To review these concepts, go to Basic Number and Integer Word Problems Study Guide.

**Basic Number and Integer Word Problems Practice Questions**

**Practice 1**

**Problems**

Match each expression with the correct value.

–1 – 5 –4 –7 + –9 –20 –3 × –4 7 –14 ÷ –2 –16 6 – 10 –6 –10 × –1 × –2 –12

**Solutions**

- –1 – 5 = –6

- –7 + –9 = –16

- 3 × –4 = –12

- –14 ÷ –2 = 7

- 6 – 10 = –4

- –10 × –1 × –2 = –20

**Practice 2**

**Problems**

- Sue and Terry each have marbles. Sue has five more than twice the number that Terry has. If Terry has 8 marbles, how many does Sue have?
- Zach scores 27 points in a basketball game. If he made one 3-point basket and every other basket he made scored 2 points, what is the total number of baskets he made?
- The low temperature on Monday is –9 degrees. If the low temperature on Tuesday is 5 degrees below this value, what is the low temperature on Tuesday?
- A diver descended 20 feet into the water from a boat at the surface of a lake. She then rose 12 feet, and then descended another 18 feet. At this point, what is her depth in the water?
- Jackson divided –350 and –7 correctly. What was the quotient?
- What is the product of –4, –2, and –5?

**Solutions**

*Read and understand the question*. This question is looking for the total number of marbles Sue has. The number that Terry has is given in the problem.*Make a plan*. Start with the fact that Terry has 8 marbles and use key words and basic operations to solve. Calculate what number is equal to*five more than twice eight marbles*.*Carry out the plan*. Five more than twice eight marbles is equal to 8 times 2, plus 5.- 8 × 2 + 5 = 16 + 5 = 21

Sue has 21 marbles.

*Check your answer*. Since Sue has 21 marbles, this is five more than twice the number of marbles Terry has. Work backward: subtract 5 and divide by 2:- 21 – 5 = 16

- 16 ÷ 2 = 8

This is the number Terry has, so this solution is checking.

*Read and understand the question*. This question is looking for the total number of baskets scored in a basketball game. Each basket Zach made scores either three or two points.*Read and understand the question*. This question gives the low temperature on Monday, and asks you to find the low temperature on Tuesday.*Read and understand the question*. This question asks for the depth of a diver in the water after she dived in at sea level.*Read and understand the question*. This question is looking for the result of a division problem. The key words are*divided*and*quotient*.*Read and understand the question*. This question is looking for the product of three values.

*Make a plan*. In this problem, subtract the points made by the 3-point basket. Then, divide the total number of points left by two.

*Carry out the plan*. Zach scored 27 points. Subtract 27 – 3 = 24 to take out the one 3-point basket. Then, divide 24 by 2 to get twelve 2-point baskets. He scored a total of 13 baskets.

*Check your answer*. To check this problem, add one 3-point basket to twelve 2-point baskets. 12 ÷2 + 3 = 24 + 3 = 27 total points. This solution is checking.

*Make a plan*. The temperature on Tuesday is 5 degrees below the low temperature on Monday. Subtract 5 from –9 to find the answer.

*Carry out the plan*. Subtract. Be sure to use the rules for subtracting integers by adding the opposite: –9 – 5 = –9 + –5 = –14. When you are adding, if the signs are the same, add the absolute values and keep the sign. The low temperature on Tuesday is –14 degrees.

*Check your answer*. To check this problem, do the opposite operation. Be sure to follow the rules for adding integers. Add –14 + 5. The signs are different, so subtract and take the sign of the number with the larger absolute value: –14 + 5 = –9. This was the temperature on Monday, so this solution is checking.

*Make a plan*. Start with the value of zero for sea level, then add or subtract as the diver descends (goes down) or rises.

*Carry out the plan*. Start at 0. She descends 20 feet, so 0 – 20 = –20 feet. She rose 12 feet, so add 12 to –20: –20 + 12 = –8. She then descends another 18 feet, so subtract –8 – 18 = –26 feet. Her depth at this point is –26 feet, or 26 feet below sea level.

*Check your work:* 0 – 20 + 12 – 18 = –20 + 12 – 18 = –8 – 18 = –26. This problem is checking.

*Make a plan*. The quotient is the result of a division problem. Divide the two numbers in the question and be aware of the signs of the numbers.

*Carry out the plan*. Divide –350 by –7 by dividing their absolute values. The result is 50. Because there are two negatives being divided, the final result is positive 50.

*Check your answer*.Check your answer by multiplying: 50 × –7 is –350. There is only one negative sign in this check so the product is negative. This solution is checking.

*Make a plan*. The key word is *product*, which means multiply. Be aware of the number of negative numbers being multiplied.

*Carry out the plan*. Multiply the absolute values of the three numbers together. There are an odd number of negative signs (3), so the result is negative: –4 × –2× –5 = –40.

*Check your answer.*Check your answer by multiplying 4 × 2 × 5 = 40. There are an odd number of negatives, so the result is –40. This solution is checking.

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