NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Problems and Solutions

Question 124

How to match each fraction: Remember: in a fraction numerator/denominator, the denominator tells total equal parts, and the numerator tells shaded (or marked) parts.

(i) Match for ( dfrac{6}{4} ) → (D)

• Step 1: Look at the denominator (4). This means “1 whole is cut into 4 equal parts.”
• Step 2: The numerator is (6). So we need “6 parts of size one-fourth.”
• Step 3: ( dfrac{6}{4} ) is an improper fraction. Change it to a mixed number: ( dfrac{6}{4} = 1 dfrac{2}{4} ).
• Step 4: ( 1 dfrac{2}{4} ) means “one whole shaded” and “another half of a whole shaded” (since ( dfrac{2}{4} = dfrac{1}{2} )).
• Step 5: Figure (D) shows exactly this: one whole region plus half of the next region shaded.

(ii) Match for ( dfrac{6}{10} ) → (E)

• Step 1: Denominator (10) means “the shape is split into 10 equal parts.”
• Step 2: Numerator (6) means “6 of those parts are shaded.”
• Step 3: So we are looking for a figure with 10 equal pieces and exactly 6 shaded.
• Step 4: Figure (E) shows 10 equal parts with 6 shaded, which matches ( dfrac{6}{10} ).

(iii) Match for ( dfrac{6}{6} ) → (A)

• Step 1: Denominator (6) → “6 equal parts make one whole.”
• Step 2: Numerator (6) → “all 6 parts are shaded.”
• Step 3: When numerator = denominator, the value is (1): ( dfrac{6}{6} = 1 ).
• Step 4: Figure (A) represents one complete whole (e.g., the point at 1 on a number line or a fully shaded whole).

(iv) Match for ( dfrac{6}{16} ) → (B)

• Step 1: Denominator (16) → “the shape is split into 16 equal parts.”
• Step 2: Numerator (6) → “6 of those parts are shaded.”
• Step 3: A common way to get 16 parts is a (4 imes 4) grid.
• Step 4: Figure (B) shows a (4 imes 4) grid (16 small squares) with 6 shaded, which matches ( dfrac{6}{16} ).
• Optional: You can simplify ( dfrac{6}{16} ) by dividing top and bottom by (2): ( dfrac{6}{16} = dfrac{3}{8} ). The picture still represents the same amount.

Final matches:

(i) ( dfrac{6}{4} ) → (D)   |   (ii) ( dfrac{6}{10} ) → (E)   |   (iii) ( dfrac{6}{6} ) → (A)   |   (iv) ( dfrac{6}{16} ) → (B)