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Think like a mathematician
3 Work with a partner to answer this question.
a The expression 
ab-(c)/(d) has a value of 24 . Write values for 
a,b,c and 
d when
i 
a,b,c and 
d are all positive numbers
ii 
a,b,c and 
d are all negative numbers
iii 
a,b,c and 
d are a mixture of positive and negative numbers.
b Discuss the methods you used, and the values you found, with other learners in your class.
c Look at the Thinking and Working Mathematically characteristics. Which characteristics do you think you have used here?

Think like a mathematician\newline33 Work with a partner to answer this question.\newlinea The expression abcd a b-\frac{c}{d} has a value of 2424 . Write values for a,b,c a, b, c and d d when\newlinei a,b,c a, b, c and d d are all positive numbers\newlineii a,b,c a, b, c and d d are all negative numbers\newlineiii a,b,c a, b, c and d d are a mixture of positive and negative numbers.\newlineb Discuss the methods you used, and the values you found, with other learners in your class.\newlinec Look at the Thinking and Working Mathematically characteristics. Which characteristics do you think you have used here?

Full solution

Q. Think like a mathematician\newline33 Work with a partner to answer this question.\newlinea The expression abcd a b-\frac{c}{d} has a value of 2424 . Write values for a,b,c a, b, c and d d when\newlinei a,b,c a, b, c and d d are all positive numbers\newlineii a,b,c a, b, c and d d are all negative numbers\newlineiii a,b,c a, b, c and d d are a mixture of positive and negative numbers.\newlineb Discuss the methods you used, and the values you found, with other learners in your class.\newlinec Look at the Thinking and Working Mathematically characteristics. Which characteristics do you think you have used here?
  1. Choose Positive Numbers: For ii, let's choose positive numbers for aa, bb, cc, and dd. Start with simple numbers like a=4a=4, b=6b=6, c=2c=2, and d=1d=1. Calculate abcdab-\frac{c}{d} to check if it equals aa00.
  2. Calculate abab: Calculate ab=4×6=24ab = 4 \times 6 = 24.
  3. Calculate (c)/(d)(c)/(d): Calculate (c)/(d)=21=2(c)/(d) = \frac{2}{1} = 2.
  4. Subtract to Check: Subtract (c)/(d)(c)/(d) from abab to get 242=2224 - 2 = 22. Oops, that's not 2424. Need to adjust the numbers.

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