Cube3D 立方体数理Maths · Primary school / Middle school
Can you split 24 blocks in the ratio 2:3?
Imagine sharing 24 units of a resource. Group A should get two equal parts for every three given to group B. If the resource is juice, you can measure fractions of a unit. If it is a pile of blocks you cannot cut, the same ratio may leave some blocks unused. The experiment lets you try both rules with the same total.
The total covers both groups
A ratio of 2:3 asks for five equal parts altogether. Start with the default total of 24 and allow fractions. Divide 24 by 5 to get 24/5 units per part. Group A gets two parts, or 48/5 = 9.6 units. Group B gets three parts, or 72/5 = 14.4 units. Adding the shares gives 24.
Keep the ratio fixed and slide the total up to 30. Now each part is six units, so the shares are 12 and 18. Both shares grow with the total. The fraction going to group A remains 2/5, because its two parts belong to a whole made up of five.
Whole blocks must come in complete sets
Return to 24 and select Whole blocks only. A complete set gives two blocks to A and three to B. Four sets use 20 blocks, giving A eight and B twelve. The four left over cannot make a fifth set. Change the total to 25 and watch the left-over squares disappear as the groups receive 10 and 15.
Try 4:6 with the total still at 25. Both numbers have a common factor of two, so 4:6 is the same ratio as 2:3. You can use a set of two for A and three for B. Requiring ten blocks in each set would leave five blocks unused even though they can be shared in the same ratio.
Check your understanding
Set the total to 29 and the ratio to 3:2. Predict the two shares and the number left unassigned in whole-block mode. Then switch to fractions and explain what happens to the leftover four units.
Show the explanation
Five complete sets give A 15 and B 10, leaving four blocks. With fractions allowed, the four units are split in the same ratio, adding 12/5 units to A and 8/5 units to B. The shares become 87/5 and 58/5, and their sum is 29.
What the model assumes
The total is an integer from 0 to 60 and each group can have 1–6 parts. Fraction mode uses exact fractions. Whole-block mode maximizes the blocks assigned while preserving the chosen ratio, and keeps any remainder separate. If the total is zero, neither group receives anything. This note is public. The interactive experiment requires Family Plus or Teacher access.