Week 7 - Rational Numbers

Question 1

Rational Numbers

Answer 1

Rational numbers are all integers, fractions,
repeating decimals and terminating decimals.

They’re any number that can be written in the form a/b

Where a and b are whole numbers but b is not equal to zero

Question 2

Fractions

Define
3/5 what does it mean example

Answer 2

Any part of a group, number or whole.

3/5 = 3 fifths
Divide a unit length into 5 equal parts and take 3 of these parts

Question 3

Different representation of rational numbers

F
D
P

Answer 3

Fractions: 3/4 is the fraction three quarters
Decimal: 0.75 (75/100) is the decimal fraction representing three quarters
Percentage: 75% means the same as 3/4 or 0.75

Question 4

Different interpretations of fractions

Answer 4

• To describe equal parts of a whole
• To describe equal parts of a collection of objects
• To denote numbers e.g. 1/2 is midway between 0 and 1
• As operators related to division e.g. 2/3 of the class
• To indicate division e.g. the truck is 3 times as long as the car, or in a ratio of 3:1

Question 5

Fractions as a number

(number line)

Answer 5

A fraction refers to a number that can be located on a number line

Fractional units in combination with whole units provide an accurate means of measuring

E.g. 1/2, 7/8, 1 3/4, 5/2 (from left to right on number line)

Question 6

Fractions as operators

Answer 6

The fraction can act as an operator related to division, that transforms a quantity by reducing (shrinking) or enlarging (stretching) the size of a quantity

E.g. 3/4 of the 16 participants at the workshop were men. How many men attended the workshop?
12

Question 7

Fractions represent division

Answer 7

A fraction can represent the result of division between two whole numbers

E.g. sharing 12 drinks between 6 kids

12 divided by 6 = 12/6 = 2/1 = 2

Question 8

Fractions represent a ratio

Answer 8

The fraction represents a multiplicative relationship to compare the size of 2 sets

E.g. the number of girls in the class is 2/3 the number of boys
= 2:3
2 girls for every 3 boys

If there are 6 boys in the class, how many girls are there?
3/2 (boys - girls)
4/10 (class is girls)
6/10 (class is boys

Question 9

Equivalent fractions

Answer 9

For whole numbers, there is only one way of representing a number of numerals (0-9)

A fraction quantity, like a decimal, can be represented by an infinite number of ways

All fractions in an equivalence class are interchangeable since they represent the same quantity

E.g. 1/2 = 2/4 = 3/6 = 4/8

The equivalent fraction is achieved by multiplying or dividing the numerator and the denominator by the same number

Question 10

Most common use of fractions

Calculating a simple fraction of a group of quantity

E.g. 1/3 off sale
Cost $60

Answer 10

1/3 of $60 = $20
60-20 = $40

Question 11

Numbers with Letter Symbols

Natural
Integers
Rational
Real Numbers
Complex

Answer 11

Natural = N
Integers = Z
Rational = Q
Real numbers = R
Complex = C

Question 12

1. Rational numbers and irrational numbers form the _____
2. Natural numbers {1, 2, 3, …} are a subset of _____
3. Integers are a subset of ________, which are ___.
4. Whole numbers are a subset of ______

Answer 12

1. set of real numbers.
2. whole numbers {0, 1, 2, 3,…}
3. rational numbers, any numbers which can be expressed as a terminating or recurring decimal or fraction
4. integers {…, -3, -2, -1, 0, 1, 2, 3, …}

Question 13

Use of fractions

4 ways

Answer 13

A part of a whole (shape half shaded in = 1/2)

Fractions as a number (number line, pointed to the middle = 1/2)

Fractions as division (1 divided by 2 = 1/2)

Fractions as part of a set (1 red ball and 1 white ball, fraction of red balls is 1/2)