Grade 7 / Relative numbers: operations 68 exercises (100% corrected)

a
-8-7-6-5-4-3-2-1O12345678 -8-7-6-5-4-3-2-1O12345678 ChingQuizz : 16 exercises available for Quizz assessment : 1. Introduction to addition E.11385 Consider the graduated line: 1 A robot A starts at the origin of the graduated line,: then moves 2 to the right, then moves 5 to the left. Place the robot A on the line. What is its x-coordinate? Hint: we will use the following simplified notation : a positive number corresponds to a movement in the positive direction on the number line, a negative number corresponds to a movement in the negative direction. 2 A robot B starts at the origin and performs two move-ments : ( − 4) , then ( − 3) Place point B on the number line. What is its x-coordinate? E.11386 Consider the graduated line: 1 Place point A whose x-coordinate is the result of calcu-lation (+2) + ( − 7) 2 Place the point B whose x-coordinate is the result of the calculation ( − 3) + ( − 5) 3 Place the point C whose x-coordinate is the result of the calculation ( − 5) + (+8) E.1876 A glider takes off at a certain altitude. The pilot can only know the altitude difference. Tell him the current altitude : Altitude de departure Dénivelé après un instant Altitude actuelle Ecriture mathématique +525 -200 +325 (+525)+(-200) +700 +120 +345 -250 +1200 +200 +2400 -1200 E.10060 A submarine undergoes an increase or decrease in depth, de-termine its current depth : Profondeur de départ Modification de la profondeur Profondeur actuelle Ecriture mathématique -12001.9cm -200 -1400 (-1200)+(-200) -7001.9cm +700 -8511.9cm +241 -14501.9cm -150 -24001.9cm +1250 E.10061 A temperature reading gives the current temperature and then the temperature change experienced. Give the new tem-perature : Température de departure Variation de la température Température actuelle Ecriture mathématique +3 -5 -2 (+3)+(-5) +5 +11 -4 -6 -7 +5 +12 -15 -5 +7 2. Addition of two terms https://chingmath.fr chapExoCorrec/11385 sacados/11385 -8-7-6-5-4-3-2-1O12345678 chapExoCorrec/11386 sacados/11386 -8-7-6-5-4-3-2-1O12345678 chapExoCorrec/1876 sacados/1876 chapExoCorrec/10060 sacados/10060 chapExoCorrec/10061 sacados/10061
DeuxnombrespositifsDeuxnombresnégatifsDeuxnombresdesignesdi∑érentsDistance à zéroSigneOnadditionnelesdis-tances à zéroOnadditionnelesdis-tances à zéroOnsoustraitlaplusgrande distance à zéro àla plus petitePositifNégatifSignedunombreayantla plus grande distance àzéro E.1294 Problem : To add two relative numbers : Calculate the following sums : a (+2) + (+5) b (+4) + ( − 8) c ( − 8) + ( − 7) d (+2) + ( − 5) e ( − 8) + (+3) f (+1) + ( − 1) E.6569 Calculate the following sums : a (+3) + (+8) b ( − 9) + ( − 5) c ( − 7) + (+6) d ( − 2) + (+5) e (+5) + ( − 2) f (+5) + ( − 12) E.10058 Calculate the following sums : a (+2) + ( − 3) b ( − 2) + ( − 3) c (+0) + ( − 7) d ( − 9) + (+4) e ( − 7) + (+10) f (+2) + (+5) E.6570 Calculate