When faced with the calculation of 330 divided by 48, approaching it with the right methods and understanding can make all the difference. Division, a fundamental mathematical operation, involves finding the number of times one number (the divisor) can be subtracted from another (the dividend) to produce zero. In this case, we aim to determine how often 48 can be taken away from 330.
Before delving into the division process, we can simplify the calculation by finding the greatest common factor (GCF) of 330 and 48. The GCF represents the largest number that divides both numbers without leaving a remainder. In this case, the GCF of 330 and 48 is 6.
Dividing both the dividend (330) and the divisor (48) by their GCF, we get:
330 ÷ 6 = 55
48 ÷ 6 = 8
Now, we have a simplified division problem: 55 divided by 8.
The most common method for performing division is the long division method. Here's a step-by-step approach:
Result:
8 ) 55
0
5
4
1
Therefore, 330 divided by 48 is 6 with a remainder of 1.
Mental Math: For small numbers, mental math techniques can be used for quick calculations. In this case, we can think of 48 as 50 and divide 330 by 50, which gives us 6.6. This provides an approximate answer to 330 divided by 48.
Fraction Method: Division can also be represented as a fraction:
330 ÷ 48 = 330 / 48 = (330/6) / (48/6) = 55 / 8
By dividing both the dividend and the divisor by their GCF (6), the division simplifies to 55 divided by 8.
Division finds numerous applications in real-life situations, including:
Table 1: Common Divisor and Remainder Pairs for 330 and 48
Divisor | Remainder |
---|---|
1 | 0 |
2 | 36 |
3 | 24 |
4 | 12 |
6 | 0 |
8 | 2 |
12 | 10 |
24 | 0 |
48 | 0 |
Table 2: Different Methods for Calculating 330 Divided by 48
Method | Result |
---|---|
Long Division | 6 with a remainder of 1 |
Mental Math | Approximately 6.6 |
Fraction Method | 55 / 8 = 6 with a remainder of 1 |
Table 3: Applications of Division in Real-Life
Application | Example |
---|---|
Distributing resources equally | Dividing a birthday cake into equal slices for party guests |
Measuring and comparing | Converting miles into kilometers by dividing the distance in miles by 1.6 |
Solving proportions | Finding the speed of a car by dividing the distance traveled by the time taken |
Story 1: A farmer has 330 apples and wants to divide them equally among his 48 sheep. How many apples will each sheep get?
Lesson: We can use division to determine the amount of resources to distribute evenly.
Story 2: A marathon runner traveled a distance of 330 kilometers in 48 hours. What was the runner's average speed?
Lesson: Division helps us compare quantities and calculate ratios.
Story 3: A company is making pizzas with a diameter of 12 inches. If the dough used for one pizza is enough for 48 slices, what is the area of each slice?
Lesson: Division allows us to find the individual contributions or components of a larger whole.
Understanding the concepts of division and applying the appropriate methods can help us tackle problems like 330 divided by 48 with confidence. By simplifying calculations, using efficient techniques, and being aware of common pitfalls, we can master division and its numerous real-life applications. Remember, practice makes perfect!
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