Which is larger? Find out without fully computing the product. (i) 14 × 26 or 16 × 24 (ii) 25 × 75 or 26 × 74

(i) 16 × 24 is larger. Both have sum 40, but 16 and 24 are closer to 20 than 14 and 26, making their product larger. (ii) 26 × 74 is larger. 26 × 74 = 1924 while 25 × 75 = 1875. — (i) For fixed sum, product is maximized when factors are equal. 16 × 24 = 384, 14 × 26 = 364. (ii) Using Identity 1C: 26 × 74 = (50-24)(50+24) = 2500 - 576 = 1924. 25 × 75 = (50-25)(50+25) = 2500 - 625 = 1875.

Which is larger? Find out without fully computing the product. (i)…

Question 27 of 27intermediate🔍 AnalyzeShort Answer3 marks

Which is larger? Find out without fully computing the product. (i) $14 \times 26$ or $16 \times 24$ (ii) $25 \times 75$ or $26 \times 74$

(i)

Answer

$16 \times 24$ is larger. Both have sum 40, but $16$ and $24$ are closer to $20$ than $14$ and $26$ , making their product larger.

(ii)

Answer

$26 \times 74$ is larger. $26 \times 74 = 1924$ while $25 \times 75 = 1875$ .

Explanation

(i) For fixed sum, product is maximized when factors are equal. $16 \times 24 = 384$ , $14 \times 26 = 364$ . (ii) Using Identity 1C: $26 \times 74 = (50-24)(50+24) = 2500 - 576 = 1924$ . $25 \times 75 = (50-25)(50+25) = 2500 - 625 = 1875$ .