Class 7 Maths Chapter 8 HOTS Question Answers - Working with Fractions

Q1: A garden is divided into 4 equal plots. Each plot is further divided into 3 equal sections, and 2/3 of each section is planted with flowers. What fraction of the entire garden is planted with flowers? If the garden’s area is 120 square meters, what is the planted area?

Ans: Each plot has 3 sections, so total sections = 4 × 3 = 12.
2/3 of each section is planted, so planted part per section = 2/3.
Total planted fraction = 12 × (2/3) = 8.
So, 8 out of 12 parts are planted = 8/12 = 2/3 of the garden.
Planted area = 2/3 × 120 = 80 square meters.

Q2: If Tsewang plants 5 saplings with 3/4 m between each pair and adds a fence around them with an additional 1/2 m border at each end, what is the total length of the fence? 

Ans: 

There are 5 saplings, so 4 gaps between them.
Distance between saplings = 4 × 3/4 = 3 m.
Border at both ends = 1/2 + 1/2 = 1 m.
Total length = 3 + 1 = 4 meters.

Q3: A painter mixes red and blue paint in the ratio 2/3 . If the total paint is 15 liters, how much red paint is used? If the painter uses 4/5 of the red paint, how much red paint remains?

Ans: Red part = 2 out of total 2 + 3 = 5 parts.
Red paint = (2/5) × 15 = 6 liters.
Used red paint = (4/5) × 6 = 4.8 liters.
Remaining red paint = 6 − 4.8 = 1.2 liters.

Q4:A rope is cut into two pieces in the ratio 3/5 . The longer piece is then cut into 4 equal parts, and 2/3  of one part is used. What fraction of the original rope is used? If the rope was 20 meters long, what is the length used?

Ans: 

Ratio 3/5. Total parts: 3 + 5 = 8. Longer piece: 5/8 of rope.

Longer piece cut into 4 parts: Each part = 5/8 ÷ 4 = 5/8 × 1/4 = 5/32.

Used portion: 2/3 × 5/32 = 10/96 = 5/48 of original rope.

Rope length: 20 m. Used length: 5/48 × 20 = 100/48 = 25/12 ≈ 2.083 m.

Q5: A rectangular plot has dimensions 5/6 m by 3/4 m. It is divided into equal squares, each with side length 1/12 m. How many squares fit in the plot? If 2/5 of the squares are planted with grass, how many squares are planted?

Ans: 

Area of the plot = (5/6) × (3/4) = 15/24 = 5/8 m².
Area of one square = (1/12) × (1/12) = 1/144 m².
Number of squares = (5/8) ÷ (1/144) = (5/8) × 144 = 90.
Squares planted = (2/5) × 90 = 36 squares.