Exercises: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers - Common Core Math - Grade 7

Work through problems with immediate feedback

Recall / Warm-Up

Which number is the additive inverse of $-\frac{2}{3}$ ?

$\frac{2}{3}$

$-\frac{2}{3}$

$\frac{3}{2}$

$-\frac{3}{2}$

What is $|-9|$ ?

$-9$

$9$

$\frac{1}{9}$

$0$

Compute $\frac{3}{4} + \frac{5}{6}$ . Express your answer as a fraction in simplest form.

Fluency Practice

$Number line from −12 to 2. Dot at −7. Leftward arrow of length 3 from −7, labeled +(−3). Question mark at endpoint.$

Compute $-7 + (-3)$ .

Compute $-8 + 13$ .

Compute $4 - 9$ .

Compute $6 - (-4)$ .

Rewrite $-3.5 - (-1.2)$ as addition. The missing addend is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , and the result is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

addend:

result:

Varied Practice

Which expression has the same value as $2 - (-7)$ ?

$2 + 7$

$2 - 7$

$-2 + 7$

$7 - 2$

$Number line from −6 to 9. Dots at p = −4 and q = 7. Solid arrow from −4 moving right 7 units, endpoint labeled '?'. Dashed double-headed arrow from −4 to 7 labeled |p − q| = ?.$

On a number line, $p = -4$ and $q = 7$ . The sum $p + q$ is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , and the distance $|p - q|$ is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

sum:

distance:

Find the distance between $-6$ and $4$ on the number line.

Which grouping most efficiently evaluates $-9 + 4 + 9 + (-4) + 11$ ?

Group $(-9 + 9)$ and $(4 + (-4))$ first, then add 11

Add the terms one at a time from left to right

Group $(-9 + 4)$ and $(9 + (-4))$ first, then add 11

Group $(-9 + 9 + 4)$ first, then add $(-4 + 11)$

Word Problems

A city's temperature at dawn was −8°F. By afternoon it had risen 15°F. What was the afternoon temperature in degrees Fahrenheit?

$Vertical number line with sea level at 0, fish at −45 m, submarine at −120 m. Double-headed arrow between them with a question mark indicating unknown distance.$

A submarine is positioned at −120 meters below sea level. A fish swims at −45 meters. How many meters apart are they?

Priya's bank account balance is −$32. She deposits $50, then pays a $27 bill, then receives a $32 refund.

What is Priya's final account balance in dollars?

What was the net change in Priya's balance from the starting amount?

A hiker's elevation changes over five trail segments: +180 ft, −110 ft, −180 ft, +110 ft, then +65 ft. Use properties of operations to find the net elevation change in feet.

Error Analysis

$Two-column card. Left (yellow): Student writes 5 − (−3) = 5 − 3 = 2 with red X. Right (teal): Correct shows 5 − (−3) = 5 + 3 = 8 with checkmark.$

A student evaluates $5 - (-3)$ :

$5 - (-3) = 5 - 3 = 2$

What error did the student make, and what is the correct answer?

Did not convert subtraction of a negative to addition of the opposite; the correct answer is 8

Subtracted in the wrong order; the correct answer is −8

Used the wrong operation; the correct answer is −2

No error was made; 2 is correct

$Two-column card. Left (yellow): Student writes −4 + (−6) = 10 with red X. Right (teal): Correct shows −4 + (−6) = −10 with checkmark.$

A student computes $-4 + (-6)$ :

$-4 + (-6) = 10$

The student says: "Two negatives make a positive."

What error did the student make, and what is the correct answer?

Applied the multiplication rule to addition; the correct answer is −10

Should have subtracted the absolute values; the correct answer is 2

The magnitude is right but the sign is wrong; the correct answer is +10

No error; two negatives do make a positive

Challenge

Use properties of operations to efficiently evaluate $-\frac{2}{3} + \frac{5}{6} + \left(-\frac{1}{3}\right) + \frac{1}{6}$ . Express your answer in simplest form.