MATHEMATICS (PAPER 1) 3 GRADE 9 ECTION A QUESTION 1 Answer questions $$ 1.1-1.5 $$ by choosing the correct answer. Circle the letter next to the correct nswer. Which of the options below contains rational numbers only? A $$ \frac{1}{4} ; \sqrt{\frac{4}{0}} ; \frac{22}{7} $$ B $$ \quad-2,5401 ; \sqrt{89} ; 4,3891016 $$ C $$ \sqrt{-100} ; 0,25 ; 4 $$ D $$ \quad-8 ;-\sqrt{144} ; 5 \frac{7}{8} $$ 1.2 To simplify $$ \left(100 p^{a}\right)^{b} \ldots $$ A add the exponents. B subtract the exponents. C multiply the exponents. D divide the exponents. (1) 1.3 Evaluate: $$ \frac{4}{5} x-\frac{1}{3} x-\frac{1}{15} x $$ A $$ \frac{2}{15} \mathrm{x} $$ B $$ \frac{2}{5} x $$ C $$ \frac{7}{15} \mathrm{x} $$ D $$ \quad \frac{2}{2} x $$

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### Question 1.1
We need to identify which option contains rational numbers only. A rational number is any number that can be expressed as the quotient or fraction of two integers.

- **Option A**: $$ \frac{1}{4} $$ is rational, $$ \sqrt{\frac{4}{0}} $$ is undefined (not rational), $$ \frac{22}{7} $$ is rational. **Not all are rational.**
  
- **Option B**: $$ -2.5401 $$ is rational, $$ \sqrt{89} $$ is irrational, $$ 4.3891016 $$ is rational. **Not all are rational.**
  
- **Option C**: $$ \sqrt{-100} $$ is imaginary (not rational), $$ 0.25 $$ is rational, $$ 4 $$ is rational. **Not all are rational.**
  
- **Option D**: $$ -8 $$ is rational, $$ -\sqrt{144} = -12 $$ is rational, $$ 5 \frac{7}{8} $$ is rational. **All are rational.**

**Correct answer: D**

### Question 1.2
To simplify $$ \left(100 p^{a}\right)^{b} $$, we apply the power of a product rule, which states that $$ (xy)^n = x^n y^n $$.

Thus, we can rewrite it as:
$$
(100)^b (p^a)^b = 100^b p^{ab}
$$
This means we multiply the exponents.

**Correct answer: C**

### Question 1.3
We need to evaluate the expression $$ \frac{4}{5} x - \frac{1}{3} x - \frac{1}{15} x $$.

First, we need a common denominator to combine these fractions. The least common multiple of $$ 5, 3, $$ and $$ 15 $$ is $$ 15 $$.

Now, we convert each term:
- $$ \frac{4}{5} x = \frac{12}{15} x $$
- $$ -\frac{1}{3} x = -\frac{5}{15} x $$
- $$ -\frac{1}{15} x = -\frac{1}{15} x $$

Now we can combine them:
$$
\frac{12}{15} x - \frac{5}{15} x - \frac{1}{15} x = \frac{12 - 5 - 1}{15} x = \frac{6}{15} x = \frac{2}{5} x
$$

**Correct answer: B**

### Summary of Answers
1.1: D  
1.2: C  
1.3: B
1.1: D 1.2: C 1.3: B

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