Division is the process of splitting a number into equal parts or groups, asking how many times one number fits into another. It is the inverse of multiplication and uses symbols like ÷, /, or a fraction bar.
- Dividing 12 by 3 means splitting 12 into 3 equal parts or seeing how many times 3 fits into 12.
- The result of division is called the quotient; any leftover part is the remainder.
- Division “undoes” multiplication: If 4 × 5 = 20, then 20 ÷ 5 = 4 and 20 ÷ 4 = 5.
The quotient of 20 divided by 4 is 5.
Multiplication is the inverse operation of division.
The quotient is the result of a division problem.
Source Material
Document: Division (Math Is Fun)
Division Vocabulary
- Dividend: The number being divided.
- Divisor: The number you divide by.
- Quotient: The result of division.
- Remainder: What is left over if the division isn’t exact.
Example: In 15 ÷ 4 = 3 R3, 15 is the dividend, 4 is the divisor, 3 is the quotient, and 3 is the remainder.
The divisor is the number you divide by, which is 6.
The quotient is the result of the division.
Dividend, divisor, quotient, and remainder are all part of division.
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Document: Division Vocabulary
Long Division
Long division breaks down tough division problems step-by-step, like a ladder:
- Divide the first digit(s) of the dividend by the divisor.
- Multiply the divisor by the quotient digit and subtract.
- Bring down the next digit of the dividend.
- Repeat until all digits are used.
Example: Divide 156 by 12 using long division.
You start by dividing the initial digit(s) of the dividend by the divisor.
Source Material
Document: How Long Division Works
After subtracting, you bring down the next digit of the dividend and repeat.
Division with Fractions
Dividing by a fraction means multiplying by its reciprocal (flip numerator and denominator).
- Division: \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \)
- Example: \( \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \)
The reciprocal of 3/4 is 4/3.
You multiply by the reciprocal of the fraction.
Source Material
Document: Dividing Fractions
Real-World Applications
Division is everywhere—from splitting bills, measuring ingredients, dividing work, to calculating speeds.
- Sharing 24 cookies among 6 friends—how many each get? (4 cookies)
- Driving 180 miles over 3 hours—what’s the average speed? (60 mph)
Division is used for splitting and sharing things equally.
Division is used to adjust recipe portions.
Source Material
Document: Everyday Math: Division
Conclusion
Division splits things into equal parts, reverses multiplication, and is vital for sharing and measuring in daily life.
- Division breaks apart numbers into equal groups or parts.
- Key terms: dividend, divisor, quotient, remainder.
- Division is used in recipes, travel, finances, and more.
Division splits things into equal parts and shows how many times one number fits into another.
Yes, division is used to solve many real-world problems.
Source Material
Document: Division