7 - 5 = 2\). Step 3: Place the result over the denominator to get \(\frac{2}{12}\). Step 4: Reduce the fraction to its simplest form by dividing both numbers by their common factor 2: \(\frac{2 \div 2}{12 \div 2} = \frac{1}{6}\). Final answer: \(\frac{1}{6}\)
• Q: Javed was given \(\frac{5}{7}\) of a basket of oranges. What fraction of oranges was left in the basket? A: Step 1: Represent the whole basket of oranges as the number 1, which can be written as a fraction \(\frac{7}{7}\) to match our denominator. Step 2: Set up the subtraction equation: \(\text{Leftover} = 1 - \frac{5}{7} = \frac{7}{7} - \frac{5}{7}\). Step 3: Subtract the numerators: \(7 - 5 = 2\) over the common denominator 7. Final answer: \(\frac{2}{7}\) of the basket of oranges was left.
• Q: Fill in the missing box: \(\frac{7}{10} - [ ] = \frac{3}{10}\) A: Step 1: To find the missing fraction, we need to subtract the result from the starting fraction. Step 2: Set up the equation: \([ ] = \frac{7}{10} - \frac{3}{10}\). Step 3: Subtract the numerators: \(7 - 3 = 4\). Step 4: Write it as \(\frac{4}{10}\), which simplifies to \(\frac{2}{5}\) when divided by 2. Final answer: \(\frac{4}{10}\) (or \(\frac{2}{5}\))
• Q: Ramesh painted \(\frac{2}{9}\) of a wall and his sister Suresh painted \(\frac{4}{9}\) of the wall space. How much did they paint together? A: Step 1: To find the total space painted, add the two individual fractions: \(\frac{2}{9} + \frac{4}{9}\). Step 2: Since the denominators are the same, add the numerators: \(2 + 4 = 6\). Step 3: Write the sum over the common denominator: \(\frac{6}{9}\). Step 4: Simplify by dividing the numerator and denominator by 3: \(\frac{6 \div 3}{9 \div 3} = \frac{2}{3}\). Final answer: They painted \(\frac{2}{3}\) of the wall together.

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