Partition a total amount into parts given in a ratio (share/split problems).
Free, timed SHSAT practice sets on dividing a quantity in a ratio— every question includes a full worked explanation, and there's no account required.
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To split a total in a ratio, think in parts:
Example: 40 marbles are red and blue in the ratio \(3:5\). There are \(3 + 5 = 8\) parts, so one part is \(40 \div 8 = 5\) marbles. Red \(= 3 \times 5 = 15\), blue \(= 5 \times 5 = 25\). Check: \(15 + 25 = 40\).
Common traps: using the wrong fraction of the total (for \(3:5\), \(\dfrac{3}{5}\) instead of \(\dfrac{3}{8}\)), stopping at the size of one part, giving the other group, and giving the size of one group when the question asks for the difference.
Total parts \(= 4 + 9 = 13\), so each part is worth \(104 \div 13 = 8\) games. Losses \(= 9 \times 8 = 72\). (Using \(9/4\) of the total instead of \(9/13\) gives 234. Finding the wins instead gives 32. Stopping at the size of one part gives 8.)
Total parts \(= 7 + 2 + 3 = 12\), so each part is worth \(60 \div 12 = 5\) marbles. Green marbles \(= 3 \times 5 = 15\). (Finding the red marbles instead gives 35. Leaving the blue marbles out of the total parts, \(60 \times 3 \div 10\), gives 18. Stopping at the size of one part gives 5.)
Basketballs \(= 3 \times 6 = 18\); soccer balls \(= 2 \times 6 = 12\). Difference \(= 18 - 12 = 6\) balls. (Subtracting 18 from the total, \(30 - 18\), gives 12, which is the number of soccer balls. Subtracting the ratio terms, \(3 - 2\), without scaling by 6 gives 1. Stopping at the number of basketballs gives 18.)