3.3 Subtract Integers

Before you get started, take this readiness quiz.

Simplify: $12 - \left(8 −1\right) .$
If you missed this problem, review the reference.

Translate the difference of $\textit{20}$ and $−\textit{15}$ into an algebraic expression.
If you missed this problem, review the reference.

Add: $−18 + 7 .$
If you missed this problem, review the reference.

Simplify:

1. ⓐ $13 - 8 \text{and} 13 + \left(−8\right)$
2. ⓑ $−17 - 9 \text{and} −17 + \left(−9\right)$

Simplify each expression:

1. ⓐ $21 - 13 \text{and} 21 + \left(−13\right)$
2. ⓑ $−11 - 7 \text{and} −11 + \left(−7\right)$

Simplify each expression:

1. ⓐ $15 - 7 \text{and} 15 + \left(−7\right)$
2. ⓑ $−14 - 8 \text{and} −14 + \left(−8\right)$

Simplify:

1. ⓐ $9 - \left(−15\right) \text{and} 9 + 15$
2. ⓑ $−7 - \left(−4\right) \text{and} −7 + 4$

Simplify each expression:

1. ⓐ $6 - \left(−13\right) \text{and} 6 + 13$
2. ⓑ $−5 - \left(−1\right) \text{and} −5 + 1$

Simplify each expression:

1. ⓐ $4 - \left(−19\right) \text{and} 4 + 19$
2. ⓐ $−4 - \left(−7\right) \text{and} −4 + 7$

Simplify: $−74 - \left(−58\right) .$

Simplify the expression:

$−67 - \left(−38\right)$

Simplify the expression:

$−83 - \left(−57\right)$

Simplify the expression:

$8 - \left(−3 - 1\right) - 9$

Simplify the expression:

$12 - \left(−9 - 6\right) - 14$

Simplify the expression:

$6 \cdot 2 - 9 \cdot 1 - 8 \cdot 9 .$

Simplify the expression:

$2 \cdot 5 - 3 \cdot 7 - 4 \cdot 9$

Evaluate each expression:

$y - 7 \text{when}$

1. ⓐ $y = 5$
2. ⓑ $y = −8$

Evaluate each expression:

$m - 3 \text{when}$

1. ⓐ $m = 1$
2. ⓑ $m = −4$

Evaluate each expression:

$17 - k \text{when}$

1. ⓐ $k = 19$
2. ⓑ $k = −19$

Evaluate each expression:

$−5 - b \text{when}$

1. ⓐ $b = 14$
2. ⓑ $b = −14$

Translate and simplify:

1. ⓐ the difference of $14$ and $−23$
2. ⓑ subtract $21$ from $−17$

Translate and simplify:

1. ⓐ the difference of $11$ and $−19$
2. ⓑ subtract $18$ from $−11$

In the morning, the temperature in Urbana, Illinois was $11$ degrees Fahrenheit. By mid-afternoon, the temperature had dropped to $−9$ degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?

In the morning, the temperature in Anchorage, Alaska was $\text{15 degrees Fahrenheit}.$ By mid-afternoon the temperature had dropped to $30 degrees$ below zero. What was the difference between the morning and afternoon temperatures?

The temperature in Denver was $−6$ degrees Fahrenheit at lunchtime. By sunset the temperature had dropped to $−\text{15 degree Fahrenheit}.$ What was the difference between the lunchtime and sunset temperatures?

Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is $14,497$ feet above sea level and the elevation of Death Valley is $282$ feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?

One day, John hiked to the $10,023 foot$ summit of Haleakala volcano in Hawaii. The next day, while scuba diving, he dove to a cave $80 feet$ below sea level. What is the difference between the elevation of the summit of Haleakala and the depth of the cave?

The submarine Nautilus is at $340 feet$ below the surface of the water and the submarine Explorer is $573 feet$ below the surface of the water. What is the difference in the position of the Nautilus and the Explorer?

Araceli has $\$\text{75}$ in her checking account and writes a check for $\$\text{27} .$

1. ⓐ What is the balance after she writes the check?
2. ⓑ She writes a second check for $\$\text{50} .$ What is the new balance?
3. ⓒ The check for $\$\text{20}$ that she sent a charity was never cashed. What is the balance in Araceli’s checking account now?

Genevieve’s bank account was overdrawn and the balance is $- \$\text{78} .$

1. ⓐ She deposits a check for $\$\text{24}$ that she earned babysitting. What is the new balance?
2. ⓑ She deposits another check for $\$\text{49} .$ Is she out of debt yet? What is her new balance?

