Subtraction: Operations in stages

To solve this problem, we'll follow these steps:

• Step 1: Identify the total number of bracelets they start with.
• Step 2: Subtract the number of bracelets given away.

Now, let's work through these steps:

Step 1: Initially, Maya has 20 bracelets and Rachel has 17 bracelets.
We add these two numbers to find the total number of bracelets they have together:

$20 + 17 = 37$

Step 2: They decide to give 7 bracelets to Danielle.
To find out how many bracelets they have left, we subtract the number of bracelets given to Danielle from the initial total:

$37 - 7 = 30$

Therefore, Maya and Rachel together have $\mathbf{30}$ bracelets remaining after giving away 7 bracelets to Danielle.

To solve this problem, follow these steps:

• Step 1: Calculate the original number of bracelets that Maya and Rachel have together. Maya has 20 bracelets, and Rachel has 17, so initially, they have $20 + 17 = 37$ bracelets.
• Step 2: Determine how many bracelets they have after giving some to Danielle. Together, they now have 30 bracelets.
• Step 3: Calculate the number of bracelets given to Danielle by finding the difference between the original total and the current total. This is given by $37 - 30$.

Now, let's compute:

Initially, Maya and Rachel collectively had $37$ bracelets. After giving some to Danielle, they have $30$ bracelets. Therefore, the number of bracelets they gave to Danielle is $37 - 30 = 7$.

The correct answer is $\mathbf{7}$ bracelets.

Thus, the correct choice from the provided options is Choice 4: $7$.

To solve this problem, we'll address each part step-by-step and verify at each stage:

• Step 1: Determine how many pencils Jonathan has after giving away pencils.
• Step 2: Determine how many pencils Daniel has after giving away pencils.
• Step 3: Add the remaining pencils of Jonathan and Daniel to find out how many they collectively have left.

Let's proceed through the steps:

Step 1: Jonathan has 15 pencils originally. He gives 2 pencils to Betty. Therefore, his remaining number of pencils is: $15 - 2 = 13$

Step 2: Daniel has 17 pencils originally. He gives 2 pencils to Betty. Therefore, his remaining number of pencils is: $17 - 2 = 15$

Step 3: To find the total number of pencils Jonathan and Daniel have left, we add their remaining pencils together: $13 + 15 = 28$

Therefore, Jonathan and Daniel have altogether $28$ pencils left.

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 $85$.

The problem requires identifying an equivalent expression for $32 - 8$.

First, calculate the result of the given equation: $32 - 8 = 24$.

Now, evaluate each choice:

• Choice 1: $32 - 4 - 2 = 32 - 6 = 26$ (not equivalent to 24)
• Choice 2: $32 - 3 - 4 = 32 - 7 = 25$ (not equivalent to 24)
• Choice 3: $32 - 2 - 6 = 32 - 8 = 24$ (this matches exactly)
• Choice 4: $32 - 1 - 5 = 32 - 6 = 26$ (not equivalent to 24)

Thus, the expression equivalent to $32 - 8$ is $32 - 2 - 6$.

To solve this problem, we’ll follow these steps:

• Step 1: Calculate the original expression $21 - 4$.
• Step 2: Compare this result with each of the provided choices to find an equivalent expression.

Now, let's work through each step:
Step 1: The original expression $21 - 4$ simplifies directly to $17$.
Step 2: Check each choice:
- Choice 1: $21 - 4 - 1 = 16$ (not equivalent)
- Choice 2: $21 - 3 - 3 = 15$ (not equivalent)
- Choice 3: $21 - 2 - 1 = 18$ (not equivalent)
- Choice 4: $21 - 1 - 3 = 17$ (equivalent)

Therefore, the expression equivalent to $21 - 4$ is $21 - 1 - 3$, which can also be written as $21 - 1 - 3$.

To solve the given problem, we must find which expression is equivalent to $14 - 6$.

• Step 1: Perform the subtraction $14 - 6$.

• Step 2: Calculate the result: $\begin{aligned} 14 - 6 &= 8 \end{aligned}$

• Step 3: Examine the answer choices to find an expression that is equivalent to $8$.

• Step 4: Evaluate each choice:

  • Choice 1: $14 - 4 - 2$

  • $-$ Break it down: $\begin{aligned} 14 - 4 &= 10 \\ 10 - 2 &= 8 \end{aligned}$ This calculation results in $8$, which matches $14 - 6$.

  • Choices 2, 3, 4 do not yield 8, as calculated similarly.

Therefore, the expression $14 - 4 - 2$ is equivalent to the given equation $14 - 6$.

To solve this problem, we need to find an expression that is equivalent to $91 - 7$. Let's work through it step by step.

