Adding And Subtracting Integers Test

Adding 14 and 9 means simply moving 9 units to the right starting from 14 on the number line. Both values are positive, so the sum will also be positive. Adding positive integers involves straightforward addition of their values without adjusting for direction on the number line. Here, 14 + 9 = 23 because there’s no sign change involved. You only need to sum the values, giving you 23.

In 1000 - 948, start from 1000 and move 948 units left. Moving left decreases the value by 1 for each unit. After 948 steps, you reach 52. Subtracting a smaller positive number from a larger one keeps the result positive since it doesn’t reach zero or turn negative. This is simple subtraction where you find the difference between 1000 and 948, resulting in 52 because no sign change is involved. Hence, 1000 - 948 = 52.

In 22 - 11, start from 22 on the number line and move left by 11. Each step left decreases the value by 1. Moving 11 units from 22 results in 11. Subtracting a smaller number from a larger one keeps the result positive because it doesn’t reach zero or go negative. This is straightforward subtraction, and 22 - 11 = 11 because you’re simply reducing the value of 22 by 11 without any sign change.

In -11 + 11, start at -11 on the number line and move right by 11. Every step right moves you closer to zero, and after 11 steps, you reach zero. When adding a number and its exact opposite, their absolute values cancel each other out, resulting in zero. This is due to the additive inverse property, which states that a number added to its opposite always equals zero. Therefore, -11 + 11 = 0.

For -86 + 60, start from -86 and move right by 60 units. Moving right adds 1 per unit, reducing the negative value. After 60 steps, you reach -26. Adding a positive number to a negative number means subtracting the absolute values, then applying the sign of the larger number. The absolute difference between 86 and 60 is 26, and the larger value is negative, so the result is -26. Thus, -86 + 60 = -26.

For -40 + 25, we start at -40 and move 25 units to the right. This means adding 25 to -40, which offsets part of the negative distance but doesn't reach zero. After moving 25 units right from -40, we end at -15. This is calculated by reducing the magnitude of -40 by 25, resulting in a final position of -15. This outcome is consistent with integer addition rules, where adding a smaller positive number to a larger negative number yields a less negative result.

When you add -5 and 7, the calculation involves moving along a number line from -5 and then going 7 units in the positive direction. Moving from -5 up by 7 cancels out the 5 negative units and adds 2 more in the positive direction, which brings the final result to 2. This is why the answer is 2, as each positive step reduces the negative number toward zero and then shifts it into positive territory. Therefore, -5 + 7 results in a net movement of 2 units to the right, which is positive 2.

When adding -3 and 4, start from -3 on the number line and move right by 4 units. Each move to the right increases the value by 1. After moving four steps, you reach 1, which is the answer. Mathematically, adding a negative and positive number involves subtracting the smaller absolute value from the larger and applying the sign of the larger number. Here, the absolute difference is 1, and the larger absolute value is positive, resulting in 1. So, -3 + 4 = 1.

For -24 + 8, start at -24 and move right by 8 units. Each movement to the right adds 1, reducing the negative value. Moving 8 steps from -24 reaches -16. When adding a positive number to a negative one, subtract the smaller absolute value from the larger and apply the sign of the larger. Here, 24 - 8 = 16, and since 24 is negative, the result is -16. So, -24 + 8 = -16.

For -100 + 176, start at -100 and move right by 176 units. Moving 100 steps reaches zero, and moving 76 more steps reaches 76. Adding a larger positive number to a smaller negative one yields a positive result, as the positive number dominates. The absolute difference between 100 and 176 is 76, and since 176 is positive, the result is positive. Therefore, -100 + 176 = 76.

Adding 6 and -3 involves moving 6 units to the right from zero and then shifting back left by 3 units. This backward shift from 6 removes 3 positive units, resulting in a final position of 3. Visually on a number line, you move 6 spaces right, followed by 3 left, and end at 3. The operation demonstrates that adding a positive number and a smaller negative number leads to a positive sum, especially when the magnitude of the positive number is greater.

For 9 - 17, begin at 9 on the number line and move 17 units left, decreasing the value with each step. After 9 steps, you reach 0, and continuing 8 more steps lands you at -8. Subtracting a larger number from a smaller one produces a negative outcome since it creates a deficit. The absolute difference between 9 and 17 is 8, and since 17 is larger, the result is -8. Therefore, 9 - 17 = -8.

The expression 15 - 20 involves taking 20 away from 15, which can be visualized on a number line as starting at 15 and moving left by 20 units. Moving left by 15 units from 15 reaches zero, then another 5 units left results in -5. Hence, 15 - 20 equals -5. This solution uses the basic rule that subtracting a larger number from a smaller one will yield a negative result, in this case, moving leftward to achieve -5 as the answer.

For -6 - 11, begin at -6 and move 11 units further to the left. Each leftward movement decreases the value by 1. After 11 steps, you arrive at -17. Subtracting a positive number from a negative number makes the result more negative because you're increasing the negative distance. Combining -6 and -11 effectively adds the absolute values, giving 6 + 11 = 17, and applying the negative sign results in -17. Hence, -6 - 11 = -17.

For -9 - 8, we start at -9 on the number line and move an additional 8 units in the negative direction. Since -9 is already negative, adding -8 means increasing the negative total. Moving from -9 by another 8 units results in -17. This is because combining two negative values leads to a more negative outcome, which is consistent with the properties of integer addition. Thus, the calculation of -9 - 8 results in a sum of -17 due to this cumulative leftward shift.