Question

The following area model shows (29 times 97) broken into parts:

a) (2000 + 800 + 140 + 27)
b) (2900 + 700 + 140 + 21)
c) (2000 + 900 + 210 + 63)
d) (2900 + 900 + 210 + 27)

Answer 1

Option c correctly expands the multiplication of 29 times 97 using an area model, resulting in 2000 + 900 + 210 + 63.

Step-by-step explanation:

The question deals with multiplying two numbers using an area model. To perform the multiplication 29 times 97, we can break it down into parts: tens and ones, which have been done differently in each given option. Let's check which option correctly represents the multiplication:

• (29 times 97) = 29 times (90 + 7)
• = 29 times 90 + 29 times 7
• = (20 times 90 + 9 times 90) + (20 times 7 + 9 times 7)
• = (1800 + 810) + (140 + 63)
• = 2000 + 900 + 210 + 63

Hence, the accurate expansion based on the area model for 29 times 97 is option c, which equals 2000 + 900 + 210 + 63.