Question

6.2a (m)

1. the venn diagram below shows how real numbers can be classified.

in which category would $-\frac{3}{8}$ appear?
a integers
b natural numbers
c rational numbers
d whole numbers

6.2d (l)

1. which fraction is greater than $\frac{1}{2}$ but less than $\frac{5}{6}$?

a $\frac{1}{4}$
b $\frac{1}{3}$
c $\frac{3}{5}$
d $\frac{3}{7}$

Explanation:

Question 1

Step1: Recall number categories

Natural Numbers: positive integers (1,2,3...). Whole Numbers: natural numbers + 0. Integers: whole numbers + negatives (-1,-2,0,1...). Rational Numbers: numbers expressible as \( \frac{a}{b} \) (a,b integers, \( b
eq 0 \)).

Step2: Analyze \( -\frac{3}{8} \)

• Not Natural (negative, not positive integer).
• Not Whole (negative, not 0 or positive integer).
• Not Integer (not a whole number, it's a fraction).
• Is Rational (expressed as \( \frac{-3}{8} \), a,b integers, \( b = 8

eq 0 \)).

Step1: Find common denominator

Convert \( \frac{1}{2} \), \( \frac{5}{6} \), and options to sixths (or common denominator) for comparison. \( \frac{1}{2} = \frac{3}{6} \), \( \frac{5}{6} = \frac{5}{6} \).

Step2: Analyze each option

• A: \( \frac{1}{4} = 0.25 \), \( \frac{1}{2} = 0.5 \), \( 0.25 < 0.5 \) → No.
• B: \( \frac{1}{3} \approx 0.33 \), \( 0.33 < 0.5 \) → No.
• C: \( \frac{3}{5} = 0.6 \), \( \frac{1}{2} = 0.5 \), \( \frac{5}{6} \approx 0.83 \). \( 0.5 < 0.6 < 0.83 \) → Yes.
• D: \( \frac{3}{7} \approx 0.43 \), \( 0.43 < 0.5 \) → No.

Answer:

C. Rational Numbers

Question 2