Number Play | FIO

Question 11

Identify the numbers marked on the number lines below, and label the remaining positions.

Put a circle around the smallest number and a box around the largest number in each of the sequences above.

Solution

We will find the interval for each number line. Then we will label all positions. Finally, we will identify the smallest and largest numbers.

Step 1 — Find the interval for (a)

Look at number line (a). We see two numbers marked. These are 2010 and 2020. Let us count the spaces between them. There are 2 spaces between 2010 and 2020. The difference between these numbers is $2020 - 2010$ . This difference is 10. So, each space is 10 divided by 2.

$\text{Interval} = \frac{2020 - 2010}{2}$

$= \frac{10}{2}$

$\boxed{5}$

Step 2 — Label number line (a)

The interval for number line (a) is 5. We start from 2010. We add 5 to move to the right. We subtract 5 to move to the left.

Let us find numbers to the right of 2010: $2010 + 5 = 2015$ $2015 + 5 = 2020$ $2020 + 5 = 2025$ $2025 + 5 = 2030$ $2030 + 5 = 2035$

Let us find numbers to the left of 2010: $2010 - 5 = 2005$ $2005 - 5 = 2000$ $2000 - 5 = 1995$ $1995 - 5 = 1990$

The labeled positions for number line (a) are: 1990, 1995, 2000, 2005, 2010, 2015, 2020, 2025, 2030, 2035.

Step 3 — Find the interval for (b)

Look at number line (b). We see two numbers marked. These are 9996 and 9997. These numbers are on adjacent marks. So, the difference between them is the interval.

$\text{Interval} = 9997 - 9996$

$\boxed{1}$

Step 4 — Label number line (b)

The interval for number line (b) is 1. We start from 9996. We add 1 to move to the right. We subtract 1 to move to the left.

Let us find numbers to the right of 9996: $9996 + 1 = 9997$ $9997 + 1 = 9998$ $9998 + 1 = 9999$ $9999 + 1 = 10000$ $10000 + 1 = 10001$ $10001 + 1 = 10002$

Let us find numbers to the left of 9996: $9996 - 1 = 9995$ $9995 - 1 = 9994$ $9994 - 1 = 9993$

The labeled positions for number line (b) are: 9993, 9994, 9995, 9996, 9997, 9998, 9999, 10000, 10001, 10002.

Step 5 — Find the interval for (c)

Look at number line (c). We see two numbers marked. These are 15077 and 15078. These numbers are on adjacent marks. So, the difference between them is the interval.

$\text{Interval} = 15078 - 15077$

$\boxed{1}$

Step 6 — Label number line (c)

The interval for number line (c) is 1. We start from 15077. We add 1 to move to the right. There are no marks to the left of 15077 shown.

Let us find numbers to the right of 15077: $15077 + 1 = 15078$ $15078 + 1 = 15079$ $15079 + 1 = 15080$ $15080 + 1 = 15081$ $15081 + 1 = 15082$ $15082 + 1 = 15083$ $15083 + 1 = 15084$ $15084 + 1 = 15085$ $15085 + 1 = 15086$

The labeled positions for number line (c) are: 15077, 15078, 15079, 15080, 15081, 15082, 15083, 15084, 15085, 15086.

Step 7 — Find the interval for (d)

Look at number line (d). We see two numbers marked. These are 86705 and 87705. These numbers are on adjacent marks. So, the difference between them is the interval.

$\text{Interval} = 87705 - 86705$

$\boxed{1000}$

Step 8 — Label number line (d)

The interval for number line (d) is 1000. We start from 86705. We add 1000 to move to the right. We subtract 1000 to move to the left.

Let us find numbers to the right of 86705: $86705 + 1000 = 87705$ $87705 + 1000 = 88705$ $88705 + 1000 = 89705$ $89705 + 1000 = 90705$ $90705 + 1000 = 91705$ $91705 + 1000 = 92705$

Let us find numbers to the left of 86705: $86705 - 1000 = 85705$ $85705 - 1000 = 84705$ $84705 - 1000 = 83705$

The labeled positions for number line (d) are: 83705, 84705, 85705, 86705, 87705, 88705, 89705, 90705, 91705, 92705.

Diagram 1

Answer

(a) Sequence a: The marked numbers are 2010 and 2020. The interval between marks is 5. The labeled positions are: 1990, 1995, 2000, 2005, 2010, 2015, 2020, 2025, 2030, 2035. Smallest number: 1990 Largest number: 2035

(b) Sequence b: The marked numbers are 9996 and 9997. The interval between marks is 1. The labeled positions are: 9993, 9994, 9995, 9996, 9997, 9998, 9999, 10000, 10001, 10002. Smallest number: 9993 Largest number: 10002

(c) Sequence c: The marked numbers are 15077, 15078, and 15083. The interval between marks is 1. The labeled positions are: 15077, 15078, 15079, 15080, 15081, 15082, 15083, 15084, 15085, 15086. Smallest number: 15077 Largest number: 15086

(d) Sequence d: The marked numbers are 86705 and 87705. The interval between marks is 1000. The labeled positions are: 83705, 84705, 85705, 86705, 87705, 88705, 89705, 90705, 91705, 92705. Smallest number: 83705 Largest number: 92705

More questions in FIO

Colour or mark the supercells in the table below.

Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells.

Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.

Out of the 9 numbers, how many supercells are there in the table above?

Find out how many supercells are possible for different numbers of cells.

Do you notice any pattern? What is the method to fill a given table to get the maximum number of supercells? Explore and share your strategy.

Can you fill a supercell table without repeating numbers such that there are no supercells? Why or why not?

Will the cell having the largest number in a table always be a supercell? Can the cell having the smallest number in a table be a supercell? Why or why not?

Fill a table such that the cell having the second largest number is not a supercell.

Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible?

Q10

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Q11

Identify the numbers marked on the number lines below, and label the remaining positions.

Put a circle around the smallest number and a box around the largest number in each of the sequences above.

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a. the difference between the largest and smallest numbers greater than $5085$ .

b. the difference between the largest and smallest numbers less than $5085$ .

c. the sum of the largest and smallest numbers greater than $9779$ .

d. the sum of the largest and smallest numbers less than $9779$ .

Q16

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Q17

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Q18

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Q19

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Q20

Always, Sometimes, Never?

Below are some statements. Think, explore and find out if each of the statement is 'Always true', 'Only sometimes true' or 'Never true'. Why do you think so? Write your reasoning and discuss this with the class.

a. 5-digit number + 5-digit number gives a 5-digit number

b. 4-digit number + 2-digit number gives a 4-digit number

c. 4-digit number + 2-digit number gives a 6-digit number

d. 5-digit number – 5-digit number gives a 5-digit number

e. 5-digit number – 2-digit number gives a 3-digit number

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Q23

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Q24

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Q25

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Q31

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Q32

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Q33

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