The area of the given design is 31/24 of the area of another design. Make a design that could be the other design. Divide each block, using dashes, into green triangles.

Question

Using pattern blocks to design this, sketch design tracing the blocks.

Answer 1

Patrick multiplied both sides by the reciprocal of 31/24 in order to get the second equation. The product of reciprocals is always 1, so this cleared the original fraction. A more visual way to think of this is that 24/24 of the other design would be the whole first design, so 31/24 of the other design could be 31 pieces compared to the original 24. If the original design was made of yellow hexagon pattern blocks, red trapezoids, or blue diamonds, they could be split up into 24 triangles, with the new design using an additional 7 triangle shapes.

Answer 2

given = (31/24) * other

(24/31) * given = other

so you multiply the area of the given design by 24 and divide by 31 to get

the area of the other design.

Build from there