Subtraction: Using the number line

To solve $65 - 6$ using two jumps on the number line, let's follow these steps:

• Step 1: Start at 65 on the number line. Our goal is to subtract 6 from 65 in two steps.

• Step 2: Make the first jump. Let's subtract 5 first. Starting at 65, move 5 steps left: $65 - 5 = 60$.

• Step 3: Make the second jump. Subtract the remaining 1 from the result: $60 - 1 = 59$.

Thus, after making two jumps on the number line, the final solution to $65 - 6$ is $59$.

Therefore, the correct answer is $\boxed{59}$.

To solve the subtraction problem $74 - 8$ using two jumps on a number line, we will follow these steps:

• Step 1: Identify the starting point and first jump length.
• Step 2: Calculate the intermediate result after the first jump.
• Step 3: Determine the remaining amount to subtract and make the second jump.
• Step 4: Calculate the final result after the second jump.

Now, let's work through each step:

Step 1: Start at 74. We need to subtract 8 in total. We begin by subtracting 4.

Step 2: From 74, subtract 4 to get the intermediate value. $74 - 4 = 70$.

Step 3: Subtract the remaining 4 (totaling 8) from the intermediate value of 70. Thus, $70 - 4 = 66$.

Therefore, the final result of $74 - 8$ is $66$.

To solve $51 - 3$ using two jumps on a number line, follow these steps:

• Step 1: Start at 51 on the number line.
• Step 2: Perform the first jump by subtracting 1: $51 - 1 = 50$.
  Now, we are at 50 on the number line.
• Step 3: Perform the second jump by subtracting 2: $50 - 2 = 48$.
  Now, we are at 48 on the number line.

Therefore, the result of the subtraction $51 - 3$ is $48$.

To solve $46 - 9$ using two jumps on the number line, we can break the subtraction into simpler steps as follows:

• Step 1: Start at 46.
• Step 2: Make the first jump backwards by 6, moving from 46 to 40.
• Step 3: Make the second jump backwards by 3, moving from 40 to 37.

Thus, by performing these two jumps, we compute $46 - 9 = 37$.

Therefore, the solution to the problem is $37$.

Let's solve the subtraction problem $83 - 5 =$ using two jumps on a number line:

• Initial Position: We start at 83 on the number line.
• First Jump: We'll subtract 3 from 83, which takes us to 80.
• Second Jump: Now subtract 2 more from 80, which lands us at 78.

By using two jumps, one subtracting 3 and another subtracting 2, we have successfully found that:

The final result is $78$.

To solve the problem of finding the sum of $88 + 7$, we will proceed with simple addition.

Step 1: Align the numbers vertically by place value:

  88
+ 07
-----

Step 2: Add starting from the rightmost column (units place):

• Add the digits in the units place: $8 + 7 = 15$. Since this is a two-digit result, write down 5 and carry over the 1 to the tens column.
• Now add the tens column: $8 + 1 = 9$ (where 8 is from the original tens place of 88, and 1 is the carry-over from the previous step).

Step 3: Write down the results:

  88
+ 07
-----
  95

Therefore, the sum of $88 + 7$ is $95$.

The calculated result, $95$, matches the first choice provided in the question options, verifying our answer.

To solve the problem $92 - 7$ using a number line, we'll break the subtraction into two smaller steps. This method can help by using round numbers and ensuring accuracy:

• Step 1: Start at 92. We choose to subtract 2 to reach a round number, 90.
• Step 2: Now at 90, subtract the remaining 5 to reach the final result.

First Jump: $92 - 2 = 90$
Second Jump: $90 - 5 = 85$

This gives us the final solution of $85$.

To solve the subtraction problem $43 - 29$ using a number line, we will proceed with the following steps:

• Step 1: Start Position: Begin at position 43 on the number line.
• Step 2: Jump Backwards: From 43, make a large jump backwards 29 units.
• Step 3: Visualize and Calculate: Moving back 10 steps takes you to 33. Another 10 steps backwards takes you to 23. Finally, moving 9 more steps backwards brings you to 14.

This process of making jumps backward clearly shows the reduction of 43 by 29, step by step. Therefore, the solution to the subtraction $43 - 29$ is $14$.

To solve $63 - 16$ using the number line, follow these steps:

• Start at $63$ on the number line.
• First, subtract $10$. This results in $63 - 10 = 53$.
• Next, subtract the remaining $6$. Thus, $53 - 6 = 47$.

So, by making jumps of $10$ and then $6$ on the number line, we conclude that the result of $63 - 16$ is $47$.

Therefore, the solution to the problem is $47$.

To solve the subtraction problem $81 - 14$ using jumps on the number line, follow these steps:

Step 1: Start at 81 on the number line.

• Visualizing this, place a marker at point 81.

Step 2: Subtract 10 by taking a large jump back to 71.

• This large jump represents subtracting 10 from 81, yielding $81 - 10 = 71$.

Step 3: Subtract the remaining 4 by taking a smaller jump back.

• From 71, jump back 4 steps to reach 67, which is calculated as $71 - 4 = 67$.

Therefore, using jumps on the number line, the solution to $81 - 14$ is $67$.

To solve this subtraction problem using jumps on a number line, we will break down the steps as follows:

• Step 1: Start at $75$ on the number line.
• Step 2: Subtract the $30$ part of $38$ by moving 30 spaces back from $75$. This gets us to $45$ because $75 - 30 = 45$.
• Step 3: Subtract the remaining $8$ by moving 8 spaces back from $45$. This lands us on $37$ because $45 - 8 = 37$.

