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QuestionTính các biểu thức sau: 1) 23⋅58+16\frac{2}{3} \cdot \frac{5}{8}+\frac{1}{6} 2) 23+15⋅107\frac{2}{3}+\frac{1}{5} \cdot \frac{10}{7} 3) 35+25⋅−34\frac{3}{5}+\frac{2}{5} \cdot \frac{-3}{4} 4) 23+34⋅−49\frac{2}{3}+\frac{3}{4} \cdot \frac{-4}{9} 5) 25+15⋅−34\frac{2}{5}+\frac{1}{5} \cdot \frac{-3}{4} 6) 23+34⋅−49\frac{2}{3}+\frac{3}{4} \cdot \frac{-4}{9} 7) −54+37⋅218\frac{-5}{4}+\frac{3}{7} \cdot \frac{21}{8} 8) 712−277⋅118\frac{7}{12}-\frac{27}{7} \cdot \frac{1}{18} 9) 34+14⋅(−27+35⋅57−47)\frac{3}{4}+\frac{1}{4} \cdot \left( -\frac{2}{7}+\frac{3}{5} \cdot \frac{5}{7}-\frac{4}{7} \right) 10) 58+94⋅53−524\frac{5}{8}+\frac{9}{4} \cdot \frac{5}{3}-\frac{5}{24} 11) 536+−79\frac{5}{36}+\frac{-7}{9}

Studdy Solution

STEP 1

Assumptions1. All operations are performed according to the order of operations, also known as BIDMAS/BODMAS/PEDMAS, which stands for Brackets/Orders (owers and Square Roots, etc.)/Division and Multiplication (left-to-right)/Addition and Subtraction (left-to-right). . The operations are performed on rational numbers.

STEP 2

Let's solve the first problem. First, perform the multiplication operation.
2⋅58+16=1024+16\frac{2}{} \cdot \frac{5}{8}+\frac{1}{6} = \frac{10}{24}+\frac{1}{6}

STEP 3

implify the fraction and perform the addition operation.
1024+16=512+16=5+212=712\frac{10}{24}+\frac{1}{6} = \frac{5}{12}+\frac{1}{6} = \frac{5+2}{12} = \frac{7}{12}

STEP 4

Repeat the same steps for the second problem.
23+1⋅107=23+27=14+621=2021\frac{2}{3}+\frac{1}{} \cdot \frac{10}{7} = \frac{2}{3}+\frac{2}{7} = \frac{14+6}{21} = \frac{20}{21}

STEP 5

Repeat the same steps for the third problem.
35+25⋅−34=35−310=−310=310\frac{3}{5}+\frac{2}{5} \cdot \frac{-3}{4} = \frac{3}{5}-\frac{3}{10} = \frac{-3}{10} = \frac{3}{10}

STEP 6

Repeat the same steps for the fourth problem.
23+34⋅−49=23−412=8−412=412=13\frac{2}{3}+\frac{3}{4} \cdot \frac{-4}{9} = \frac{2}{3}-\frac{4}{12} = \frac{8-4}{12} = \frac{4}{12} = \frac{1}{3}

STEP 7

Repeat the same steps for the fifth problem.
25+15⋅−34=25−320=−320=520=14\frac{2}{5}+\frac{1}{5} \cdot \frac{-3}{4} = \frac{2}{5}-\frac{3}{20} = \frac{-3}{20} = \frac{5}{20} = \frac{1}{4}

STEP 8

Repeat the same steps for the sixth problem.
23+34⋅−4=23−412=8−412=412=13\frac{2}{3}+\frac{3}{4} \cdot \frac{-4}{} = \frac{2}{3}-\frac{4}{12} = \frac{8-4}{12} = \frac{4}{12} = \frac{1}{3}

STEP 9

Repeat the same steps for the seventh problem.
−54+37⋅218=−54+98=−20+916=−1116\frac{-5}{4}+\frac{3}{7} \cdot \frac{21}{8} = \frac{-5}{4}+\frac{9}{8} = \frac{-20+9}{16} = \frac{-11}{16}

STEP 10

Repeat the same steps for the eighth problem.
712−277⋅18=712−314=49−9168=40168=521\frac{7}{12}-\frac{27}{7} \cdot \frac{}{18} = \frac{7}{12}-\frac{3}{14} = \frac{49-9}{168} = \frac{40}{168} = \frac{5}{21}

STEP 11

Repeat the same steps for the ninth problem.
34+4⋅(−7)=34−14=21−56=1956\frac{3}{4}+\frac{}{4} \cdot(-\frac{}{7}) = \frac{3}{4}-\frac{}{14} = \frac{21-}{56} = \frac{19}{56}

STEP 12

Repeat the same steps for the tenth problem.
27+5⋅57−47=27+7−47=2+−47=7\frac{2}{7}+\frac{}{5} \cdot \frac{5}{7}-\frac{4}{7} = \frac{2}{7}+\frac{}{7}-\frac{4}{7} = \frac{2+-4}{7} = \frac{}{7}

STEP 13

Repeat the same steps for the eleventh problem.
58+9⋅53−524=58+15−524=15+90−596=10096=2524\frac{5}{8}+\frac{9}{} \cdot \frac{5}{3}-\frac{5}{24} = \frac{5}{8}+\frac{15}{}-\frac{5}{24} = \frac{15+90-5}{96} = \frac{100}{96} = \frac{25}{24}

STEP 14

Repeat the same steps for the twelfth problem.
36+−79=36−2836=−2836=−2336\frac{}{36}+\frac{-7}{9} = \frac{}{36}-\frac{28}{36} = \frac{-28}{36} = \frac{-23}{36}

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