the following sums : a ( − 5) + (+6) b (+12) + (+7) c ( − 8) + (+15) d ( − 3) + ( − 8) e (+13) + ( − 5) f (+17) + ( − 20) E.1295 Calculate the following sums : a (+3) + ( − 7) b ( − 3) + (+5) c (+2) + ( − 7) d ( − 15) + ( − 6) E.6576 Calculate the following sums : a (+3) + (+5) b (+7) + ( − 2) c ( − 5) + (+9) d ( − 3) + ( − 8) e ( − 12) + (+7) f (+2) + ( − 5) E.6655 Complete the blanks correctly: a : : : : : : + ( − 5) = ( − 2) b (+7) + : : : : : : = ( − 3) c ( − 4) + : : : : : : = ( − 2) d : : : : : : + ( − 5) = (+2) e : : : : : : + (+4) = (+12) f (+9) + : : : : : : = (+2) E.6674 Complete the blanks correctly: a : : : : : : + ( − 3) = ( − 5) b (+7) + : : : : : : = (+2) c ( − 5) + : : : : : : = ( − 2) d : : : : : : + ( − 2) = (+3) e : : : : : : + (+12) = (+4) f (+9) + : : : : : : = ( − 2) E.10059 Calculate the following sums : a (+4.5) + (+6) b ( − 5.89) + ( − 4.11) c (+3.5) + ( − 1.8) d ( − 2.8) + (+1.1) E.1274 Calculate the following sums : a (+2.4) + (+5.6) b (+5.2) + ( − 5.2) c ( − 4.1) + (+1.5) d ( − 3.2) + (+12.5) E.10062 Calculate the following sums : a (+7.7) + ( − 11.4) b (+2.3) + (+7.6) c ( − 2.5) + ( − 1.5) d (+2.7) + (+1.5) 3. Additions E.1930 Note: when an expression consists only of additions, we can add the terms in any order. In this case, it’s best to put strictly positive terms together and strictly negative terms together. ( − 3) + ( − 4) + (+2) + ( − 8) + (+5) = (+2) + (+5) + ( − 3) + ( − 4) + ( − 8) = (+7) + ( − 15) = − 8 Leaving the steps of your calculation conduct, determine the value of the sums : a (+7) + ( − 5) + ( − 4) + ( − 1) + (+14) b ( − 3) + ( − 5) + (+7) + (+2) + ( − 10) E.1279 Leaving the steps of your calculation conduct, determine the value of the sums : a (+7) + ( − 4) + (+3) + ( − 5) + (+4) + ( − 10) b (+4) + ( − 7) + ( − 2) + (+2) + ( − 5) + ( − 7) + (+12) E.1297 By leaving the steps of your calcu-lation, determine the value of the sums : a (+1) + ( − 3) + (+4) + (+2) + ( − 3) + ( − 7) b (+7) + ( − 4) + (+3) + ( − 5) + (+4) + ( − 10) E.1306 By leaving the steps of your calcu-lation, determine the value of the sums : a (+2) + (+3) + ( − 4) + (+12) + ( − 17) + ( − 3) b (+2) + (+4) + ( − 4) + ( − 2) + (+9 ; 1) https://chingmath.fr chapExoCorrec/1294 sacados/1294 DeuxnombrespositifsDeuxnombresnégatifsDeuxnombresdesignesdi∑érentsDistance à zéroSigneOnadditionnelesdis-tances à zéroOnadditionnelesdis-tances à zéroOnsoustraitlaplusgrande distance à zéro àla plus petitePositifNégatifSignedunombreayantla plus grande distance àzéro chapExoCorrec/6569 sacados/6569 chapExoCorrec/10058 sacados/10058 chapExoCorrec/6570 sacados/6570 chapExoCorrec/1295 sacados/1295 chapExoCorrec/6576 sacados/6576 chapExoCorrec/6655 sacados/6655 chapExoCorrec/6674 sacados/6674 chapExoCorrec/10059 sacados/10059 chapExoCorrec/1274 sacados/1274 chapExoCorrec/10062 sacados/10062 chapExoCorrec/1930 sacados/1930 chapExoCorrec/1279 sacados/1279 chapExoCorrec/1297 sacados/1297 chapExoCorrec/1306 sacados/1306
