https://www.khanacademy.org/math/class-6-ncf/x04ca845a9a148c80:the-other-side-of-zero/x04ca845a9a148c80:the-token-model/v/adding-with-integer-chips-indian-accent 2025-06-08T17:08:59.076161332Z Adding with integer chips Let's model and evaluate sums using integer chip diagrams. When all the integer chips are negative, we can just count up our total negatives. When we have a positive integer chip and negative integer chip, those pair up to equal zero. So our sum is whatever chips are left over. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Adding with integer chips Let's model and evaluate sums using integer chip diagrams. When all the integer chips are negative, we can just count up our total negatives. When we have a positive integer chip and negative integer chip, those pair up to equal zero. So our sum is whatever chips are left over. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by https://cdn.kastatic.org/ka-youtube-converted/GpgtfqGhIfA.mp4/GpgtfqGhIfA.mp4 212 Operation with Integers https://www.khanacademy.org/math/class-6-ncf/x04ca845a9a148c80:the-other-side-of-zero/x04ca845a9a148c80:the-token-model/v/adding-the-opposite-with-integer-chips-indian-accent 2025-06-08T17:08:59.076161332Z Adding the opposite with integer chips Use integer chips to explore the conjecture that subtracting a number gives the same result as adding the opposite of the number. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Adding the opposite with integer chips Use integer chips to explore the conjecture that subtracting a number gives the same result as adding the opposite of the number. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (add course link here) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by https://cdn.kastatic.org/ka-youtube-converted/YS6rtKsxwUg.mp4/YS6rtKsxwUg.mp4 280 Operation with Integers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-and-sub-integers/v/adding-integers-find-the-missing-value 2023-08-31T15:42:23.143811656Z Adding integers: find the missing value Use number lines to find missing addends in addition equations with integers. When we add a positive value, we move to the right on the number line. When we add a negative value, we move to the left. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/431df0b5-84e3-4548-988e-3ccedc32383c_1280_720_base.png Adding integers: find the missing value Use number lines to find missing addends in addition equations with integers. When we add a positive value, we move to the right on the number line. When we add a negative value, we move to the left. https://cdn.kastatic.org/ka-youtube-converted/jA1vyOrzlOE.mp4/jA1vyOrzlOE.mp4 182 Operation with Integers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-negatives/e/add-with-integer-chips 2025-02-13T21:04:37.380846713Z Add with integer chips Add integers with the support of integer chip diagrams. Charlie Auen exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-sub-neg-intro/v/subtracting-with-integer-chips 2023-08-31T15:42:23.143811656Z Subtracting with integer chips Let's model subtraction expressions using positive and negative integer chips. To subtract, we'll take away the appropriate number of chips. What if we don't have enough chips to take away? We can add as many zero pairs as we need, because they don't change the value of the expression. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/315bfd81-0ca7-434e-9009-ebfe02428f26_1280_720_base.png Subtracting with integer chips Let's model subtraction expressions using positive and negative integer chips. To subtract, we'll take away the appropriate number of chips. What if we don't have enough chips to take away? We can add as many zero pairs as we need, because they don't change the value of the expression. https://cdn.kastatic.org/ka-youtube-converted/yTqhzgpt_9Y.mp4/yTqhzgpt_9Y.mp4 330 Operation with Integers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-sub-neg-intro/e/subtract-with-integer-chips 2025-02-13T21:04:37.380846713Z Subtract with integer chips Write subtraction equations and subtract integers with the support of integer chip diagrams. Charlie Auen exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-negatives/v/zero-pairs-worked-example 2023-08-31T15:42:23.143811656Z Zero pairs worked example When we have a positive unit and a negative unit, they add up to zero. We call that a zero pair. Let's use integer chips to represent the number -2, but not just with 2 negative chips. This will open the door for us to add and subtract with negative numbers. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/9ef5f9da-6765-46dc-a5fd-4d06f6abe8eb_1280_720_base.png Zero pairs worked example When we have a positive unit and a negative unit, they add up to zero. We call that a zero pair. Let's use integer chips to represent the number -2, but not just with 2 negative chips. This will open the door for us to add and subtract with negative numbers. https://cdn.kastatic.org/ka-youtube-converted/hwK33GvGIK4.mp4/hwK33GvGIK4.mp4 127 Operation with Integers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-negatives/e/zero-pairs 2025-02-13T21:04:37.380846713Z Zero pairs Interpret integer chip diagrams with zero pairs. Charlie Auen exercise https://www.khanacademy.org/math/class-6-ncf/x04ca845a9a148c80:the-other-side-of-zero/x04ca845a9a148c80:integers-in-other-places/e/integers-3-c 2024-01-03T14:27:06.234883329Z Addition and subtraction of integers Addition and subtraction of integers, word problems ashish exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/multiplying-positive-negative-numbers-india 2025-03-28T07:05:36.573142233Z Multiplying positive & negative numbers Multiplying positive & negative numbers (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Multiplying positive & negative numbers Multiplying positive & negative numbers (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/0OCU0QBrcw0.mp4/0OCU0QBrcw0.mp4 309 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/why-a-negative-times-a-negative-makes-sense-indian-accent 2025-06-03T03:42:04.110515269Z Why a negative times a negative makes sense Why a negative times a negative makes sense Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Why a