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16 (a) Work out - OCR - GCSE Maths - Question 17 - 2023 - Paper 5
Question 17
16 (a) Work out. \[ \frac{2}{64^{\frac{3}{2}}} \] (b) \[ \frac{p}{q} + 0.13 = \frac{5}{9} \] where \( \frac{p}{q} \) is a fraction in its lowest terms. Find the va... show full transcript
Worked Solution & Example Answer:16 (a) Work out - OCR - GCSE Maths - Question 17 - 2023 - Paper 5
Step 1
Step 2
Find the value of p and the value of q.
Answer
Given ( \frac{p}{q} + 0.13 = \frac{5}{9} ), we first convert ( 0.13 ) to a fraction: [ 0.13 = \frac{13}{100} ]
Now, substituting this into the equation: [ \frac{p}{q} + \frac{13}{100} = \frac{5}{9} ]
Next, subtract ( \frac{13}{100} ) from both sides: [ \frac{p}{q} = \frac{5}{9} - \frac{13}{100} ]
To perform this subtraction, we need a common denominator, which would be 900: [ \frac{5}{9} = \frac{500}{900} ] [ \frac{13}{100} = \frac{117}{900} ]
So, [ \frac{p}{q} = \frac{500 - 117}{900} = \frac{383}{900} ]
Thus, ( p = 383 ) and ( q = 900 ), provided that the fraction is in its lowest terms.