−? −? −−(−?−5 −−(−? -6 -5−−−−−− -10-3-7+12+4+3Étape1 -10-3+12+4+3Étape2 E.11508 By leaving the steps of your calcu-lation, determine the value of the sums : a ( − 4) + ( − 7) + (+3) + (+1) + ( − 5) + (+12) b (+7) + ( − 4) + ( − 4) + (+9) + ( − 7) + (+4) E.10079 Leaving the steps of your calcula-tion conduct, determine the value of the sums : a (+3) + ( − 4.2) + ( − 3) + (+7) + ( − 5.8) b ( − 3.1) + ( − 4) + (+15.2) + (+13.1) + (+4) + ( − 5) E.1895 By leaving the steps of your calcu-lation process, determine the value of the sums : a ( − 2 ; 2) + (+5 ; 8) + (+4 ; 2) + ( − 7 ; 8) b ( − 232 ; 7) + (+0 ; 2) + (+32 ; 7) + ( − 25 ; 2) E.10063 Leaving the steps of your calcula-tion conduct, determine the value of the sums : a (+3.2) + ( − 7.7) + ( − 5.75) + ( − 3.2) + (+7.7) b ( − 7.2) + (+2.7) + ( − 2.1) + (+8.1) + ( − 5.7) E.1282 Leaving the steps of your calculation conduct, determine the value of the sums : a (+4) + (+1.5) + ( − 2.3) + (+0.5) + ( − 7.7) b (+4) + (+1.5) + ( − 2.3) + (+0.5) + ( − 7.7) 4. Subtraction: Introduction E.1892 1 Complete the following table line by line: Chercher la valeur manquante En déduire la value of the difference Trouver la valeur manquante ♠ + (+4) = (+9) . . . . . . . . . . . . . . . . . . . . (+9) − (+4) = (+9) + ♣ = (+5) ♠ + (+5) = (+1) . . . . . . . . . . . . . . . . . . . . (+1) − (+5) = (+1) + ♣ = ( − 4) ♠ + ( − 6) = ( − 5) . . . . . . . . . . . . . . . . . . . . ( − 5) − ( − 6) = ( − 5) + ♣ = (+1) ♠ + ( − 11) = (+4) . . . . . . . . . . . . . . . . . . . . (+4) − ( − 11) = (+4) + ♣ = (+15) 2 a What can be said about the following pairs of calcu-lations : (+9) − (+4) et (+9)+( − 4) ; (+1) − (+5) et (+1)+( − 5) ; ( − 5) − ( − 6) et ( − 5)+(+6) ; (+4) − ( − 11) et (+4)+(+11) . b Complete the following sentence : ˇSubtracting a relative number is equiva-lent to adding its . . . . . . . . . . . . ı E.11690 1 a Compléter chacun des tableaux ci-dessous : b Compléter les pointillés: ( − 6) − (+4)= ::: ; (+10) − (+4)= ::: 2 a Compléter le tableau : b Compléter les pointillés: ( − 5) − ( − 3)= ::: ; (+1) − ( − 3)= ::: E.11698 On considère une voiture en carton (on suppose qu’elle ne pèse rien) soumise à des ballons qui la soulèvent et de poids qui la rabaissent. Voici deux configurations : 1 Donner le poids de ces deux configurations. 2 a Expliquer pourquoi le calcul ( − 1) − ( − 7) représente le poids de l’étape 2. b Compléter : ( − 1) − ( − 7) = : : : https://chingmath.fr chapExoCorrec/11508 sacados/11508 chapExoCorrec/10079 sacados/10079 chapExoCorrec/1895 sacados/1895 chapExoCorrec/10063 sacados/10063 chapExoCorrec/1282 sacados/1282 chapExoCorrec/1892 sacados/1892 −? −? −−(−?−5 −−(−? chapExoCorrec/11690 sacados/11690 -6 -5−−−−−− chapExoCorrec/11698 sacados/11698 -10-3-7+12+4+3Étape1 -10-3+12+4+3Étape2
