Addition: 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 this problem, we will follow these steps:

• Step 1: Start at the number 18 on the number line.
• Step 2: Add 2 in the first jump to reach 20.
• Step 3: Add another 2 in the second jump to reach 22.

Now, let's work through each step:

Step 1: We start at 18, as indicated by the initial position on the number line.

Step 2: For the first jump, we add 2 to 18, which gets us to 20.

Step 3: For the second jump, we again add 2 to 20, which brings us to 22.

Therefore, the solution to the problem $18 + 4$ using two jumps on the number line is $22$.

To solve $25 + 8$ using two jumps on a number line, we follow these steps:

• Step 1: Start at the number 25 on the number line.
• Step 2: Make the first jump by adding 5. This takes us from 25 to 30.
• Step 3: Make the second jump by adding the remaining 3. Move from 30 to 33.

By making these two jumps, we effectively add 8 to 25.

Therefore, the result of $25 + 8$ is $33$.

To solve the problem of adding $34 + 9$ using two jumps on a number line, follow these steps:

• Step 1: Start at 34 on the number line.
• Step 2: Make the first jump of $+6$ from 34, which lands you at 40.
• Step 3: Make the second jump of $+3$ from 40, landing you at 43.

Therefore, by completing the two jumps on the number line, we find that $34 + 9 = 43$.

The solution to the addition problem is $43$.

To solve $16 + 6$, we will proceed as follows:

• Step 1: Identify the numbers to add: 16 and 6.
• Step 2: Add the numbers: $16 + 6 = 22$.
• Step 3: Verify by recalculating or using a number line if needed.

Using our calculation, $16 + 6$ results in 22.

Therefore, the correct answer is $22$.

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

• Step 1: Start at the number 17 on the number line.
• Step 2: Make the first jump of $+3$.
• Step 3: Make the second jump of $+4$.
• Step 4: Record the final position.

Now, let's work through each step:
Step 1: We begin at 17 and plan our jumps.
Step 2: The first jump of $+3$ takes us from 17 to $17 + 3 = 20$.
Step 3: The second jump of $+4$ takes us from 20 to $20 + 4 = 24$.

Therefore, the solution to the problem, using two jumps on the number line, is $24$.

To solve the problem $26 + 9$, we will simplify the addition by breaking down the number 9 into two smaller numbers. Here's how we can do it step-by-step:

• Step 1: Break down the number 9. We can express 9 as $4 + 5$.

• Step 2: Add 4 to 26. Starting with 26, add 4: $26 + 4 = 30$.

• Step 3: Add the remaining 5 to the result of step 2. Now, add 5 to 30: $30 + 5 = 35$.

So, the sum of 26 and 9 is 35, which can be expressed as the equivalent expression $26 + 4 + 5$.

Therefore, according to the given choices, the correct expression equivalent to $26 + 9$ is $26 + 4 + 5$.

To solve this problem, we will follow these steps:

• Step 1: Consider the original addition problem $19 + 8$.
• Step 2: Break down the number 8 into $1 + 7$ for simpler addition.
• Step 3: First, add 1 to 19. This gives $19 + 1 = 20$.
• Step 4: Next, add 7 to 20. This gives $20 + 7 = 27$.
• Step 5: Verify the solution aligns with the given correct answer format.

Following these steps, $19 + 8$ can be rewritten and solved as $19 + 1 + 7 = 27$.

Therefore, the equivalent expression and solution to this problem is $19 + 1 + 7$.

To solve $15 + 7$, we can simplify the calculation by using a breakdown approach. Let's follow the steps:

• First, recognize that $7$ can be split into $5 + 2$.
• Next, calculate $15 + 5$, which equals $20$.
• Then, add the remaining $2$ to the sum $20$.
• This gives us a final answer of $22$.

The correct expression that represents this process is $15+5+2$, which simplifies to $22$.

The given choices allow us to express the original problem differently. The choice that correctly represents our breakdown is:

$15+5+2$

To solve the problem of finding the equivalent expression for $89 + 8$, we can break down the number 8 into components that simplify the addition process. By breaking it down as $8 = 1 + 7$, we can rephrase the addition:

• Step 1: Break down the number 8 as $8 = 1 + 7$.
• Step 2: Add 1 to 89, which gives us 90.
• Step 3: Then add 7 to 90, yielding 97.

Thus, the breakdown of $89 + 8$ can be written as $89 + 1 + 7$, which is equivalent to the original addition.

Now, examining the answer choices:

• Choice 1 ($33 + 2 + 5$) does not add to 97, it adds to 40.
• Choice 2 ($89 + 1 + 6$) results in 96, which is incorrect.
• Choice 3 ($89 + 2 + 7$) results in 98, which is incorrect.
• Choice 4 ($89 + 1 + 7$) is the correct breakdown, resulting in 97.

