Addition and Subtraction of Integers: A Grade 6 Guide

You add integers by their signs, and you subtract by adding the opposite. I teach it this way: same signs add and keep the sign, different signs subtract and keep the bigger sign. Subtracting a negative turns into adding, so 5 – (-4) becomes 5 + 4, which is 9, and that one change makes most integer questions easy.

How Do You Add Integers With the Same Sign?

When two integers share the same sign, add their absolute values and keep that sign, because both numbers pull in the same direction on the number line. Two negatives make a bigger negative, and two positives make a bigger positive, so (-7) + (-3) equals -10 and 6 + 4 equals 10.

Think of two debts. You owe 7 pounds and then you owe 3 more, so you owe 10 pounds in all. The sign stays negative, because nothing pulled the other way.

I say it like this in class: same sign, add and keep. Children chant it once, then they own it. The absolute value is just the size of the number without its sign, so 7 and 3 add to 10.

Try (-5) + (-8). Both signs are negative, so add 5 + 8 to get 13 and keep the negative sign. The answer is -13, and the number line shows a move of 13 steps left from zero.

How Do You Add Integers With Different Signs?

When the signs differ, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value, because the bigger pull wins. For (-12) + 9, the gap is 3 and the negative number is bigger, so the answer is -3, not 3.

Picture a tug of war. One side pulls with 12 and the other pulls with 9, so the stronger side wins by 3. That gap is the answer, and the sign belongs to the stronger pull.

Start with the bigger absolute value, take away the smaller one, and keep the bigger sign. In (-12) + 9, 12 beats 9 by 3, and 12 is negative, so the answer is -3. I make children point at the bigger number first, before they touch a pencil.

Watch the zero pair too. When a number meets its opposite, like 6 and -6, they cancel to zero. That pair saves time in long sums, and it shows up in the laws work later.

Why Does Subtracting a Negative Number Give a Bigger Answer?

Subtracting a negative gives a bigger answer because you change subtraction into adding the opposite, and adding a positive moves you right on the number line. The sign of the number being subtracted flips, so 5 – (-4) becomes 5 + 4, which is 9, and the answer grows instead of shrinking.

Say it out loud: minus a minus turns plus. The two minus signs do not cancel by magic, they change the job from taking away to adding on. Once children hear that plain sentence, the fear drops.

The same flip helps when you reorder a sum. I lean on the commutative law there, and I explain all three laws in my Laws of Integers guide.

Work 8 – (-3) with me. Flip it to 8 + 3 and the answer is 11. Check it on the number line: start at 8 and move 3 steps right, and you land on 11.

How Does the Number Line Show Adding and Subtracting Integers?

The number line turns steps into a move: adding a positive moves right, adding a negative moves left, subtracting a positive moves left, and subtracting a negative moves right. Start on the first number, move as the sign tells you, and you land there, so 3 + (-5) lands on -2.

Walk it with your finger. Start on the first number, then move right for adding a positive or subtracting a negative, and move left for adding a negative or subtracting a positive. The landing spot is the answer, every time.

Take 3 + (-5). Start at 3, move 5 steps left, and land on -2.

Take 2 – (-3) next: flip it to 2 + 3, move 3 steps right, and land on 5. I ask children to say the move before they write the answer, because the saying fixes the direction.

What Mistakes Do Children Make Most With Integer Subtraction?

The common mistake is keeping the wrong sign on the number being subtracted, because children change the sign but forget to flip the second number too. They read ‘minus a minus’ as minus, so 5 – (-4) comes out as 1 instead of 9, and that one slipped sign costs the question.

The fix is a two-part check. First, change the operation sign. Second, flip the sign of the number after it.

Children who check both parts stop losing marks here, and I praise the check out loud when I see it.

One more trap: children drop the sign when they copy a sum. They write -7 as 7 and the whole answer flips. I tell them to carry the sign with the number, like a name tag, from the first line to the last.

A Real-Life Case: Temperature on a Cold Day

Here is one case, worked in full, the way I do it in class.

Step 1: At 6 in the morning the temperature is -4 degrees. By noon it rises 9 degrees, so I write -4 + 9. The signs differ, so I take 9 – 4 = 5 and keep the positive sign. Noon is 5 degrees.

Step 2: By evening the temperature falls 6 degrees, so I write 5 – 6. That gives -1. Evening is -1 degree, just below freezing.

Step 3: Check it on the number line. Start at -4, move 9 right to 5, then move 6 left to -1. The moves match the sums, so the answer stands.

Try It Yourself: 3 Practice Questions

Cover the answers, try all three, then check. For a full page of the same practice, print my free Addition and Subtraction of Integers Worksheet for Grade 6.

1. Work out (-7) + (-3).
2. Work out 5 – (-4).
3. Work out (-12) + 9.

Answers

1. -10. Both signs are negative, so add 7 + 3 and keep the negative sign.
2. 9. Subtracting a negative turns into adding, so 5 + 4 = 9.
3. -3. The signs differ, so 12 – 9 = 3, and the bigger number is negative.

Key Takeaways

• Same sign: add the sizes and keep the sign.
• Different signs: subtract the sizes and keep the bigger sign.
• Minus a minus: flip it to adding, and the answer grows.
• Number line: right for adding a positive or subtracting a negative, left for the other two.
• Check both signs before you trust an answer.

If your child handled these three questions, she is ready for a longer page. For more free practice at this level, browse our Grade 6 math worksheets page. Every sheet is free to print.