-3-5-6+1+7+4Étape1 -3-5-6+1+7Étape2 3;5−2;−2;−2;−2;−2;−2; 4;;;;;; E.11699 On considère une voiture en carton (on suppose qu’elle ne pèse rien) soumise à des ballons qui la soulève et de poids qui la rabaisse. Voici deux configurations : 1 Donner le poids de ces deux configurations. 2 a Expliquer pourquoi le calcul ( − 2) − (+4) représente le poids de l’étape 2. b Compléter : ( − 2) − (+4) = : : : E.11730 1 a Compléter chacun des tableaux ci-dessous : b Compléter les pointillés: (3 ; 5) − ( − 2 ; 5)= ::: ; ( − 4) − ( − 2 ; 5)= ::: 2 a Compléter le tableau : b Compléter les pointillés: (+4) − (+1 ; 2)= ::: ; (+0 ; 4) − (+1 ; 2)= ::: 5. Subtractions E.1893 Proposal: To subtract two relative numbers, add the first term to the opposite of the second term. Example: (+5) − ( − 7) = (+5) + (+7) = +12 Copy and complete the dotted lines to show your calculation process for performing the subtractions : a ( − 3) − (+2) = ( − 3) + : : : : : : = : : : b (+2) − ( − 7) = (+2) + : : : : : : = : : : c ( − 5) − ( − 9) = ( − 5) + : : : : : : = : : : d (+4) − (+7) = (+4) + : : : : : : = : : : E.1907 Following the steps in your calcula-tion, perform the subtractions : a (+2) − (+4) b ( − 9) − ( − 9) c ( − 7) − (+2) d (+1) − ( − 4) E.6675 Leaving the steps of your calculation conduct, perform the subtractions : a ( − 2) − (+2) b (+4) − ( − 4) c ( − 7) − ( − 3) d (+5) − (+12) E.10067 Leaving the steps of your calcula-tion conduct, perform the subtractions : a (+2) − (+4) b ( − 7) − (+5) c ( − 12) − ( − 5) d (+1) − (+5) E.10064 Leaving the steps of your calcula-tion conduct, perform the subtractions : a (+6) − ( − 1.5) b ( − 4.2) − (+2.2) c ( − 5.4) − ( − 3.2) d (+6.2) − ( − 4.7) 6. Addition and subtraction E.1304 Without showing the steps in your calculation, perform the following operations : a (+2) + ( − 5) b (+4) − ( − 8) c ( − 8) + ( − 7) d (+2) − (+5) E.10065 Leaving the steps of your calcula-tion conduct, perform the operations : a ( − 8.2) − (+1.8) b (+2.3) + ( − 7.7) c ( − 2.1) − ( − 3.7) d (+3.5) − ( − 7.8) E.1275 Without showing the steps in your calculation, perform the following operations : a (+2 ; 1) + ( − 5 ; 2) b (+4 ; 3) − (+5 ; 8) c ( − 14 ; 5) − (+3 ; 9) d ( − 3) + ( − 5 ; 2) E.1277 Without showing the steps in your calculation, perform the following operations : a (+3 ; 4) + ( − 5 ; 2) b (+4 ; 3) − (+3 ; 2) c ( − 14 ; 5) − (+4 ; 1) d ( − 3) + (+9 ; 8) https://chingmath.fr chapExoCorrec/11699 sacados/11699 -3-5-6+1+7+4Étape1 -3-5-6+1+7Étape2 chapExoCorrec/11730 sacados/11730 3;5−2;−2;−2;−2;−2;−2; 4;;;;;; chapExoCorrec/1893 sacados/1893 chapExoCorrec/1907 sacados/1907 chapExoCorrec/6675 sacados/6675 chapExoCorrec/10067 sacados/10067 chapExoCorrec/10064 sacados/10064 chapExoCorrec/1304 sacados/1304 chapExoCorrec/10065 sacados/10065 chapExoCorrec/1275 sacados/1275 chapExoCorrec/1277 sacados/1277