Therefore, the correct choice is Choice 4: $89 + 1 + 7$.

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

• Step 1: Break down the number 5 into smaller components to simplify the addition. One convenient way is to write $5 = 3 + 2$.
• Step 2: Add these components sequentially to 67. Start with $67 + 3$ and then add the remaining 2:

Breaking down the addition as described:

1. $67 + 3 = 70$

2. $70 + 2 = 72$

Thus, calculating step by step confirms:

$67 + 5 = 67 + 3 + 2 = 72$

Therefore, the expression equivalent to $67 + 5$ as broken into two components is $67 + 3 + 2$.

Analyzing the available choices, the correct equivalent is given by choice 3: $67 + 3 + 2$.

To solve this problem, we can use the technique of breaking down numbers for easier mental addition.

Step 1: We start with the expression $54 + 8$.
Step 2: We can decompose the number 8 into two numbers that are easier to add in parts. A simple break down is $8 = 6 + 2$.
Step 3: We substitute the breakdown into the original expression:

• First, add 54 and 6 to get 60.
• Next, add 2 to 60 to get 62.

Thus, the expression $54 + 6 + 2$ is equivalent to $54 + 8$, giving us the correct answer.

Therefore, the correct equivalent expression is $54 + 6 + 2$.

To solve this problem, we need to determine which expression is equivalent to $48+5$. The sum $48+5$ equals $53$. We will rewrite $5$ as the sum of two numbers that add to 5, matching one of the provided choices.

Let's decompose $5$ in potential ways: $5 = 2 + 3$. Now let's rewrite the equation using this decomposition:

$48 + 5 = 48 + (2 + 3) = 48 + 2 + 3$

This step has shown that $48+2+3$ equals $53$, the same result as $48 + 5$.

Therefore, the expression equivalent to $48+5$ is $48+2+3$, corresponding to choice 2.

To solve the problem $36 + 7$, follow these steps:

• Step 1: Add $36$ and $7$. This results in $43$.
• Step 2: Decompose $7$ into two parts to match the given choices: $4 + 3$.
• Step 3: Rewrite the problem as $36 + 4 + 3$, which simplifies to the same total, $43$.

Therefore, the equivalent expression for $36 + 7$ is $36 + 4 + 3$, which matches choice 4.

To solve the expression $33 + 9$ by breaking down $9$, follow these steps:

• Step 1: Decompose $9$ into $7 + 2$.
• Step 2: First, add $33 + 7$. This gives you $40$.
• Step 3: Next, add the remaining part of $9$, which is $2$, to $40$.
• Step 4: The result of $40 + 2$ is $42$.

Thus, the detailed decomposition to match the answer format is: $33 + 7 + 2$.

To solve the addition problem $34 + 47$ using a number line, we'll follow these steps:

• Step 1: Start at the number 34 on the number line.
• Step 2: Add the tens from 47, which is 40. This takes us from 34 to 74.
• Step 3: Add the units from 47, which is 7. This takes us from 74 to 81.

Here's the detailed breakdown of each step:

Step 1: We start at 34.

Step 2: We add 40 (the tens from the number 47):
Adding 40 to 34 gives us $34 + 40 = 74$.

Step 3: We add 7 (the units from the number 47):
Adding 7 to 74 gives us $74 + 7 = 81$.

Therefore, the sum of $34 + 47$ is $81$.

Thus, the final answer is $\textbf{81}$, which corresponds to choice 3 in the given multiple-choice options.

To solve the addition problem $49 + 27$ using a number line, follow these steps:

• Start at 49 on the number line.
• Decompose 27 into tens and ones: $27 = 20 + 7$.
• First jump 20 units forward from 49: $49 + 20 = 69$. Now you're at 69.
• Next, jump 7 more units forward from 69. Break this into a jump of 6 then 1:
• Jump 6 units: $69 + 6 = 75$.
• Jump 1 more unit: $75 + 1 = 76$.

Thus, the final position on the number line is 76. Therefore, the solution to the addition is $76$.

To solve the addition problem $15 + 56$, we'll use jumps on a number line:

• Step 1: Start at 15 on the number line.
• Step 2: Break down the second number (56) into smaller, manageable increments. For simplicity, we can use increments of 10.
• Step 3: Make five jumps of 10 from 15. This will bring us to $15 + 50 = 65$.
• Step 4: Add the remaining 6 by jumping from 65 to 71.

This method effectively demonstrates that $15 + 56$ equals 71 by reaching the end point after all the incremental jumps on the number line.

Therefore, the solution to the problem is $71$.