Class 5 Mathematics

Chapter 5 Solutions — Far and Near

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Solutions

Overview

Step-by-step NCERT solutions for Far and Near (Chapter 5, NCERT Class 5 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Far and Near textbook chapter.

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What these solutions cover

All 34 questions in Far and Near are solved in the PDF. Here's what's inside, exercise by exercise:

Let Us Find — Units for measuring quantities (p. 57)

1.
Identify the appropriate units for measuring each of the following.
- (a) Height of India Gate
- (b) Length of a handkerchief
- (c) Depth of a well
- (d) Length of a mobile phone
- (e) Length of an elephant's trunk
- (f) Distance between two buttons on a shirt

Different Units but Same Measure — Matching saris/stoles on a double number line (p. 57)

Shikha and Sonu are measuring lengths of saris and stoles. The double number line shows cm on top (100 cm, 200 cm, 400 cm, 500 cm, 700 cm) and metres below (1 m, 2 m, ___ m, ___ m, ___ m). Fill in the blanks on the number line and match each measurement on the left with the same length on the right. Left side: 204 cm, 540 cm, 750 cm, 240 cm, 404 cm Right side: 5 metre 40 cm, 2 metre 204 cm, 2…

Let Us Compare

1.
Ritika is comparing the lengths of different rods. Compare them using <, =, > signs.
- (a) 456 cm ____ 5 m
- (b) 55 cm + 200 cm ____ 200 cm + 54 cm
- (c) 6 m 5 cm ___ 6 m 50 cm
- (d) 2 m 150 cm ___ 3 m 50 cm
- (e) 238 cm ____ 138 cm + 1 m
2.
World's tallest statues (heights given in the picture): Statue of Unity, India — 182 m Spring Temple Buddha, China — 128 m Guanyin of Nanshan, China — 108 m The Motherland Calls, Russia — 91 m Statue of Liberty, USA — 93 m Christ the Redeemer, Brazil — 38 m
- (a) What is the difference between the height of the tallest statue in the world and the Statue of Liberty?
- (b) Identify the statues whose…

Let Us Do — Measuring distances in school playground (p. 59)

1.
Measure 100 m and 200 m on your school playground using a Long Tape. Mark these points and draw a straight line. Walk on the lines and count your steps. Use the steps-to-distance relationship to find distances for at least 3 locations around you.
- (a) Identify and write the locations that are the nearest and the farthest from your home.
- (b) Write the distances obtained above in increasing order…

Let Us Explore — Ropes needed to make 1 km (p. 59)

1,000 m = 1 km. Fill in the table: how many ropes of each length are needed to make 1 km? Length of rope: 1,000 m, 100 m, 10 m, 200 m, 500 m, 250 m

Kilometre Race — Arrangements for a 3 km race (p. 60)

Sheena and Jennifer are helping to organise a 3-km race. Water stations are to be arranged after every 500 m. How many water stations must be set up? At what positions from the starting point will these water stations be placed?
Children need to stand at an interval of 300 m to direct the runners. How many children are needed? At what positions from the starting point will the children be standing?
Red and blue flags are to be placed alternately at every 50 m. How many red and blue flags are needed till the finish line?

Let Us Do — Longest Train Journey (Vivek Express route) (p. 60)

The total length of the route from Dibrugarh to Kanniyakumari is _______________ km.
The distance between Vijayawada and Jalpaiguri Road is _______________.
Distance between Vijayawada and Visakhapatnam is _______________.
Which two stations are farther apart — Guwahati and Dimapur or Bhubaneswar and Jalpaiguri Road?
What is the distance between Guwahati and Coimbatore JN?

Let Us Explore

Look at the scale (ruler). Count how many marks are there between 1 cm and 2 cm.

Let Us Measure — Measure lines in a design in cm and mm (p. 61)

Measure the lines in the design and write their measurements in cm and mm.

Let Us Do — Measuring sprout growth in mm over 4 days (p. 62)

Soak moong or chana seeds overnight. Wrap in moist cloth to sprout. Over 4 days, take out one seed each day and measure the length of the sprout in mm. Record in the table: Day 1, Day 2, Day 3, Day 4.

