On very cold day, the temperature might be −10. If the temperature rises 8 degrees, exactly how will you discover the brand-new temperature? Knowing exactly how to add integers is vital here and also in lot of algebra.

You are watching: Two integers with the same sign

Since confident integers room the very same as herbal numbers, adding two positive integers is the exact same as adding two herbal numbers.

Try the end the interactive number heat below. Choose a few pairs of confident integers to add. Click and drag the blue and red dots, and watch how the enhancement works.

To add integers top top the number line, you relocate forward, and you confront right (the optimistic direction) once you include a hopeful number.

As with positive numbers, to add an adverse integers ~ above the number line, you relocate forward, however you confront left (the an adverse direction) when you include a negative number.

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In both cases, the total number of units relocated is the complete distance moved. Since the street of a number indigenous 0 is the absolute worth of the number, climate the absolute worth of the amount of the integers is the sum of the absolute worths of the addends.

When both numbers room negative, you relocate left in a an unfavorable direction, and the sum is negative. Once both numbers space positive, you move right in a positive direction, and the amount is positive.

 To include two numbers through the very same sign (both confident or both negative): · include their absolute values and give the amount the exact same sign.

 Example Problem Find −23 + (−16). Both addends have the exact same sign (negative). So, include their absolute values: |−23| = 23 and |−16| = 16. The amount of those number is 23 + 16 = 39. Since both addends room negative, the amount is negative. Answer −23 + (−16) = −39

With much more than 2 addends that have actually the very same sign, usage the same process with every addends.

 Example Problem Find −27 + (−138) + (−55). All addends have the very same sign (negative). So, add their absolute values: |−27| = 27, |−138| = 138, and also |−55| = 55. The sum of those numbers is 27 + 138 + 55 = 220. Since every addends are negative, the sum is negative. Answer −27 + (−138) + (−55) = −220

Find −32 + (−14).

A) 46

B) 18

C) −18

D) −46

A) 46

Incorrect. You uncovered the sum of the pure values, however the sum need to be negative, together you are adding two an adverse numbers. The exactly answer −46.

B) 18

Incorrect. Girlfriend subtracted 14 from 32. The amount is discovered by first adding the absolute values of the addends: |−32| + |−14| = 32 + 14 = 46. Climate you must provide the sum the very same sign as the two addends. The exactly answer is −46.

C) −18

Incorrect. The sum is discovered by an initial adding the absolute values of the addends:

|−32| + |−14| = 32 + 14 = 46. Then you must offer the sum the very same sign as the two addends. The exactly answer is −46.

D) −46

Correct. The amount is found by an initial adding the absolute worths of the addends:

|−32| + |−14| = 32 + 14 = 46. Then you must provide the sum the very same sign together the 2 addends, so the answer is −46.

What happens when the addends have various signs, like in the temperature problem in the introduction? If the −10 degrees, and also then the temperature rises 8 degrees, the brand-new temperature is −10 + 8. How can you calculation the new temperature?

Using the number line below, you move forward come add, just as before. Face and also move in a confident direction (right) to add a positive number, and move front in a an adverse direction (left) to include a an unfavorable number.

Try adding integers with various signs with this interactive number line. View if friend can find a ascendancy for adding numbers without using the number line.

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Notice that once you add a hopeful integer and also a an unfavorable integer, you relocate forward in the confident (right) direction come the an initial number, and also then relocate forward in the an adverse (left) direction to include the negative integer.

Since the ranges overlap, the absolute worth of the amount is the distinction of your distances. Therefore to add a positive number and also a an adverse number, you subtract their absolute values (their ranges from 0.)

What is the authorize of the sum? that pretty basic to number out. If girlfriend moved more to the right than girlfriend did to the left, you ended to the appropriate of 0, and the prize is positive; and if you move additional to the left, the answer is negative. If girlfriend didn’t have actually the number line to express to, girlfriend can discover the sum of −1 + 4 by

· subtracting the distances from zero (the absolute values) 4 – 1 = 3 and also then

· using the authorize of the one furthest native zero (the largest absolute value). In this case, 4 is more from 0 보다 −1, so the answer is positive: −1 + 4 = 3

Look at the illustration below. If you didn’t have the number line to to express to, girlfriend can discover the sum of −3 + 2 by

subtracting the ranges from zero (the absolute values) 3 – 2 = 1 and also then applying the authorize of the one furthest native zero (the largest absolute value). In this case, |−3| > |2|, so the price is negative: −3 + 2 = −1

 To include two number with different signs (one positive and one negative): · find the distinction of their pure values. · give the amount the very same sign together the number v the higher absolute value.

Note that once you discover the distinction of the absolute values, you constantly subtract the lesser absolute worth from the higher one. The example below shows you how to deal with the temperature concern that you thought about earlier.

 Example Problem Find 8 + (−10). The addends have different signs. So discover the difference of their pure values. |−10| = 10 and also |8| = 8. The distinction of the absolute values is 10 – 8 = 2. Since 10 > 8, the sum has actually the very same sign together −10. Answer 8 + (−10) = −2

 Example Problem Evaluate x + 37 as soon as x = −22. x + 37 −22 + 37 Substitute −22 for x in the expression. |−22| = 22 and also |37| = 37 37 – 22 = 15 The addends have different signs. So find the distinction of their pure values. Since |37| > |−22|, the sum has the very same sign together 37. Answer −22 + 37 = 15

 Example Problem Find −27 + (−138) + 55. Add 2 at a time, starting with −27 + (−138). |−27| = 27 and |−138| = 138 27 + 138 = 165 −27 + −138 = −165 Since they have the very same signs, you add their pure values and also use the very same sign. −165 + 55 |−165| = 165 and |55| = 55 165 – 55 = 110 −165 + 55 = −110 Now add −165 + 55. Because −165 and also 55 have various signs, you add them by subtracting their pure values. Since 165 > 55, the authorize of the final sum is the same as the authorize of −165. Answer −27 + (−138) + 55 = −110

A) 46

Incorrect. You discovered the amount of the absolute values. Since the addends have various signs, girlfriend must discover the difference of the pure values. |32| = 32 and |−14| = 14. The distinction is 32 – 14 = 18. The authorize of the sum is the same as the addend v the better absolute value. Since |32| > |−14|, the amount is positive, the exact same sign together 32. The correct answer is 18.

B) 18

Correct. Since the addends have various signs, girlfriend must find the difference of the pure values. |32| = 32 and |−14| = 14. The difference is 32 – 14 = 18. The sign of the amount is the same as the addend through the higher absolute value. Since |32| > |−14|, the amount is positive.

C) −18

Incorrect. You discovered the distinction of the absolute worths of the addends. However, because |32| > |−14|, the authorize of the sum must be the same sign as 32. The exactly answer is 18.

D) −46

Incorrect. You added the absolute values of the addends, and gave the amount the not correct sign. Since the addends have different signs, you must find the distinction of the pure values. |32| = 32 and |−14| = 14. The difference is 32 – 14 = 18. The sign of the amount is the exact same as the addend with the greater absolute value. Because |32| > |−14|, the amount is positive, the exact same sign together 32. The exactly answer is 18.

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There room two instances to think about when adding integers. When the indicators are the same, you add the absolute worths of the addends and use the exact same sign. Once the indications are different, you uncover the difference of the absolute values and also use the same sign together the addend v the better absolute value.