Solve part-to-whole ratio problems

Part-to-whole ratio problems represent a whole as a specified number of equal-sized ratio units: for a ratio $a:b$ , the whole contains $a+b$ units, so each part is found by scaling this unit value. Reasoning includes distinguishing a part-to-part ratio from a part-to-whole relationship and representing solutions with diagrams, tables, double number lines, or equations; the focus is on positive whole-number quantities and proportional scaling, not more advanced generalized ratio or algebraic cases.

Detailed Explanation: Solve part-to-whole ratio problems

A part-to-whole ratio tells how the parts compare and gives the total number of equal ratio units.

For a ratio of $a:b$ :

Add the ratio numbers to find the total number of units:

a+b

Divide the whole amount by the number of units to find the value of one unit.
Multiply by the ratio number for each part.

Example

A basket has red and blue apples in a ratio of $2:3$ . There are $25$ apples altogether. How many are red and how many are blue?

Step 1: Find the total number of ratio units.

The ratio is $2:3$ , so the whole has:

2+3=5\text{ units}

The ratio numbers describe parts of the whole, not the actual number of apples yet.

Step 2: Find the value of one unit.

There are $25$ apples in $5$ equal units:

25\div 5=5

So, each ratio unit represents $5$ apples.

Step 3: Find each part.

Red apples:

2\times 5=10

Blue apples:

3\times 5=15

Check:

10+15=25

So, there are 10 red apples and 15 blue apples.

Learn by doing: Solve part-to-whole ratio problems

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Ratios - Calculate Total from Item Ratio

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