# Integers and Fractions Homework This sheet gives you practice adding, subtracting, multiplying, and dividing positive and negative numbers ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20871), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20875), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879)) and practice multiplying and dividing positive fractions ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20891), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20895), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893)). Show your work in the space provided so your teacher can see how you reached each answer. ## Exercises **1. Integer addition, subtraction, and order of operations** Find each value. Remember that subtracting a number is the same as adding its opposite ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20873), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20874)), and that the order of operations applies to integers just as it does to whole numbers ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20905), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20907)). a) −8 + 5 = ______ b) 12 − (−7) = ______ c) −3 − 9 = ______ d) 6 + (−14) = ______ e) −5 + 3 × (−2) = ______ **2. Sign of a product or quotient** Circle the correct sign for each expression, then work out the answer on the line ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879), [Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20877)). a) (−4) × (−6) A) positive B) negative Answer: ______ b) 15 ÷ (−3) A) positive B) negative Answer: ______ c) (−9) × 2 × (−1) A) positive B) negative Answer: ______ d) (−36) ÷ (−9) A) positive B) negative Answer: ______ **3. Multiplying fractions** Multiply each pair of fractions and write your answer in simplest form. Multiplying two proper fractions can be pictured as taking a part of a part ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20895), [Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20894)), and the product is found by multiplying numerators and multiplying denominators ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20893)). a) 2/3 × 3/5 = ______ b) 5/6 × 4/7 = ______ c) 1/2 × 2/9 = ______ **4. Dividing fractions** Dividing by a fraction is the same as multiplying by its reciprocal ([Knowledge](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20897)). Solve each and write your answer in simplest form. a) 3/4 ÷ 1/2 = ______ b) 5 ÷ 2/3 = ______ c) 7/8 ÷ 7/8 = ______ **5. Matching reciprocals** The reciprocal of a fraction is the number you multiply it by to get 1 ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20899)). Match each number in Column A to its reciprocal in Column B by writing the correct letter on the line. | Column A | Match | Column B | |---|---|---| | 1) 3/4 | ______ | A) 5/2 | | 2) 2/5 | ______ | B) 4/3 | | 3) 7 | ______ | C) 1/7 | | 4) 5/9 | ______ | D) 9/5 | **6. Word problems** Solve each problem. Write the expression you use before you solve it ([Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20898), [Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/20879)). a) A research submarine descends 3/4 of a kilometre every hour. How many hours will it take to reach a depth of 6 kilometres? Expression: ______________________ Answer: ______ b) The temperature starts at 3°C and drops 2°C every hour for 5 hours. What is the temperature after 5 hours? Expression: ______________________ Answer: ______ ## Answer key 1. a) −3 b) 19 c) −12 d) −8 e) −11 2. a) positive, 24 b) negative, −5 c) positive, 18 d) positive, 4 3. a) 2/5 b) 10/21 c) 1/9 4. a) 3/2 (1 1/2) b) 15/2 (7 1/2) c) 1 5. 1, B, 2, A, 3, C, 4, D 6. a) 6 ÷ 3/4 = 8 hours b) 3 + 5 × (−2) = −7°C --- *AILI homework sheet · language en · model claude-sonnet-5 · generated 2026-09-17 · id 4609a6c5-5295-4461-a6d1-0a1022d677f3* ### 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)