Ella colored 3/20 of a rectangle green and another 2/5 of it red. She divided the rest of the rectangle into several small rectangles.

Question

Ella colored 3/20 of a rectangle green and another 2/5 of it red. She divided the rest of the rectangle into several small rectangles. The area of each small rectangle was 1/40 of the area of the whole rectangle.

Answer 1

I assume you are asking HOW MANY LITTLE RECTANGLES are in the remaining area of the rectangle?

Remember fractions are portions of a whole and LESS THAN one (unless its a MIXED number.) For example, 3/20 = 0.15 of 1 and is LESS THAN 1

Since an area for the rectangle was not given, you can assume that the AREA of the rectangle 1 to make things easier. So the THREE parts of how she broken up the rectangle will equal to the total AREA, 1 in this case.

³/₂₀ + ²/₅ + ? = A (A, the total area of the rectangle = 1)

Say ? is the THIRD section of the rectangle that she broken up into little rectangles, each one is 1/40 of A

? = numbers of rectangles x 1/40 = x(1/40)

³/₂₀ + ²/₅ + x(¹/₄₀) = 1

To add fractions with different denominators, you need the Lowest Common Denominator, LCD.

Here the LCD is 40

Multiply EACH fraction (numerator & denominator) by the factor needed so that the denominators are 40 EXCEPT for the last term because its denominator is already 40

(²/₂)(³/₂₀) + (⁸/₈)(²/₅) + x(¹/₄₀) = 1

⁶_/40 + ¹⁶/₄₀ + ^x/₄₀ = 1

(6 + 16 + x) /40 = 1

22 + x = 40

x = 40 -22

x = 18 the number of little rectangles in the THIRD area of the rectangle.

Hope this helps!