Simplify each expression.

1. ⓐ $15 - 6$
2. ⓑ $15 + \left(−6\right)$

Simplify each expression.

1. ⓐ $44 - 28$
2. ⓑ $44 + \left(−28\right)$

Simplify each expression.

1. ⓐ $8 - \left(−9\right)$
2. ⓑ $8 + 9$

Simplify each expression.

1. ⓐ $27 - \left(−18\right)$
2. ⓑ $27 + 18$

Simplify each expression.

$15 - \left(−12\right)$

Simplify each expression.

$10 - \left(−19\right)$

Simplify each expression.

$48 - 87$

Simplify each expression.

$31 - 79$

Simplify each expression.

$−31 - 11$

Simplify each expression.

$−17 - 42$

Simplify each expression.

$−103 - \left(−52\right)$

Simplify each expression.

$−45 - \left(−54\right)$

Simplify each expression.

$8 - 3 - 7$

Simplify each expression.

$−5 - 4 + 7$

Simplify each expression.

$−14 - \left(−27\right) + 9$

Simplify each expression.

$71 + \left(−10\right) - 8$

Simplify each expression.

$−16 - \left(−4 + 1\right) - 7$

Simplify each expression.

$\left(2 - 7\right) - \left(3 - 8\right)$

Simplify each expression.

$- \left(6 - 8\right) - \left(2 - 4\right)$

Simplify each expression.

$25 - \left[10 - \left(3 - 12\right)\right]$

Simplify each expression.

$6 \cdot 3 - 4 \cdot 3 - 7 \cdot 2$

Simplify each expression.

$5^{2} - 6^{2}$

Evaluate each expression for the given values.

$x - 6 \text{when}$

1. ⓐ $x = 3$
2. ⓑ $x = −3$

Evaluate each expression for the given values.

$5 - y \text{when}$

1. ⓐ $y = 2$
2. ⓑ $y = −2$

Evaluate each expression for the given values.

$4 x^{2} - 15 x + 1 \text{when} x = 3$

Evaluate each expression for the given values.

$−12 - 5 x^{2} \text{when} x = 6$

Translate each phrase into an algebraic expression and then simplify.

1. ⓐ The difference of $3$ and $−10$
2. ⓑ Subtract $−20$ from $45$

Translate each phrase into an algebraic expression and then simplify.

1. ⓐ The difference of $−6$ and $9$
2. ⓑ Subtract $−12$ from $−16$

Translate each phrase into an algebraic expression and then simplify.

1. ⓐ $8$ less than $−17$
2. ⓑ $- 24$ minus $37$

Translate each phrase into an algebraic expression and then simplify.

1. ⓐ $21$ less than$6$
2. ⓑ $31$ subtracted from $−19$

Solve the following applications.

Temperature One morning, the temperature in Urbana, Illinois, was $\text{28}°\text{ Fahrenheit}.$ By evening, the temperature had dropped $\text{38}°\text{ Fahrenheit}.$ What was the temperature that evening?

Solve the following applications.

Temperature On January 15, the high temperature in Anaheim, California, was $\text{84}°\text{ Fahrenheit}.$ That same day, the high temperature in Embarrass, Minnesota was $−\text{12}°\text{ Fahrenheit}.$ What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Solve the following applications.

Football At the first down, the Warriors football team had the ball on their $\text{30}-\text{yard line}.$ On the next three downs, they gained $\text{2 yards},$ lost $\text{7 yards},$ and lost $\text{4 yards}.$ What was the yard line at the end of the third down?

Solve the following applications.

Checking Account John has $\$\text{148}$ in his checking account. He writes a check for $\$\text{83}.$ What is the new balance in his checking account?

Solve the following applications.

Checking Account Gina has $\$\text{210}$ in her checking account. She writes a check for $\$\text{250}.$ What is the new balance in her checking account?

Solve the following applications.

Checking Account Bill has a balance of $−\$\text{14}$ in his checking account. He deposits $\$\text{40}$ to the account. What is the new balance?

Camping Rene is on an Alpine hike. The temperature is$- \textbf{7} ° .$ Rene’s sleeping bag is rated “comfortable to $- \textbf{20} °\".$ How much can the temperature change before it is too cold for Rene’s sleeping bag?

Explain why the difference of $9$ and $−6$ is $15 .$