Let Us Draw — Draw lines of given lengths using a scale (p. 62)

Draw lines of the following lengths in your notebook using a scale. 1. 5 cm 5 mm 2. 3 cm 6 mm 3. 8 cm 3 mm 4. 36 mm 5. 67 mm How did you draw lines of lengths 36 mm and 67 mm? Share your thoughts in class.

Let Us Do — Double number lines and unit conversions (p. 63)

1.
Fill in the blanks appropriately in the double number lines given below.
- (a) Top (cm): 1 cm, 7 cm, 15 cm, ___ cm, ___ cm, ___ cm, 50 cm. Bottom (mm): 10 mm, ___ mm, ___ mm, 250 mm, 320 mm, 450 mm, ___ m.
- (b) Top (m): 1 m, 4 m, 10 m, ___ m, ___ m, ___ m, 21 m. Bottom (cm): ___ cm, ___ cm, ___ cm, 1,200 cm, 1,400 cm, 1,700 cm, ___ cm.
- (c) Top (km): 1 km, 9 km, 25 km, ___ km, ___ km, ___ km, 82 km…
2.
Use your understanding from above to fill in the blanks appropriately.
- (a) 4 cm 5 mm = ______ mm
- (b) 89 mm = ____ cm ____ mm
- (c) 234 cm = ____ mm
- (d) 514 mm = ____ cm ____ mm
- (e) 6 m 34 cm = ____ cm
- (f) 20 m 12 cm = ____ cm
- (g) 397 m = ______ cm
- (h) 5,792 cm = ______m ______ cm
- (i) 9,108 cm = ______ m ______ cm
- (j) 34 km = _______ m
- (k) 6,870 m = ____ km ____ m
- (l) 10,552 m = ____ km ___ m (m)…

Let Us Do — Adding and Subtracting Lengths (p. 66)

Rani has two red-coloured ribbon rolls, one of length 3 m 75 cm and another 2 m 25 cm long. How much ribbon does she have?
The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on the way, and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?
Gulmarg Gondola in Gulmarg, Kashmir is the second longest and second highest cable car in the world. It is divided into two sections. The first section covers 2 km 300 m and the second section covers 2 km 650 m. What is the total distance covered by the cable car?
4.
Circle the bigger length and find the difference.
- (a) 11 mm and 1 cm
- (b) 26 mm and 2 cm
- (c) 20 cm and 201 mm
- (d) 1,020 mm and 1 m
- (e) 2 m and 245 cm
- (f) 5,678 m and 6 km
- (g) 6 km 1,480 m and 7 km 479 m

Multiplying and Dividing Lengths

We need a 1 m 80 cm cloth to make a shirt for a 10-year-old child. How much cloth will be needed to make shirts for 20 such children? (The book shows: 20 x 1 m 80 cm = 20 x 1 m and 20 x 80 cm = 20 m + 1,600 cm = 20 m + 16 m = 36 m.)
A shop sells cloth for making bags at Rs 100 for 5 m. How much money is needed to buy a 1 m cloth? Now use the double number line (5 m = Rs 100; 10 m = Rs ___; 20 m = Rs ___; 40 m = Rs ___; ___ m = Rs 2,000) to find the cost or length.
Anita is making an embroidery on the border of a sari. She needs a 1 m long thread to embroider a 50 cm sari. How much thread would she need for a 5 m sari border? A 1 m long thread costs Rs 50. How much money will be needed to buy the thread?
A road 12 km 600 m long is being laid in a town. The workers lay an equal length of road each day, and complete the work in 6 days. How much road-laying work is done on each day?

Let Us Estimate

Estimate the height of the tallest building in your neighbourhood. What did you use as a reference to estimate the height?
Estimate the height of the tallest tree in your neighbourhood. What did you use as a reference?
Estimate the depth of a well or swimming pool in your neighbourhood. How did you find out?