−5−3− 5(−3(−4(5−3−4(5(−3−7−700Simpli∏cationConduitedecalculCalculs E.1276 Without showing the steps in your calculation, perform the following operations : a (+2 ; 1) + ( − 5 ; 2) b (+4 ; 3) − (+5 ; 8) c ( − 14 ; 5) − (+3 ; 9) d ( − 3) + ( − 5 ; 2) E.1280 Complete the calculations below cor-rectly: a + ( − 3.2) = − 1.1 b ( − 5.5) + = +2.7 c − (+5.3) = +10.5 d − ( − 2.3) = +5 E.1296 Leaving the steps of your calculation conduct, perform the operations : a ( − 7) + ( − 2) + (+8) − ( − 2) − ( − 7) b ( − 4) + ( − 9) − (+5) − ( − 4) + (+8) E.1278 Leaving the steps of your calculation conduct, perform the operations : a ( − 2) − (+4) + (+8) − ( − 7) b (+5) − ( − 4) + ( − 4) − (+12) + ( − 7) E.10066 Leaving the steps of your calcula-tion process, perform the following operations : a (+4) − (+2)+(+7) − ( − 7)+(+1) − (+4) − ( − 2) − ( − 9)+( − 2) b ( − 5) − ( − 6) − (+12) + (+16) + ( − 2) E.10068 Leaving the steps of your calcula- tion conduct, perform the operations : b (+7.1) − ( − 0.5) + ( − 5.4) − (+7.2) b (+5) − ( − 8) + ( − 1) − ( − 4) − (+5) E.1270 A calculation program is given in the form of a diagram below : 1 Fill in the blanks in the diagram. 2 Using parentheses, translate this calculation program into an expression. E.10069 Leaving the steps of your calcula-tion conduct, perform the operations : a (+3) − (+12) − ( − 2) − (+3) b ( − 3) − (+5) − ( − 2) + ( − 4) − ( − 6) E.1305 Leaving the steps of your calculation conduct, perform the operations : a ( − 5) − ( − 6) − (+12) + (+16) + ( − 2) b (+3) − (+12) − ( − 2) − (+3) 7. Simplification of sums E.6676 Writing simplification : To make it easier to write relative number operations, we introduce the following rules. If an operation involves only addition : parentheses and addition signs are not written. if the operation begins with the positive sign, it is not written. Exemple: Simplify the expressions below, then perform these opera-tions, leaving a trace of your calculation conduct : a (+2) + (+4) + ( − 8) + (+2) + ( − 5) b ( − 4) + (+2) + ( − 11) + (+3) + ( − 1) + ( − 5) E.10075 Simplify the expressions below, then perform these operations, leaving a record of your com-putational conduct : a (+3) + (+5) + ( − 8) + ( − 2) + ( − 4) b ( − 9) + (+2) + ( − 3) + (+7) E.1299 Leaving the steps in your calculation pipeline, perform the following operations : a − 2 − 4 + 5 − 3 + 7 b 3 + 5 − 4 + 7 E.1307 Leaving the steps in your calculation pipeline, perform the following operations : a − 4 − 5 + 8 + 12 − 7 + 1 − 8 b − 4 + 7 − 2 − 5 + 4 + 2 − 7 E.10072 Leaving the steps in your calcula-tion pipeline, perform the following operations : a − 2 + 5 + 7 − 4 + 6 − 10 b 2 − 5 − 7 + 6 − 15 − 2 + 4 − 1 E.10074 Leaving the steps in your calcula-tion pipeline, perform the following operations : a − 3 + 5 − 4 − 6 + 10 − 5 + 12 b 5 − 12 − 3 + 4 + 5 − 2 + 14 https://chingmath.fr chapExoCorrec/1276 sacados/1276 chapExoCorrec/1280 sacados/1280 chapExoCorrec/1296 sacados/1296 chapExoCorrec/1278 sacados/1278 chapExoCorrec/10066 sacados/10066 chapExoCorrec/10068 sacados/10068 chapExoCorrec/1270 sacados/1270 −5−3− chapExoCorrec/10069 sacados/10069 chapExoCorrec/1305 sacados/1305 chapExoCorrec/6676 sacados/6676 5(−3(−4(5−3−4(5(−3−7−700Simpli∏cationConduitedecalculCalculs chapExoCorrec/10075 sacados/10075 chapExoCorrec/1299 sacados/1299 chapExoCorrec/1307 sacados/1307 chapExoCorrec/10072 sacados/10072 chapExoCorrec/10074 sacados/10074