Each movement on the number line helps visualize the subtraction in stages. By splitting the subtraction of $38$ into $30 + 8$, the student appreciates each component's effect on the original number.

Therefore, the solution to the subtraction problem $75 - 38$ is $37$.

To solve the subtraction $96 - 67$ using a number line, we follow these steps:

• Initial Position: Start at 96 on the number line. This is our minuend.
• First Jump: Subtract 60 by making a large jump of 60 units backward, landing at $96 - 60 = 36$.
• Second Jump: Next, subtract the remaining 7 units. Jump 7 units back from 36 to reach $36 - 7 = 29$.

By effectively using the jumps on a number line, we deduce that $96 - 67 = 29$.

Thus, the solution to the subtraction exercise is $29$.

To solve the equation $55 - \Box = 28$ using a number line, start at 55 and jump to 50, an easy anchor point, requiring a jump of 5 units.

Next, move from 50 to 28, which requires a further jump of 22 units.

Adding these jumps, $5 + 22$, gives us the total jump needed from 55 to reach 28. Therefore, $\Box = 27$.

Thus, the solution to the problem is $\Box = 27$, which corresponds to the answer choice:

$27$

To solve the subtraction problem $78 - \Box = 44$ using two jumps on a number line, we'll proceed as follows:

• Step 1: Start at 78 on the number line.
• Step 2: Make the first jump to the next convenient round number, which is 70 (as it simplifies the calculation).
• Step 3: Calculate this first jump as $78 - 70 = 8$.
• Step 4: Make the second jump from 70 directly to 44 (the target number).
• Step 5: Calculate this second jump as $70 - 44 = 26$.
• Step 6: Add the two jumps together: $8 + 26 = 34$.

Therefore, the missing number that satisfies $78 - \Box = 44$ is $\Box = 34$.

To solve the problem $15 - \Box = 9$ using two jumps on a number line, we need to break down this subtraction into simpler parts.

If we think of the subtraction using two jumps, one effective strategy is:

• First, subtract 5 from 15 to reach the intermediate round number, 10: $15 - 5 = 10$.
• Second, subtract from the intermediate number, 10, to reach the target, 9: $10 - 1 = 9$.

Adding both jumps together, $5 + 1 = 6$. Thus, the missing number in the original expression is $6$.

The final solution to the problem is $\Box = 6$.

To solve this subtraction exercise, we will use two jumps on the number line:

• Step 1: Start at 34 and make the first jump to the nearest round number, which is 30. This jump represents subtracting 4 from 34, so $34 - 4 = 30$.
• Step 2: From 30, make the second jump to 26. This jump represents subtracting another 4, so $30 - 4 = 26$.
• Now, adding the two jumps: $4 + 4 = 8$.

Therefore, the value in the equation $34 - \Box = 26$ is $8$.

To solve the problem $43 - \Box = 17$ using a number line with two jumps, follow these steps:

• Step 1: Start at 43 on the number line.
• Step 2: Make the first jump to the nearest round number, which is 40. Thus, the first jump is $43 - 40 = 3$.
• Step 3: From 40, make another jump to reach 17. Thus, the second jump is $40 - 17 = 23$.
• Step 4: Now, add the two jumps: $3 + 23 = 26$.

Therefore, the value of the missing number is $\Box = 26$.

Let's solve the problem step by step.

The problem is to find the number to subtract from 74 so that the result is 38, using two jumps on a number line.

We start at 74 and need to end at 38. To do this efficiently and using the number line strategy, we break it down into two jumps:

• First, consider an easy first jump to a round number from 74. The nearest round number less than 74 is 70.
  This first jump is from 74 to 70, which is a jump of $74 - 70 = 4$.
• Now, from 70, we need to reach the desired 38. Calculate the second jump: $70 - 38 = 32$.

By making these two jumps, we have:

• First jump: 74 to 70, subtracting 4.
• Second jump: 70 to 38, subtracting 32.

Adding the two jumps: $4 + 32 = 36$.

Therefore, the solution to $74 - \Box = 38$ is $\Box = 36$.

The correct choice from the options provided is 36.

In conclusion, the missing number in the subtraction is $\Box = 36$.

To solve $95 - \Box = 87$, we will use the number line, making two jumps from 95 to 87.

First, identify the numbers on the number line:

• Start at: 95
• End at: 87

Step 1: Make the first jump to the next round number below 95, which is 90. Calculate this jump:

• Jump from 95 to 90: $95 - 90 = 5$

Step 2: Make the second jump from 90 to 87. Calculate this jump:

• Jump from 90 to 87: $90 - 87 = 3$

Add the two jumps together to find the total subtraction:

• Total subtraction: $5 + 3 = 8$

Therefore, the missing number is $\Box = 8$.

The correct answer is $8$.

To solve the subtraction $82 - \Box = 78$ using jumps on a number line, follow these steps:

• Step 1: Start at the number 82 on the number line.
• Step 2: Make the first small jump down to 80, the closest round number below 82.
• Step 3: Calculate the size of this jump. The jump from 82 to 80 is 82 - 80 = 2.
• Step 4: From 80, make a second jump down to 78.
• Step 5: Calculate the size of this second jump. The jump from 80 to 78 is 80 - 78 = 2.
• Step 6: Add the sizes of both jumps to determine the total subtracted value: 2 + 2 = 4.

Therefore, the value of $\Box$ in the subtraction problem $82 - \Box = 78$ is $4$.