Integers

Adding Integers

Add positive and negative integers using absolute values and sign rules: same signs add, different signs subtract and keep the sign of the larger.

add-integers To add two integers: - Same signs: add absolute values, keep the sign. - Different signs: subtract absolute values, keep the sign of the integer with the larger absolute value.

Example

Add integers by comparing signs and magnitudes. When the signs differ, the sum keeps the sign of the term with the larger absolute value (magnitude), not simply the larger number.

highlighted = computed this step

Step 1 — Different signs

Set up the expression.

−7+3-7 + 3
Start at 0, move left 7 to -7.move left 70-7The first addend -7 moves left from 0.

Step 2 — Compare magnitudes

Find magnitudes: |-7| = 7 and |3| = 3.

∣−7∣=7∣3∣=3| -7 |= \hl{7} \quad | 3 |= \hl{3}
Then +3 moves right 3.move left 70-7move right 3-4A positive addend moves right: -7 + 3.

Step 3 — Subtract magnitudes

Different signs: subtract magnitudes, 7 - 3 = 4.

different signs7−3=4\text{different signs} \quad 7 - 3 = \hl{4}
Right 3 cancels part of left 7.move left 70-7move right 3-4The net distance left is 7 - 3.

Step 4 — Keep larger sign

The larger magnitude is from -7, so the result is -4.

−7+3=-4-7 + 3 = \hl{-4}
The movement ends at -4.move left 70-7move right 3-4So -7 + 3 = -4.

Step 5 — Same signs

Set up the expression.

−5+(−2)-5 + ( -2 )
Start at 0, move left 5 to -5.move left 50-5The first addend -5 moves left from 0.

Step 6 — Add magnitudes

Same signs: add magnitudes, 5 + 2 = 7.

same signs5+2=7\text{same signs} \quad 5 + 2 = \hl{7}
Then -2 moves left 2.move left 50-5move left 2-7A negative addend moves left again: -5 + (-2).

Step 7 — Keep common sign

Both numbers are negative, so keep the negative sign: -7.

−5+(−2)=-7-5 + ( -2 )= \hl{-7}
The movement ends at -7.move left 50-5move left 2-7So -5 + (-2) = -7.

Step 8 — Result

Read the final result.

−4−7-4 \quad -7
Read each sum as signed movement.-730-7-4-7 + 3 = -4-5-20-5-7-5 + (-2) = -7Right means positive; left means negative.