Ratios and Direct Proportion

What you’ll learn

Scale equivalent ratios and find a missing proportional value.

ពង្រីកសមាមាត្រ និងរកតម្លៃដែលបាត់ក្នុងសមាមាត្រផ្ទាល់។

Meaning and use

A ratio compares quantities in an order. Equivalent ratios multiply both parts by the same nonzero factor. In direct proportion, one quantity is a constant multiple of another. Do not use direct proportion when a fixed starting fee or another changing condition breaks that relationship.

ផលធៀបប្រៀបធៀបបរិមាណតាមលំដាប់។ សមាមាត្រផ្ទាល់មានមេគុណថេរ។ ត្រូវប្ដូរឯកតាឱ្យដូចគ្នាមុនប្រៀបធៀប និងពិនិត្យថាទំនាក់ទំនងមានមេគុណថេរ។

Formulas

Equivalent ratios

\[a:b=ka:kb\]

Direct proportion

\[y=kx\]

Symbols and units

Symbol	Meaning	Unit or restriction
a, b	Ordered ratio quantities	Use a common unit when comparing the same type of quantity
x, y	Input and corresponding output	Context-dependent
k	Constant of proportionality	Output unit per input unit, when applicable

Conditions and limits

• A direct-proportion model requires a constant ratio y/x for nonzero x.
• Keep the order of quantities and convert units before forming comparable ratios.
• បើមានថ្លៃដើមថេរ y អាចមិនសមាមាត្រផ្ទាល់នឹង x ទេ។

Worked examples

Sharing in a ratio

Share 50 notebooks in the ratio 2:3.

1. Total parts: \(2+3=5\).
2. One part: \(50\div5=10\) notebooks.
3. Shares: \(2\times10=20\) and \(3\times10=30\).

20 notebooks and 30 notebooks

ចែកសរុបតាមចំនួនភាគទាំងអស់ រួចគុណភាគនីមួយៗ។

A constant unit price

Three notebooks cost 6 dollars, with no fixed fee. Find the cost of five.

1. Unit price \(k=6/3=2\) dollars per notebook.
2. Use \(y=kx\).
3. Calculate \(y=2\times5=10\) dollars.

$10

គណនាតម្លៃមួយក្បាលមុន ដោយសន្មតថាតម្លៃក្នុងមួយឯកតាថេរ។

Common mistakes

Instead of	Use	Why
2:3 = 4:5	2:3 = 4:6	Multiply both parts by the same factor.
1 m : 50 cm = 1:50	1 m : 50 cm = 100:50 = 2:1	Convert to the same unit first.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Simplify 12:18.
2. If y = 4x, find y when x = 7.
3. Share 24 in the ratio 1:2.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 2:3

   Divide both parts by their common factor 6.

2. 28

   Substitute: y = 4 × 7.

3. 8 and 16

   There are three parts; each is 8.

Quick recap

• Ratio order matters.
• Scale both parts equally.
• Use direct proportion only when the constant-rate assumption fits.