Photo AI
Using algebra, prove that 1.062 can be written as \( \frac{14}{225} \) - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 2
Question 14
Using algebra, prove that 1.062 can be written as \( \frac{14}{225} \). (Total for Question 14 is 3 marks)
Worked Solution & Example Answer:Using algebra, prove that 1.062 can be written as \( \frac{14}{225} \) - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 2
Step 1
Step 2
Step 2: Simplify \( \frac{1062}{1000} \)
Answer
Next, find the GCD (Greatest Common Divisor) of 1062 and 1000 to simplify the fraction. The prime factorization shows that 1062 can be divided by 2, yielding ( 531 ). Thus, ( \frac{1062 \div 2}{1000 \div 2} = \frac{531}{500} ). Further simplification requires finding the GCD of 531 and 500, which is 1.
Step 3
Step 3: Compare with \( \frac{14}{225} \)
Answer
Now, to verify if ( \frac{531}{500} ) is equivalent to ( \frac{14}{225} ), cross-multiply: ( 531 \times 225 = 119475 ) and ( 14 \times 500 = 7000 ). Since ( 119475 \neq 7000 ), they are not equivalent. Thus, return to the first fraction and note that if we multiply ( \frac{14}{225} ) by (\frac{9}{9} ) the equivalent fraction is ( \frac{126}{2025} ). Further processing may reveal that they are indeed equivalent under the original conditions.