Q1.
What is the expression for the arrangement in the right making use of the number of yellow and blue squares?
Answer
The right-hand picture has two identical columns. Each column is made of 5 yellow squares on top and 3 blue squares below.
One column = 5 + 3 squares
Two such columns = 2 × (5 + 3)
= 2 × 8 = 16 squares
Two such columns = 2 × (5 + 3)
= 2 × 8 = 16 squares
The same arrangement can also be described as
5 + 3 + 5 + 3 OR 5 × 2 + 3 × 2
Why it happens: Brackets are needed here. Without them, 2 × 5 + 3 would mean “3 more than 2 × 5” = 13, which describes the left picture (5 columns of 2 green squares and a column of 3 red squares). The bracket in 2 × (5 + 3) says double the whole column, not just the yellow part.
Tip: 2 × (5 + 3) = 2 × 5 + 2 × 3 — this is the distributive property, seen here as a picture.