Sure, let's solve the division [tex]\(360 \div 70\)[/tex] using two different strategies: a tape diagram and the standard algorithm.
### 51. Tape Diagram
A tape diagram is a visual model that uses rectangles to represent the parts of a division or multiplication problem.
1. Represent the total quantity: Draw a long rectangle to represent the total quantity, 360.
2. Divide the rectangle: Since we are dividing by 70, we need to divide this long rectangle into smaller rectangles, each representing 70.
3. Count the sections: Divide the rectangle until you reach as close to 360 as possible without exceeding it.
#### Step-by-Step Process:
1. Draw a long rectangle labeled 360.
2. Begin dividing it into sections. Each section will represent 70.
- First section: 70
- Second section: 70
- Third section: 70
- Fourth section: 70
- Fifth section: 70
Now, we have 5 sections of 70 each, which sums up to [tex]\(5 \times 70 = 350\)[/tex].
3. Determine the remainder: The difference between the dividend and the sum of sections multiplied by the divisor is [tex]\(360 - 350 = 10\)[/tex].
#### Final Result:
- Quotient: 5
- Remainder: 10
### 52. Standard Algorithm
The standard algorithm for division involves dividing, multiplying, subtracting, and bringing down the next digit repeatedly until the division is complete.
1. Divide: Start by determining how many times 70 can fit into the initial digits (360).
- [tex]\(70\)[/tex] goes into [tex]\(360\)[/tex] five times because [tex]\(70 \times 5 = 350\)[/tex].
2. Multiply: Multiply 5 (the partial quotient) by 70.
- [tex]\(5 \times 70 = 350\)[/tex]
3. Subtract: Subtract the result from the original number.
- [tex]\(360 - 350 = 10\)[/tex]
4. Result: There are no more digits to bring down, so the division process is complete.
#### Final Result:
- Quotient: 5
- Remainder: 10
So, both visualization methods and the standard algorithm confirm that [tex]\(360 \div 70\)[/tex] has a quotient of 5 and a remainder of 10.
