Рациональные числа
Сложение и вычитание дробей
Ответы к стр. 100
Вычислите (503-514):
504. а) -1/3 + 2/3; б) — 1/4 + 3/4; в) 1/5 + -3/5;
г) 3/7 + -4/7; д) 8/13 + -12/13; е) 19/25 + -24/25.
а) -1/3 + 2/3 = -1+2/3 = 1/3;
б) — 1/4 + 3/4 = -1+3/4 = 2/4 = 1/2;
в) 1/5 + -3/5 = 1-3/5 = -2/5 = — 2/5;
г) 3/7 + -4/7 = 3-4/7 = -1/7 = — 1/7;
д) 8/13 + -12/13 = 8-12/13 = -4/13 = — 4/13;
е) 19/25 + -24/25 = 19-24/25 = -5/25 = — 1/5.
505. а) 1/2 + -1/2; б) -5/6 + 5/6; в) -2/3 + 2/3.
а) 1/2 + -1/2 = 1-1/2 = 0/2 = 0;
б) -5/6 + 5/6 = -5+5/6 = 0/6 =0;
в) -2/3 + 2/3 = -2+2/3 = 0/3 = 0.
506. а) 1/3 — 2/3; б) 1/4 — 3/4; в) 2/7 — 5/7;
г) 7/12 — 11/12; д) -8/11 — 3/11; е) — 5/17 — 10/17.
а) 1/3 — 2/3 = 1-2/3= -1/3 = — 1/3;
б) 1/4 — 3/4 = 1-3/4 = -2/4 = — 1/2;
в) 2/7 — 5/7 = 2-5/7 = -3/7 = — 3/7;
г) 7/12 — 11/12 = 7-11/12 = -4/12 = — 1/3;
д) -8/11 — 3/11 = -8-3/11 = -11/11 = -1;
е) — 5/17 — 10/17 = -5-10/17 = -15/17 = — 15/17.
507. а) -2/7 — -5/7; б) -4/9 — -8/9; в)- 1/10 — -7/10;
г) — 12/19 — 7/19; д) -4/5 — -3/5; е) — 1/24 — 11/24.
а) -2/7 — -5/7 = -2-(-5)/7 = -2+5/7 = 3/7;
б) -4/9 — -8/9 = -4-(-8)/9 = -4+8/9 = 4/9;
в) — 1/10 — -7/10 = -1-(-7)/10 = -1+7/10 = 6/10 = 3/5;
г) — 12/19 — 7/19 = -12-7/19 = -19/19 = -1;
д) -4/5 — -3/5 = -4-(-3)/5 = -4+3/5 = -1/5 = — 1/5;
е) — 1/24 — 11/24 = -1-11/24 = -12/24 = — 1/2.
508. а) -1/2 + -1/4; б) -1/3 + 1/6; в) — 1/2 + 1/6; г) 1/8 + -1/4; д) 3/10 + -7/100.
а) -1/2 + -1/4 = -2/4 + -1/4 = -2-1/4 = -3/4 = — 3/4;
б) -1/3 + 1/6 = -2/6 + 1/6 = -2+1/6 = -1/6 = — 1/6;
в) — 1/2 + 1/6 = -3/6 + 1/6 = -3+1/6 = -2/6 = — 1/3;
г) 1/8 + -1/4 = 1/8 + -2/8 = 1-2/8 = -1/8 = — 1/8;
д) 3/10 + -7/100 = 30/100 + -7/100 = 30-7/100 = 23/100.
509. а) — 3/5 — 9/10; б) — 15/24 — 3/8; в) -2/3 — 5/6;
г) — 7/6 — 5/24; д) 2/5 — 13/50; е) — 50/160 — 9/16.
а) — 3/5 — 9/10 = -6/10 — 9/10 = -6-9/10 = -15/10 = — 3/2 = -1 1/2;
б) — 15/24 — 3/8 = -15/24 — 9/24 = -15-9/24 = -24/24 = -1;
в) -2/3 — 5/6 = -4/6 — 5/6 = -4-5/6 = -9/6 = — 3/2 = -1 1/2;
г) — 7/6 — 5/24 = -28/24 — 5/24 = -28-5/24 = -33/24 = — 11/8 = -1 3/8;
д) 2/5 — 13/50 = 20/50 — 13/50 = 20-13/50 = 7/50;
е) — 50/160 — 9/16 = -5/16 — 9/16 = -5-9/16 = -14/16 = — 7/8.
