To help Ilya solve the equation [tex]\( 4,348 \div 6 \)[/tex], let's follow his method of splitting the rectangle into parts that are easy to divide by 6 and a remainder.
First, identify the given units:
[tex]\[ a = 700 \text{ units } \][/tex]
[tex]\[ b = 20 \text{ units } \][/tex]
Next, we need to determine the value of [tex]\( c \)[/tex] such that the total [tex]\( a + b + c \)[/tex] equals the target result of the division. We first calculate the initial sum of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ a + b = 700 + 20 = 720 \][/tex]
We know the result of [tex]\( 4,348 \div 6 \)[/tex] divided into these parts will be:
[tex]\[ \frac{4,348}{6} = 724.6666666666666 \][/tex]
The initial allocated sum [tex]\( a + b \)[/tex] is 720 units. So, to find [tex]\( c \)[/tex]:
[tex]\[ c = 724.6666666666666 - 720 = 4.666666666666629 \][/tex]
Hence, we've found:
[tex]\[ c = 4.666666666666629 \text{ units } \][/tex]
Next, we calculate the total sum [tex]\( h \)[/tex]:
[tex]\[ h = a + b + c = 700 + 20 + 4.666666666666629 = 724.6666666666666 \][/tex]
Then, the result of [tex]\( 4,348 \div 6 \)[/tex] is:
[tex]\[ \frac{4,348}{6} = 724 \text{ (quotient)},\, \text{ remainder } = 4 \][/tex]
Let's fill in the equations completely:
[tex]\[ a = 700 \text{ units } \][/tex]
[tex]\[ b = 20 \text{ units } \][/tex]
[tex]\[ c = 4.666666666666629 \text{ units } \][/tex]
[tex]\[ h = a + b + c = 724.6666666666666 \text{ units } \][/tex]
[tex]\[ 4,348 \div 6 = 724.6666666666666 \][/tex]
[tex]\[ \text{ remainder } = 4 \][/tex]
This step-by-step process demonstrates how Ilya split the area and arrived at the division result and the remainder.
