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QuestionBài 1. Tính các biểu thức sau: a) 2+342+\frac{3}{4} b) 13+32−74\frac{1}{3}+\frac{3}{2}-\frac{7}{4} c) 56+58−14\frac{5}{6}+\frac{5}{8}-\frac{1}{4} d) 512+38×49\frac{5}{12}+\frac{3}{8} \times \frac{4}{9} e) 45−15×72\frac{4}{5}-\frac{1}{5} \times \frac{7}{2} f) 169−415:25\frac{16}{9}-\frac{4}{15}: \frac{2}{5}

Studdy Solution

STEP 1

Assumptions1. We are performing basic arithmetic operations on fractions. . The operations need to be performed in the order of BODMAS (Bracket, Orders, Division and Multiplication, Addition and Subtraction).

STEP 2

Let's solve part a) 2+42+\frac{}{4}2+42+\frac{}{4}

STEP 3

Convert the integer2 into a fraction with denominator.
8+3\frac{8}{}+\frac{3}{}

STEP 4

Add the two fractions.
8+34=114\frac{8+3}{4} = \frac{11}{4}

STEP 5

Now, let's solve part b) 13+32−74\frac{1}{3}+\frac{3}{2}-\frac{7}{4}13+32−74\frac{1}{3}+\frac{3}{2}-\frac{7}{4}

STEP 6

Find a common denominator for the fractions, which is12.
412+1812−2112\frac{4}{12}+\frac{18}{12}-\frac{21}{12}

STEP 7

Perform the addition and subtraction.
4+18−2112=112\frac{4+18-21}{12} = \frac{1}{12}

STEP 8

Now, let's solve part c) 56+58−14\frac{5}{6}+\frac{5}{8}-\frac{1}{4}56+58−14\frac{5}{6}+\frac{5}{8}-\frac{1}{4}

STEP 9

Find a common denominator for the fractions, which is24.
2024+1524−624\frac{20}{24}+\frac{15}{24}-\frac{6}{24}

STEP 10

Perform the addition and subtraction.
20+15−624=2924\frac{20+15-6}{24} = \frac{29}{24}

STEP 11

Now, let's solve part d) 5+38×49\frac{5}{}+\frac{3}{8} \times \frac{4}{9}5+38×49\frac{5}{}+\frac{3}{8} \times \frac{4}{9}

STEP 12

First, perform the multiplication.
512+×48×9\frac{5}{12}+\frac{ \times4}{8 \times9}

STEP 13

implify the multiplication.
512+1272\frac{5}{12}+\frac{12}{72}

STEP 14

implify the fraction.
12+6\frac{}{12}+\frac{}{6}

STEP 15

Find a common denominator for the fractions, which is12.
512+212\frac{5}{12}+\frac{2}{12}

STEP 16

Perform the addition.
5+212=12\frac{5+2}{12} = \frac{}{12}

STEP 17

Now, let's solve part e) 45−5×72\frac{4}{5}-\frac{}{5} \times \frac{7}{2}45−5×72\frac{4}{5}-\frac{}{5} \times \frac{7}{2}

STEP 18

First, perform the multiplication.
45−×75×2\frac{4}{5}-\frac{ \times7}{5 \times2}

STEP 19

implify the multiplication.
45−710\frac{4}{5}-\frac{7}{10}

STEP 20

Find a common denominator for the fractions, which is10.
810−710\frac{8}{10}-\frac{7}{10}

STEP 21

Perform the subtraction.
8−710=110\frac{8-7}{10} = \frac{1}{10}

STEP 22

Now, let's solve part f) 169−415:5\frac{16}{9}-\frac{4}{15}: \frac{}{5}169−415:5\frac{16}{9}-\frac{4}{15}: \frac{}{5}

STEP 23

First, perform the division.
169−15×5\frac{16}{9}-\frac{}{15} \times \frac{5}{}

STEP 24

implify the multiplication.
169−2030\frac{16}{9}-\frac{20}{30}

STEP 25

implify the fraction.
169−3\frac{16}{9}-\frac{}{3}

STEP 26

Find a common denominator for the fractions, which is9.
169−69\frac{16}{9}-\frac{6}{9}

STEP 27

Perform the subtraction.
16−69=109\frac{16-6}{9} = \frac{10}{9}So, the solutions area) 114\frac{11}{4} b) 112\frac{1}{12} c) 2924\frac{29}{24} d) 712\frac{7}{12} e) 110\frac{1}{10} f) 109\frac{10}{9}

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