# Integers and Fractions Quiz

*Time: 20 min. 6 questions.*

## Instructions

Answer all six questions in the space provided or on a separate sheet. Show your work for any question that involves a calculation. You may use a calculator to check your answers, but you must show the steps you used to get there.

## Questions

**1.** What is the sign of the product when you multiply two negative integers together, such as (−6) × (−5)?

A) Positive
B) Negative
C) Zero
D) It depends on which two numbers you choose

([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877))

**2.** A reciprocal is the multiplicative inverse of a fraction, and the product of a fraction and its reciprocal is 1. In your own words, explain what a reciprocal is, and write the reciprocal of 5/8. Then show that 5/8 multiplied by its reciprocal equals 1.

([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897))

**3.** A recipe calls for 2/3 cup of flour, but you are only making 3/4 of the recipe. Explain how you would calculate the amount of flour needed, and show your work to find the answer as a fraction in simplest form.

([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893))

**4.** True or false: The expression a − b can also be written as a + (−b).

([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873))

**5.** In the expression 5 − 3 × (−2) + 4, which operation should be performed first, according to the conventional order of operations?

A) 5 − 3
B) 3 × (−2)
C) (−2) + 4
D) It does not matter which operation comes first

([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905))

**6.** A weather balloon descends 84 m in 12 equal stages, moving down the same distance each stage. Compute the change in height for one stage using a division statement with integers.

([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879))

## Curriculum coverage

| Question | Outcome alias |
|---|---|
| 1 | [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877) |
| 2 | [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897) |
| 3 | [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893) |
| 4 | [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873) |
| 5 | [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905) |
| 6 | [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879) |

## Answer key

**1.** A) Positive. The product of two negative integers is always positive.

**2.** The reciprocal of 5/8 is 8/5. Multiplying 5/8 × 8/5 gives 40/40, which equals 1, confirming that a fraction and its reciprocal always multiply to 1.

**3.** 1/2 cup. Multiply 2/3 × 3/4 by multiplying numerators (2 × 3 = 6) and denominators (3 × 4 = 12) to get 6/12, which simplifies to 1/2.

**4.** True. Subtracting a number gives the same result as adding its negative, so a − b = a + (−b).

**5.** B) 3 × (−2). The order of operations requires multiplication to be completed before addition or subtraction.

**6.** −84 ÷ 12 = −7. The change in height for one stage is −7 m, where the negative sign indicates the balloon is descending.

---
*AILI quiz · language en · model claude-sonnet-5 · generated 2026-09-17 · id 3e0c44d8-3580-4682-83d1-50ac98bdf33b*

### Sources

- node:n1: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891)
- node:n2: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871)
- node:n3: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897)
- node:n4: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20898)
- node:n5: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20899)
- node:n6: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20902)
- node:n7: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20901)
- node:n8: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20903)
- node:n9: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20895)
- node:n10: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893)
- node:n11: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20894)
- node:n12: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905)
- node:n13: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20906)
- node:n14: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can multiplication and division be generalized? › Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20907)
- node:n15: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873)
- node:n16: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20875)
- node:n17: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20874)
- node:n18: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879)
- node:n19: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20878)
- node:n20: Mathematics › Mathematics (7–9) › Grade 7 › Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculation… › How can operations on positive and negative numbers be understood? › Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877)