Adding, Multiplying, and Dividing Fractions

What you’ll learn

Use common denominators and reciprocal division.

ប្រើភាគបែងរួម និងចំនួនច្រាសក្នុងការចែកប្រភាគ។

Meaning and use

A fraction represents a number through a numerator and a nonzero denominator. Addition needs a common denominator; multiplication multiplies numerators and denominators. To divide by a nonzero fraction, multiply by its reciprocal. Simplify by cancelling common factors, not terms joined by addition.

ប្រភាគមានភាគយក និងភាគបែងដែលមិនសូន្យ។ ពេលបូក ត្រូវមានភាគបែងរួម។ ពេលចែកនឹងប្រភាគមិនសូន្យ គុណនឹងចំនួនច្រាសរបស់វា។

Formulas

Addition

\[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]

Multiplication and division

\[\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd},\qquad \frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}\]

Symbols and units

Symbol	Meaning	Unit or restriction
a, c	Numerators	Same contextual units for addition
b, d	Denominators	Nonzero
c/d as divisor	The fraction being divided by	Must also be nonzero

Conditions and limits

• Denominators b and d cannot be zero; for division, c cannot be zero either.
• Add only quantities of compatible units.
• អាចកាត់តែតួគុណរួម មិនអាចកាត់តួបូកដោយផ្ទាល់ទេ។

Worked examples

Adding unequal denominators

Find \(\frac12+\frac13\).

1. Use denominator 6.
2. Write \(\frac36+\frac26\).
3. Add the numerators: \(\frac56\).

\(\frac56\)

ប្ដូរទៅភាគបែងរួម 6 មុនបូក។

Dividing fractions

Find \(\frac34\div\frac12\).

1. Invert only the divisor: \(\frac12\to\frac21\).
2. Multiply \(\frac34\times\frac21=\frac64\).
3. Simplify \(\frac64=\frac32\).

\(\frac32\)

យកប្រភាគទីមួយគុណនឹងចំនួនច្រាសរបស់ប្រភាគទីពីរ។

Common mistakes

Instead of	Use	Why
1/2 + 1/3 = 2/5	1/2 + 1/3 = 5/6	Do not add denominators; use a common denominator.
3/4 ÷ 1/2 = 3/8	3/4 ÷ 1/2 = 3/2	Division by a fraction requires multiplying by its reciprocal.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find 2/5 + 1/5.
2. Find 2/3 × 9/10.
3. Find 4/7 ÷ 2/7.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 3/5

   The denominators match, so add the numerators.

2. 3/5

   Multiply to get 18/30, then divide numerator and denominator by 6.

3. 2

   Multiply 4/7 by 7/2 to obtain 4/2 = 2.

Quick recap

• Use common denominators for addition.
• Multiply straight across for products.
• Invert the divisor, not both fractions.