Let Us Explore — Inches and feet; measuring your height (p. 68–69)

Look at your ruler to see if inches are marked on it. Find out how many cm and mm equal 1 inch. (The picture in the book shows 1 inch spans from 0 to 1 inch on the cm scale.)
Measure Your Height: Stand against a wall and mark your height. Measure the distance between the floor and the marked point in feet and inches. Find out who is the tallest student in your class and their height in feet and inches.

Try This — Operation sign Latin square puzzle (p. 69)

Put appropriate operation sign (+, -, x, /) such that each row, each column, and each 2x2 box (4 quadrants of the 4x4 grid) should not repeat the sign. The grid has these signs already filled in: row 1 col 1 = /, row 1 col 4 = +; row 2 col 2 = x; row 3 col 3 = +; row 4 col 4 = -.

Sample

Worked examples

3 questions from Far and Near, solved step by step.

Kilometre Race — Arrangements for a 3 km race (p. 60)

Sheena and Jennifer are helping to organise a 3-km race. Water stations are to be arranged after every 500 m. How many water stations must be set up? At what positions from the starting point will these water stations be placed?

Total race = 3 km = 3,000 m.

Water station every 500 m.

Number of stations = 3,000 / 500 = 6 stations.

Positions from start: 500 m, 1,000 m, 1,500 m, 2,000 m, 2,500 m, 3,000 m (finish line).

Answer: 6 water stations, at 500 m, 1,000 m, 1,500 m, 2,000 m, 2,500 m, and 3,000 m from the starting point.

Let Us Do — Longest Train Journey (Vivek Express route) (p. 60)

Which two stations are farther apart — Guwahati and Dimapur or Bhubaneswar and Jalpaiguri Road?

Guwahati (556 km) and Dimapur (306 km): distance = 556 - 306 = 250 km.

Bhubaneswar (2,007 km) and Jalpaiguri Road (983 km): distance = 2,007 - 983 = 1,024 km.

1,024 km > 250 km.

Bhubaneswar and Jalpaiguri Road are farther apart.

Answer: Bhubaneswar and Jalpaiguri Road are farther apart (1,024 km vs 250 km).

Let Us Do — Adding and Subtracting Lengths (p. 66)

The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on the way, and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?

Distance from waterfall to Sanchi = Total distance - Distance to waterfall.

= 48 km 700 m - 17 km 900 m.

Convert to metres: 48,700 m - 17,900 m = 30,800 m.

30,800 m = 30,000 m + 800 m = 30 km 800 m.

Answer: 30 km 800 m

All 34 questions in Far and Near are solved step by step in the Solutions PDF above.

Keep solving

Chapter 5 Solutions — Far and Near

Overview

What these solutions cover

Let Us Find — Units for measuring quantities (p. 57)

Different Units but Same Measure — Matching saris/stoles on a double number line (p. 57)

Let Us Compare

Let Us Do — Measuring distances in school playground (p. 59)

Let Us Explore — Ropes needed to make 1 km (p. 59)

Kilometre Race — Arrangements for a 3 km race (p. 60)

Let Us Do — Longest Train Journey (Vivek Express route) (p. 60)

Let Us Explore

Let Us Measure — Measure lines in a design in cm and mm (p. 61)

Let Us Do — Measuring sprout growth in mm over 4 days (p. 62)

Let Us Draw — Draw lines of given lengths using a scale (p. 62)

Let Us Do — Double number lines and unit conversions (p. 63)

Let Us Do — Adding and Subtracting Lengths (p. 66)

Multiplying and Dividing Lengths

Let Us Estimate

Let Us Explore — Inches and feet; measuring your height (p. 68–69)

Try This — Operation sign Latin square puzzle (p. 69)

Worked examples

Sheena and Jennifer are helping to organise a 3-km race. Water stations are to be arranged after every 500 m. How many water stations must be set up? At what positions from the starting point will these water stations be placed?

Which two stations are farther apart — Guwahati and Dimapur or Bhubaneswar and Jalpaiguri Road?

The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on the way, and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?

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