7th Grade · 7.NS.A.1

Adding and subtracting integers in 7th grade

Adding and subtracting integers means working with positive and negative numbers. Integers are the whole numbers and their negatives, such as $-3$ , 0 and 5. In 7th grade, your child learns to add and subtract them on a number line, then uses the same rules for negative fractions and decimals.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.1.a Describe situations in which opposite quantities combine to make 0.
7.NS.A.1.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
7.NS.A.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.A.1.d Apply properties of operations as strategies to add and subtract rational numbers.

What it means, in plain words

Negative numbers sit to the left of 0 on a number line. Every number has an opposite, the same distance from 0 on the other side: the opposite of 4 is $-4$ . A number and its opposite always add up to 0. Taking 6 steps forward and then 6 steps back puts you where you started.

Adding integers is moving along the number line. Start at the first number. Adding a positive number moves right, and adding a negative number moves left. So $2 + (-5)$ starts at 2 and moves 5 steps left, to $-3$ .

Subtracting integers means adding the opposite: $3 - (-2)$ becomes $3 + 2 = 5$ . Subtraction also measures distance. The absolute value of a number is its distance from 0, so it is never negative. The distance between two numbers is the absolute value of their difference: $-3$ and 5 are $|5 - (-3)| = 8$ apart. In 7th grade, adding and subtracting integers leads straight into the same work with fractions and decimals, such as $-2.5 + 1$ .

Your child should be able to:

Place positive and negative numbers on a number line
Explain why a number and its opposite add up to 0
Add integers by moving left or right on a number line
Rewrite a subtraction as adding the opposite and find the distance between two numbers

Example

An elevator stops at level $-2$ , two floors below the ground floor (level 0). It goes up 7 floors, then down 9 floors. Where does it stop?

Going up 7 floors: $-2 + 7 = 5$ .
Going down 9 floors adds $-9$ : $5 + (-9) = -4$ .
The elevator stops at level $-4$ , four floors below the ground floor.

Example

What is $4 - (-7)$ ?

Subtracting a number is the same as adding its opposite. The opposite of $-7$ is 7.
$4 - (-7) = 4 + 7 = 11$
Check with distance: 4 and $-7$ are 11 steps apart on the number line.
So $4 - (-7) = 11$ .

Where children usually get stuck

Your child writes $-8 + 5 = -13$ .
The rule "add the numbers and keep the sign" only works when both numbers have the same sign. Here the signs differ, so the 5 moves the answer back toward 0.
What helps. Draw a number line on scrap paper. Start at $-8$ and count 5 steps to the right together. You land on $-3$ .
Your child writes $3 - (-5) = -2$ .
The two minus signs look like one subtraction, so the child takes 5 away from 3. Subtracting a negative number is the same as adding a positive one.
What helps. Ask your child to rewrite every subtraction as adding the opposite before working it out: $3 - (-5) = 3 + 5 = 8$ .
Asked for the distance between $-4$ and 6, your child answers 2.
The child works out $6 - 4$ and drops the minus sign. The two numbers sit on opposite sides of 0, so the distance is $4 + 6 = 10$ .
What helps. Count the steps from $-4$ to 6 on a number line together. Then show that $|6 - (-4)| = 10$ gives the same answer.

