Draw a model to represent the following problem 42 divide 7 Answer
The Correct Answer and Explanation is :
To represent the problem of dividing 42 by 7, we can visualize it using a model. A simple way to illustrate this is through a set model and a number line model.
Set Model
- Group the Total: Start with a total of 42 objects (you can think of these as 42 apples).
- Create Equal Groups: We want to divide these 42 objects into 7 equal groups since we are dividing by 7. To find out how many objects go into each group, we distribute the 42 objects evenly across the 7 groups. [
42 \div 7 = ?
] - Count the Objects in Each Group: Each group will contain ( \frac{42}{7} ) objects. By distributing the objects, we find that each group has 6 objects:
- Group 1: 6
- Group 2: 6
- Group 3: 6
- Group 4: 6
- Group 5: 6
- Group 6: 6
- Group 7: 6
Thus, the answer is 6.
Number Line Model
To visualize the division on a number line:
- Draw a Number Line: Mark points from 0 to 42.
- Equal Segments: Since we are dividing by 7, we can mark equal segments on the number line. Each segment represents one group of the total. The total distance from 0 to 42 is divided into 7 equal parts. Each part is 6 units long: [
0, 6, 12, 18, 24, 30, 36, 42
]
From this, we can see that there are 7 intervals, and each interval represents a group of 6, confirming that ( 42 \div 7 = 6 ).
Explanation
Division is essentially finding out how many times one number (the divisor) fits into another number (the dividend). In this case, we are looking for how many groups of 7 can be formed from 42. By either distributing the total evenly among groups or using a number line, we determine that 42 can be evenly divided into 7 groups of 6.
The significance of division extends beyond simple arithmetic; it applies to real-life situations, such as dividing resources, splitting bills, or grouping items. Understanding division as equal distribution helps build a strong foundation for more complex mathematical concepts, including fractions and ratios.