510. а) — 1/6 + 1/9; б) 3/10 — 2/15; в) — 2/10 — 6/15;
г) 3/8 — 2/9; д) — 5/12 + 4/15; е) 2/16 — -3/39.
а) — 1/6 + 1/9 = -3/18 + 2/18 = -3+2/18 = -1/18 = — 1/18;
б) 3/10 — 2/15 = 9/30 — 4/30 = 9-4/30 = 5/30 = 1/6;
в) — 2/10 — 6/15 = -6/30 — 12/30 = -6-12/30 = -18/30 = — 3/5;
г) 3/8 — 2/9 = 27/72 — 16/72 = 27-16/72 = 11/72;
д) — 5/12 + 4/15 = -25/60 + 16/60 = -25+16/60 = -9/60 = — 3/20;
е) 2/16 — -3/39 = 78/624 — -48/624 = 78-(-48)/624 = 78+48/624 = 126/624 = 21/104.
511. а) 5/8 + (- 9/8); б) — 3/13 + (- 8/13); в) — 2/5 + 4/5;
г) 3/8 + (- 3/4); д) — 7/15 + (- 2/3); е) — 7/8 — 15/16;
ж) 1/3 + (- 1/2); з) — 1/4 + 1/3; и) — 2/21 + 3/14.
а) 5/8 + (- 9/8) = 5/8 — 9/8 = 5-9/8 = -4/8 = — 1/2;
б) — 3/13 + (- 8/13) = -3/13 — 8/13 = -3-8/13 = -11/13 = — 11/13;
в) — 2/5 + 4/5 = -2/5 + 4/5 = -2+4/5 = 2/5;
г) 3/8 + (- 3/4) = 3/8 — 3/4 = 3/8 — 6/8 = 3-6/8 = -3/8 = — 3/8;
д) — 7/15 + (- 2/3) = -7/15 — 2/3 = -7/15 — 10/15 = -7-10/15 = -17/15 = -1 2/15;
е) — 7/8 — 15/16 = -14/16 — 15/16 = -14-15/16 = -29/16 = -1 13/16;
ж) 1/3 + (- 1/2) = 1/3 — 1/2 = 2/6 — 3/2 = 2-3/6 = -1/6 = — 1/6;
з) — 1/4 + 1/3 = -3/12 + 4/12 = -3+4/12 = 1/12;
и) — 2/21 + 3/14 = -4/42 + 9/42 = -4+9/42 = 5/42.
512. а) — 9/180 — 7/120; б) — 4/210 + 5/140; в) -7/480 + 8/180.
а) — 9/180 — 7/120 = -18/360 — 21/360 = -18-21/360 = -39/360 = — 13/120;
б) — 4/210 + 5/140 = -8/420 + 15/420 = -8+15/420 = 7/420 = 1/60;
в) -7/480 + 8/180 = -21/1440 + 64/1440 = -21+64/1440 = 43/1440.
513. а) — 7/15 + 2/15 — 1/5; б) — 1/6 — 5/12 — 7/24; в) — 3/13 — 5/13 + 3/26;
г) 9/28 — 4/7 — 1/4; д) 10/27 — 5/18 + 8/9; е) 2/5 + 1/6 + 1/15.
а) — 7/15 + 2/15 — 1/5 = -7/15 + 2/15 — 3/15 = -7+2-3/15 = -8/15 = — 8/15;
б) — 1/6 — 5/12 — 7/24 = -4/24 — 10/24 — 7/24 = -4-10-7/24 = -21/24 = — 7/8;
в) — 3/13 — 5/13 + 3/26 = -6/26 — 10/26 + 3/26 = -6-10+3/26 = -13/26 = — 1/2;
г) 9/28 — 4/7 — 1/4 = 9/28 — 16/28 — 7/28 = 9-16-7/28 = -14/28 = — 1/2;
д) 10/27 — 5/18 + 8/9 = 20/54 — 15/54 + 48/54 = 20-15+48/54 = 53/54;
е) 2/5 + 1/6 + 1/15 = 12/30 + 5/30 + 2/30 = 12+5+2/30 = 19/30.
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Ответы по математике. 6 класс. Учебник. Никольский С.М., Потапов М.К., Решетников Н.Н., Шевкин А.В.