Chapter 1: Beginnings in Numbers

Question 1

Where are roman numerals commonly used?

Answer 1

Roman numerals are commonly used:

• in the prefaces of books to indicate the page number
• on the faces to clocks to indicate time
• on buildings to indicate the date of construction

Question 2

What does “MCMLXXXVII” mean ?

Answer 2

“MCMLXXXVII” means “1987”

• I means 1
• V means 5
• X means 10
• L means 50
• C means 100
• D means 500
• M means 1000

Also, putting a smaller unit in front of a larger unit means “subtract the smaller unit from the bigger unit”. For example:

• IV = 5 - 1 = 4
• CM = 1000 - 100 = 900

How to remember what they mean:

I Value Xylophones Like Cows Dig Milk

( I=1, V=5, X=10, L= 50, C=100, D=500, M=1,000). -

Question 3

Describe the invention of Hindu-Arabic numerals.

Answer 3

Hindu-Arabic numerals:

• Invented by Hindus in India
• Invented around 300 BC
• Spread quickly through Europe
• Has place value
• Has a symbol for zero
• Evolved into what we use today!

Question 4

Write the following numeral in words:

927 004

Answer 4

927 004 in words is:

nine hundred, twenty seven thousand, and four

Question 5

Write the following words as a numeral:

thirty-seven million, seventy thousand, eight hundred and forty-seven

Answer 5

“Thirty-seven million, seventy thousand, eight hundred and forty-seven” in numerals is:

37,070,847

Question 6

What is the opposite of “addition”?

What is the opposite of “multiplication”?

Answer 6

The opposite of addition is subtraction.

The opposite of multiplication is division.

Question 7

What are the steps to long division?

Solve using long division:

156 divided by 12

Answer 7

Question 8

When do we use a power?

Write the following as powers:

• 5 x 5 x 5
• 4 x 4 x 4 x 4 x 4
• 3 x 3 x 3 x 3

Answer 8

A power is used when a number

is used more than once in a product.

(dots between numbers means multiply,

so 2 • 2 is the same as 2 x 2)

Question 9

1. How do you say “4²” ?
2. How do you say “6³” ?
3. How do you say “2⁵”?

Answer 9

1. Four squared
2. Six cubed
3. Two to the power of five

Question 10

Write “2³” as a basic numeral.

Answer 10

A basic numeral is the simplest answer.

(stars/asteriks between numbers means multiply,

so 2 * 2 is the same as 2 x 2)

The basic numeral in this problem is 8.

Question 11

What does it mean to write a power using expanded form?

Write the expanded form of 2⁵.

Answer 11

Writing a power using expanded form means

to write out the number using multiplication symbols instead of the exponent.

The expanded form of 2⁵ is 2 x 2 x 2 x 2 x 2.

Question 12

What does it mean to write a number in expanded notation?

Write 95,164 in expanded notation.

Answer 12

Expanded notation is when you write a number

representing each place value with a power of ten.

95,164 in expanded notation is:

(9x 10⁴) + (5 x 10³) + (1 x 10²) + (6 x 10¹) + 4

Question 13

What does it mean to estimate using leading figure estimation?

Estimate the answer using leading figure estimation.for each number:

8342 - 2625

Answer 13

Leading figure estimation means that you round the number to the highest place value.

For example:

• 371 using leading figure estimation is 400.
• 21 using leading figure estimation is 20.
• 4536 using leading figure estimation is 5000.

To estimate the answer to a problem using leading figure estimation,

• Round each of the numbers using leading figure estimation.
• THEN subtract to get the estimated answer.

Example:

8342 - 2625

estimated numbers: 8000 - 3000 = 5000

The estimated answer is 5000

Question 14

Identify each symbol in ID Card 2:

Answer 14

ID Card 2: Symbols

1. plus
2. minus
3. times (multiply by)
4. divided by
5. equals
6. is approximately
7. does not equal
8. is less than
9. is less than or equal to
10. is not less than
11. is greater than
12. is greater than or equal to
13. is not greater than
14. is not greater than or equal to
15. four squared
16. four cubed
17. the square root of twenty five
18. the cube root of twenty five
19. percent
20. therefore
21. for example
22. in other words
23. numerator of a fraction
24. denominator of a fraction

Question 15

Identify each meaning of each phrase on ID Card 3.

Answer 15

1. 6 - 2 (minus means subtract)
2. 6 + 2 (sum means add)
3. 6 ÷ 2
4. 6 - 2
5. 6 ÷ 2 (the quotient is the answer after you divide)
6. the divisor is 2 (the number on the left)
7. the dividend is 6 (the number inside the radical)
8. 6 x 2 (lots means multiply)
9. 6 - 2
10. 6 x 2 (product means multiply)
11. 2 + 6
12. 6 - 2
13. 6² (6² = 6 x 6)
14. √ 36
15. 6 - 2 (take away means subtract)
16. 6 x 2
17. the average of a set of numbers is the sum of all the numbers, divided by how many numbers were in the set. In this case, the average of 6 and 2 is (6 + 2) ÷ 2 = (8) ÷ 2 = 4
18. 6 + 2
19. 6² (this is the same as saying six squared)
20. 6 - 2 (less means subtract)
21. 6 - 2 (difference means subtract)
22. 6 + 2 (increase means add)
23. 6 ÷ 2 (share means divide)
24. 6 + 2 (total means add)