CBSE Class 6 Maths NCERT Solutions: Chapter 4 - Fractions and Decimals

To determine which fraction is not equal to 4/5, we can simplify each option:

• (A) 40/50: Divide both numerator and denominator by 10, which gives 4/5.
• (B) 12/15: Divide both numerator and denominator by 3, which gives 4/5.
• (C) 16/20: Divide both numerator and denominator by 4, which gives 4/5.
• (D) 9/15: Divide both numerator and denominator by 3, which gives 3/5.

The fraction 9/15 simplifies to 3/5, which is not equal to 4/5. Therefore, option (D) is the correct answer.

To find the consecutive integers between which the fraction 5/7 lies, we can convert the fraction to a decimal.

$5\; \backslash div\; 7\; \backslash approx\; 0.71$

The decimal value 0.71 is greater than 0 and less than 1. Therefore, the fraction 5/7 lies between the consecutive integers 0 and 1. Option (B) is correct.

We are given the fraction $\backslash frac\{1\}\{4\}$ and we need to find an equivalent fraction with a denominator of 12. To change the denominator from 4 to 12, we must multiply it by 3 (since $4\; \backslash times\; 3\; =\; 12$). To keep the fraction equivalent, we must also multiply the numerator by the same number.

So, the new fraction is $\backslash frac\{1\; \backslash times\; 3\}\{4\; \backslash times\; 3\}\; =\; \backslash frac\{3\}\{12\}$.

The numerator of this equivalent fraction is 3. Therefore, option (A) is correct.

A fraction is in its lowest form if the greatest common divisor (GCD) of its numerator and denominator is 1. Let's examine each option:

• (A) 7/5: The GCD of 7 and 5 is 1. So, 7/5 is in the lowest form.
• (B) 15/20: The GCD of 15 and 20 is 5. Since the GCD is not 1, this fraction is not in the lowest form. It can be simplified to $\backslash frac\{15\; \backslash div\; 5\}\{20\; \backslash div\; 5\}\; =\; \backslash frac\{3\}\{4\}$.
• (C) 13/33: The GCD of 13 and 33 is 1. So, 13/33 is in the lowest form.
• (D) 27/28: The GCD of 27 and 28 is 1. So, 27/28 is in the lowest form.

Therefore, the fraction 15/20 is not in the lowest form. Option (B) is correct.

We are given the equation $$\backslash frac\{5\}\{8\}\; =\; \backslash frac\{20\}\{p\}$$.

To find the value of p, we can use cross-multiplication:

$5\; \backslash times\; p\; =\; 8\; \backslash times\; 20$

$5p\; =\; 160$

Now, divide both sides by 5 to solve for p:

$p\; =\; \backslash frac\{160\}\{5\}$

$p\; =\; 32$

Thus, the value of p is 32. Option (C) is correct.

To find which fraction is not equal to the others, we need to simplify each fraction to its lowest terms:

• (A) 6/8: Divide both numerator and denominator by their GCD, which is 2. $\backslash frac\{6\; \backslash div\; 2\}\{8\; \backslash div\; 2\}\; =\; \backslash frac\{3\}\{4\}$.
• (B) 12/16: Divide both numerator and denominator by their GCD, which is 4. $\backslash frac\{12\; \backslash div\; 4\}\{16\; \backslash div\; 4\}\; =\; \backslash frac\{3\}\{4\}$.
• (C) 15/25: Divide both numerator and denominator by their GCD, which is 5. $\backslash frac\{15\; \backslash div\; 5\}\{25\; \backslash div\; 5\}\; =\; \backslash frac\{3\}\{5\}$.
• (D) 18/24: Divide both numerator and denominator by their GCD, which is 6. $\backslash frac\{18\; \backslash div\; 6\}\{24\; \backslash div\; 6\}\; =\; \backslash frac\{3\}\{4\}$.

Fractions (A), (B), and (D) all simplify to 3/4. Fraction (C) simplifies to 3/5. Therefore, 15/25 is not equal to the others. Option (C) is correct.

When comparing fractions that have the same numerator, the fraction with the smallest denominator is the greatest. This is because the numerator represents a fixed number of parts, and a smaller denominator means each part is larger.

In this case, all fractions have the numerator 5. We compare the denominators: 7, 6, 9, and 8.

The smallest denominator among these is 6.

Therefore, the fraction 5/6 is the greatest. Option (B) is correct.