Try four practice questions

Real 7th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
A temperature changes by -5 degrees. Mia says -5 degrees would make the total change 0, and the chip model shows both changes together. What should Mia change?
A
Correct
B
Change the sign only
C
Change the amount only
D
Change both the sign and the amount
Show the answer and how to solve it
The answer is Change the sign only because -5 has the correct magnitude but the wrong sign. Mia needs +5 to make the total change 0.
1. 1The chip model shows 10 negative chips and 0 positive chips.
2. 2With no positive chips, no zero pairs can form. The total is -10, not 0.
3. 3To reach 0, Mia needs the opposite of -5, which is +5. She used the right amount (5) but the wrong sign. So choose Change the sign only.
Common mistake. A common mistake is thinking that two groups of negative chips cancel each other. Chips cancel only when a positive chip pairs with a negative chip — all 10 chips here are negative, so none cancel.
The idea underneath. To make a total change of 0, the second change must be the additive inverse of the first: the same amount with the opposite sign.
2On level
The temperature fell 7 degrees. Which action would cancel that change to 0?
A
rose 7 degrees
B
fell 7 degrees
C
rose 5 degrees
D
fell 5 degrees
Show the answer and how to solve it
The answer is "rose 7 degrees" because it is the opposite direction with the same amount, and those two changes cancel to 0.
1. 1A fall of 7 degrees means a change of -7.
2. 2To cancel -7 and return to 0, you need the opposite change with the same amount: +7.
3. 3A rise of 7 degrees means +7, so the correct choice is "rose 7 degrees."
Common mistake. A common mistake is choosing "fell 7 degrees" because the 7 matches. The amount must match, but the direction also has to reverse so the two changes cancel.
The idea underneath. Two actions cancel when they have the same absolute value and opposite directions; they are additive inverses.
3On level
A thermometer rose 7 degrees and then fell 3 degrees. Click the total change on the number line.
Tap or click the number line to place your point. Drag it to move, or tap it again to remove.
Show the answer and how to solve it
The answer is 4 because +7 + (−3) = 4, so the net temperature change is 4 degrees upward.
1. 1Rising 7 degrees is +7 and falling 3 degrees is -3 — they are opposite in sign.
2. 2The fall only partially cancels the rise.
3. 3The rise has the larger absolute value, so the net change is positive. Click 4 on the number line.
Common mistake. A common mistake is clicking 0 because the temperature went both up and down. They cancel to 0 only when the amounts are equal, and 7 and 3 are not equal.
The idea underneath. Opposite signed quantities only make 0 when their absolute values are equal; otherwise the result keeps the sign of the larger absolute value.
4Stretch
Sort each situation into the correct category.
Drag each item into the group where it belongs, or tap the item, then tap the group.
A climber gains 9 m in elevation and loses 9 m.
A player earns 7 points and loses 8 points.
A diver descends 5 m and descends 5 m more.
An account is credited $12 and debited $12.
The temperature drops 6° and rises 4°.
A hiker climbs 3 m and then climbs 11 m.
The quantities are opposites and make 0
Drag or tap items here
The changes have opposite directions and different sizes
Drag or tap items here
The changes have the same direction
Drag or tap items here
Keyboard instructions: focus an item and press Enter or Space to pick it up. Move focus to a bin or the bank and press Enter or Space to drop it. Press Escape to cancel.
Show the answer and how to solve it
The climber and account stories go in 'The quantities are opposites and make 0'. The player and temperature stories go in 'The changes have opposite directions and different sizes'. The diver and hiker stories go in 'The changes have the same direction'.
1. 1For each card, check two things: are the two quantities opposite in direction, and are their sizes equal? Both must be true for the quantities to make 0.
2. 2Climber: gains 9 m is $+9$ and loses 9 m is $-9$ . They are opposite in direction and equal in size, so this card goes in 'The quantities are opposites and make 0'.
3. 3Player: earns 7 points is $+7$ and loses 8 points is $-8$ . The directions are opposite, but the sizes 7 and 8 differ by 1, so this card goes in 'The changes have opposite directions and different sizes'.
4. 4Diver: descends 5 m is $-5$ and descends 5 m more is also $-5$ . The sizes match, but both quantities go in the same direction, so this card goes in 'The changes have the same direction'.
5. 5Account: a credit of $12 is $+12$ and a debit of $12 is $-12$ . They are opposite in direction and equal in size, so this card goes in 'The quantities are opposites and make 0'.
6. 6Temperature: a drop of $6^{\circ}$ is $-6$ and a rise of $4^{\circ}$ is $+4$ . The directions are opposite, but the sizes $6$ and $4$ differ by $2$ , so this card goes in 'The changes have opposite directions and different sizes'.
7. 7Hiker: climbs 3 m is $+3$ and climbs 11 m is $+11$ . Both quantities go in the same positive direction, so this card goes in 'The changes have the same direction'.
Common mistake. A common mistake is placing the player card in 'makes zero' because 'earns' and 'loses' sound like opposites — but the sizes 7 and 8 are different. Another mistake is placing the diver card in 'makes zero' because 5 appears twice — but both motions are descents in the same direction.
The idea underneath. A zero-sum situation is an additive inverse pair: opposite signs and equal absolute values.