First, let's compute $91 - 7$:

$91 - 7 = 84$

Next, we need to find which of the given choices results in $84$. The simplest way to do this is to break down the subtraction $91 - 7$ into two steps, reducing from $91$ in stages, and match these to the choices:

We can express $7$ as the sum of two smaller numbers, such as $1 + 6$. This breakdown results in:

$91 - 7 = 91 - (1 + 6)$

This can then be rewritten as two separate subtractions:

$91 - 1 - 6$

Now, compare this with the provided choices:

• Choice 1: $91 - 1 - 6$, which equals $84$.
• Choice 2: $91 - 3 - 2$, which equals $86$.
• Choice 3: $91 - 2 - 4$, which equals $85$.
• Choice 4: $91 - 1 - 5$, which equals $85$.

The expression $91 - 1 - 6$ is equivalent to $91 - 7$ because both evaluations result in $84$.

Therefore, the correct answer is $91 - 1 - 6$.

To solve this problem, we'll convert $83 - 6$ into an equivalent expression.

• Step 1: Begin by calculating the subtraction $83 - 6$, which equals 77.
• Step 2: Since we're looking for an equivalent expression, we should express 6 as a sum of two numbers. Possible pairs include: $(3,3)$, $(2,4)$, $(1,5)$, etc.
• Step 3: We need an expression that mirrors 77. Among provided choices, one provides $83 - 3 - 3$.
• Step 4: Check if $83 - 3 - 3$ equals 77: Subtract 3 from 83 to get 80, and then subtract another 3 to result in 77.
• Step 5: This confirms that the original equation $83 - 6$ is indeed equivalent to the expression $83 - 3 - 3$.

Therefore, the expression equivalent to $83 - 6$ is $83 - 3 - 3$.

To solve this problem, we need to determine which expression is equivalent to $43 - 4$.

The expression $43 - 4$ can be broken down as follows:

• We know that $4 = 3 + 1$, so we can rewrite the expression as $43 - (3 + 1)$.
• This expression simplifies by subtracting in stages: first subtract $3$, then subtract $1$.
• Therefore, $43 - 4$ is equivalent to $43 - 3 - 1$.

Among the provided choices, option 4, $43 - 3 - 1$, is equivalent to $43 - 4$.

Thus, the solution to the problem is $43 - 3 - 1$.

To solve the problem of finding an equivalent expression for $55 - 7$, we will rewrite 7 as a sum of two numbers and then translate that into a two-step subtraction:

• Step 1: Decompose 7 as a sum of two numbers. For instance, 7 can be written as $5 + 2$. That means $7 = 5 + 2$.
• Step 2: Rewrite the original expression $55 - 7$ using this decomposition: $55 - 7 = 55 - (5 + 2).$
• Step 3: Apply sequential subtraction, which translates to: $55 - 5 - 2.$
• Step 4: Verify: We perform the subtraction operations: - $55 - 5 = 50$ - $50 - 2 = 48$

The expression $55 - 5 - 2$ evaluates to the same result as $55 - 7$, which is 48. The solution indicated that this is the correct choice as shown in the answer choices.

Therefore, the equivalent expression to the equation $55 - 7$ is $55 - 5 - 2$.

To solve the problem, we need to find an equivalent expression for $66 - 9$.

• We start with the original expression $66 - 9$ and consider simplifying it.
• Notice that the number 9 can be broken into two smaller numbers: 6 and 3, such that $6 + 3 = 9$.
• This means we can rewrite the expression $66 - 9$ as $66 - 6 - 3$.

Now, let's verify:

Perform $66 - 6 = 60$.
Then perform $60 - 3 = 57$.

Therefore, the expression $66 - 6 - 3$ simplifies to 57, which is the same as the result of $66 - 9$.

Hence, the expression $66 - 6 - 3$ is equivalent to $66 - 9$.

Therefore, the correct choice is $66 - 6 - 3$.

Thus, the solution to the problem is $66 - 6 - 3$.

To find an equivalent expression to $78 - 9$, we'll follow these steps:

• Step 1: Calculate the original expression $78 - 9$.
  The result of this subtraction is $69$.

• Step 2: Identify an expression that will also equal $69$ using equivalent smaller subtractions.

• Step 3: Examine $9$ and represent it as $8 + 1$. Hence, the original expression can be rewritten as $78 - 8 - 1$.
  Both: $\begin{aligned} &78 - 9 = 69 \\ &78 - 8 - 1 = 69 \end{aligned}$.

• Step 4: Compare the stepwise approach with the provided choices.

Among the options provided, $78-8-1$ is equivalent to $78-9$ as both yield the same result of $69$.

Therefore, the expression that is equivalent to $78 - 9$ is $78 - 8 - 1$.

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 $14$.