negative times a negative makes sense Why a negative times a negative makes sense https://cdn.kastatic.org/ka-youtube-converted/90shhVUiGjg.mp4/90shhVUiGjg.mp4 302 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/why-a-negative-times-a-negative-is-a-positive-india 2025-03-28T07:05:36.573142233Z Why a negative times a negative is a positive Why a negative times a negative is a positive (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Why a negative times a negative is a positive Why a negative times a negative is a positive (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/nC85vRx_XUg.mp4/nC85vRx_XUg.mp4 327 Operation with Integers https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-negatives/e/multiplying_and_dividing_negative_numbers 2026-03-05T15:50:38.258710261Z Multiplying negative numbers Practice multiplying single-digit integers. Jason Persampieri exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/e/integers-3-d 2024-05-01T13:20:24.831874259Z Multiplication of integers Multiplication of integers, properties ashish exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/e/signs-of-expressions-after-multiplication 2026-02-25T07:20:34.029274687Z Signs of expressions after multiplication In this exercise students learn about the signs of the expressions when two numbers are multiplied. Devashish Phadnis exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/x6b17ba59:multiply-with-negatives/a/multiplying-negative-numbers 2023-07-25T21:57:42.946009538Z Multiplying a positive and a negative number Discover what it means to multiply by negative numbers by using repeated addition and using the distributive property. article https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/x6b17ba59:multiply-with-negatives/a/multiplying-two-negative-numbers 2023-07-25T21:57:42.946009538Z Multiplying two negative numbers If 3(-8) can be 3 equal groups of -8, what does -3(-8) mean? What does it mean to multiply any two negative numbers? Let's use the distributive property and other properties of multiplication to find out. article https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/patterns-in-integer-multiplication 2026-01-13T05:46:23.044828344Z Patterns in Integer Multiplication In this video, we discussed three key patterns related to multiplicand and multipliers of integer multiplication. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Patterns in Integer Multiplication In this video, we discussed three key patterns related to multiplicand and multipliers of integer multiplication. https://cdn.kastatic.org/ka-youtube-converted/YvuxzLrg_xA.mp4/YvuxzLrg_xA.mp4 228 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/properties-of-integer-multiplication 2026-01-13T05:46:23.044828344Z Properties of Integer Multiplication In this video, we discussed important properties of Integer Multiplication such as Commutativity, Multiplicative identity, multiplication with (-1), Associativity and Distributive property of integer multiplication. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Properties of Integer Multiplication In this video, we discussed important properties of Integer Multiplication such as Commutativity, Multiplicative identity, multiplication with (-1), Associativity and Distributive property of integer multiplication. https://cdn.kastatic.org/ka-youtube-converted/sPXt0cNETPo.mp4/sPXt0cNETPo.mp4 435 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:multiplication-of-integers/v/a-magic-grid-of-numbers 2026-01-13T05:46:23.044828344Z A Magic Grid of Numbers In this video, we play a game of grid which is called a magic grid and explain the magic that happens in the background. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw A Magic Grid of Numbers In this video, we play a game of grid which is called a magic grid and explain the magic that happens in the background. https://cdn.kastatic.org/ka-youtube-converted/l2OD6bf74d8.mp4/l2OD6bf74d8.mp4 247 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:division-of-integers/v/dividing-positive-and-negative-numbers-indian-accent 2025-06-03T03:42:04.110515269Z Dividing positive and negative numbers Discover the basics of dividing with negative numbers. Skyloom (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Dividing positive and negative numbers Discover the basics of dividing with negative numbers. https://cdn.kastatic.org/ka-youtube-converted/WP690DTdL_4.mp4/WP690DTdL_4.mp4 272 Operation with Integers https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:division-of-integers/e/sign-of-expression-after-division 2025-06-11T13:22:56.260762255Z Sign of expression after division In this exercise students learn about sign of expressions after two integers are divided Devashish Phadnis exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:division-of-integers/e/integers-3-e 2024-01-03T14:27:06.234883329Z Division of integers Division of integers, properties ashish exercise https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-negatives/e/dividing-negative-numbers 2025-02-10T05:04:39.155459793Z Dividing negative numbers Practice dividing integers (single-digit divisors and quotients). Lindsay exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:division-of-integers/e/multiplying-dividing-integers-word-problems 2024-06-14T18:47:09.706463896Z Multiplying and dividing integers word problems Learners apply their understanding of integer interpretation and multiplication and division to real-world problems. Lafeesah Waalee exercise https://www.khanacademy.org/math/cc-third-grade-math/imp-multiplication-and-division/associative-property-of-multiplication/e/associative-property-of-multiplication- 2025-02-04T09:38:17.081068692Z Associative property of multiplication Practice changing the grouping of factors in multiplication problems and see how it affects the product. Priya exercise https://www.khanacademy.org/math/class-7-ncf/x063f95a40c290960:operation-with-integers/x063f95a40c290960:expressions-using-integers/e/distributivity-of-multiplication-over-addition-for-integers 2025-02-10T09:17:49.615690606Z Distributive property of integers Distributivity of multiplication over addition and subtraction for integers anmol exercise