# Integers and Fractions Check-In

*Time: 25 min. 6 questions.*

## Instructions

Answer all six questions on your own paper, showing your work for the short answer and numeric questions. You may use a number line or fraction model to support your thinking. Calculators are not needed for this check-in.

## Questions

1. Which expression correctly rewrites the subtraction 8 − 5 as an addition statement?
A) 8 + 5
B) 8 + (−5)
C) −8 + 5
D) −8 + (−5)
([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873))

2. Kayla is mixing paint and needs to add 3/4 of a litre of blue to 1/6 of a litre of white. Find the total amount of paint, in litres, and show the step where you convert the fractions to a common denominator. ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34141))

3. True or false: the product of two negative integers is a negative number. ([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873))

4. A submarine is at a depth of −85 metres. It rises 32 metres, then dives another 14 metres. Compute the submarine's final depth, as a signed number in metres. ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34142))

5. The temperature in Edmonton one morning is −7°C, and in Calgary it is 4°C. Which statement correctly compares the two temperatures using absolute value?
A) |−7| < |4|, so Edmonton is closer to zero
B) |−7| > |4|, so Edmonton is farther from zero
C) |−7| = |4|, so both cities are the same distance from zero
D) |−7| > |4|, so Edmonton is warmer than Calgary
([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20867))

6. Explain, using the example 2/3 × 3/4, why the product of two proper fractions is always less than either factor. ([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893))

## Curriculum coverage

| Question | Outcome alias |
|---|---|
| 1 | [Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873) |
| 2 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34141) |
| 3 | [Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873) |
| 4 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34142) |
| 5 | [Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20867) |
| 6 | [Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893) |

## Answer key

1. B) 8 + (−5). Subtraction can always be rewritten as adding the opposite of the number being subtracted.

2. 11/12 litre. Converting 3/4 to 9/12 and 1/6 to 2/12 gives a common denominator, and 9/12 + 2/12 = 11/12.

3. False. The product of two negative integers is positive, not negative.

4. −67 metres. Starting at −85, rising 32 gives −53, and diving another 14 gives −67.

5. B) |−7| > |4|, so Edmonton is farther from zero. Absolute value measures distance from zero regardless of sign, and 7 is greater than 4.

6. The product is smaller because multiplying by a fraction less than 1 means taking a part of a part: 2/3 × 3/4 = 6/12 = 1/2, which is less than both 2/3 and 3/4.

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*AILI quiz · language en · model claude-sonnet-5 · generated 2026-09-17 · id e5ccdd7a-3407-429b-b695-163ebd252abc*

### Sources

- node:n1: Number (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34135)
- node:n2: Develop number sense. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34136)
- node:n3: Demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and betwee (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34140)
- node:n4: Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denomi (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34141)
- node:n5: Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolically. [C, CN,  (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34142)
- node:n6: Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using: - benchmarks - plac (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/34143)
- node:n7: Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20863)
- node:n8: How can the symmetry of the number line contribute to a sense of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20864)
- node:n9: Students analyze positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20865)
- node:n10: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20867)
- node:n11: How can operations on positive and negative numbers be understood? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20870)
- node:n12: Students apply operations to positive and negative numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871)
- node:n13: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873)
- node:n14: How can multiplication and division be generalized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20890)
- node:n15: Students interpret multiplication and division of positive fractions and of positive decimal numbers. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891)
- node:n16: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893)
- node:n17: In what ways can proportional relationships be characterized? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20908)
- node:n18: Students analyze multiplicative relationships between equivalent ratios. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20909)
- node:n19: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20911)