E.10070 Leaving the steps in your calcula-tion pipeline, perform the following operations : a 7.3 − 5.1 + 1.2 − 4 − 5.5 + 1 b − 3.2 + 4.1 − 9.1 + 3.2 + 4.7 E.10073 Leaving the steps in your calcula-tion pipeline, perform the following operations : a − 2.1 + 5.6 − 7.8 b 6.4 − 3.5 − 4.1 E.6661 Leaving the steps in your calculation pipeline, perform the following operations : a 15.2 + 3.4 − 7.2 − 8.4 + 5.3 − 3 b 5.2 − 3.4 + 2.8 − 7.6 + 4 E.1284 A magic square is a square filled with numbers so that each column, each row and both diagonals have the same value. − 4.4 − 0.4 3 − 1 − 5 Reproduce in your notebook and complete the square oppo-site so that it becomes ˇmagicı. 8. Priority of operations and relative numbers E.1281 Leaving the steps in your calculation pipeline, perform the following operations : a 8 + 2 − 4 − ( − 2 − 5) + 4 b − 7 + 3 − (5 − 3) + 4 E.1302 Leaving the steps in your calculation pipeline, perform the following operations : a − 5 + ( − 2 + 5) b ( − 2 − 4) − (5 − 7) E.10078 Leaving the steps in your calcula-tion pipeline, perform the following operations : a +5 − 3 − ( − 4 − 7) b − 5 + 7 + (5 − 9) E.1285 Leaving the steps in your calculation pipeline, perform the following operations : A 3 − (5 + 4) − 2 b − 5 − (6 − 9) + (8 − 3) E.1308 Leaving the steps in your calculation pipeline, perform the following operations : a − 5 + 4 + 3 b − 3 + 5 + 4 − 2 − 5) c 7 − 3 − 4 + 7 − 12 + 2 E.1300 Leaving the steps in your calculation pipeline, perform the following operations : a 3 − 3 + ( − 5) b 3 − ( − 5) − (12 − 6) E.10077 Leaving the steps in your calcula-tion pipeline, perform the following operations : a − 5 − (4 − 3) − 4 b − 5 + 3 − 2 − 8 − 12 E.1301 Leaving the steps in your calculation pipeline, perform the following operations : a (3 − 5) + 2 − 2 × (5 − 3) − 5 b 5 − 7 + 3 − 7 − (9 − 7) E.10076 Leaving the steps in your calcula-tion pipeline, perform the following operations : a 3 − ( − 5 + 2) − 6 + 6 + (3 − 5) b − 3 + 5 + ( − 4 − 8) − (12 − 8) 9. And algebra E.1283 Reproduce the following table and complete it. a b c b − c a − ( b − c ) a − b a − b + c 12 7 15 − 3 5 − 7 https://chingmath.fr chapExoCorrec/10070 sacados/10070 chapExoCorrec/10073 sacados/10073 chapExoCorrec/6661 sacados/6661 chapExoCorrec/1284 sacados/1284 chapExoCorrec/1281 sacados/1281 chapExoCorrec/1302 sacados/1302 chapExoCorrec/10078 sacados/10078 chapExoCorrec/1285 sacados/1285 chapExoCorrec/1308 sacados/1308 chapExoCorrec/1300 sacados/1300 chapExoCorrec/10077 sacados/10077 chapExoCorrec/1301 sacados/1301 chapExoCorrec/10076 sacados/10076 chapExoCorrec/1283 sacados/1283