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This essential trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 5-6, Math Kangaroo 7-8.

Suppose we have a quantity Q and it must be divided in parts that have sizes in a given ratio.

Example:

Divide the number 2210 in three parts that are in a ratio of 4:5:8.

Compute the smallest number of equal size parts in which we have to divide the number:

equation

Divide the quantity to the number of parts to find the size of a part:

equation

Finally, multiply the multiple ratio by the size of the part to find the desired quantities:

equation

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The number 2210 can be divided into parts of sizes: 52, 65 and 104 that are in the same ratios as the numbers 4, 5 and 8.

figure