Question

1) 15/20+42/30-56/40 2) (1/2-1/3)+(1/3-1/4) 3) 17/51+19/57-13/39 4)2/3+1½-1/4 5)(3/6-1/4)+(1/2-1/3) 6) (1⅗-3/10)+(1/4-1/8)

Answer 1

Відповідь:

Давайте рассчитаем каждое из выражений:

1) \(492 + 51 - 98 + 51^2\)

\(= 492 + 51 - 98 + 2601\)

\(= 3046\)

2) \(19^2 + 38 - 11 + 11^2\)

\(= 361 + 38 - 11 + 121\)

\(= 509\)

3) \(183^2 + 183 - 93 + 93^2\)

\(= 33489 + 183 - 93 + 8649\)

\(= 42228\)

4) \(53^2 - 53 - 94 + 47^2\)

\(= 2809 - 53 - 94 + 2209\)

\(= 3871\)

5) \(153^2 - 47^2\)

\(= 23409 - 2209\)

\(= 21200\)

6) \(43.732 - 43.73 - 56.27 + 56.27^2\)

\(= -0.002 + 3160.5729\)

\(= 3160.5709\)

7) \(43.73^3 + 56.27^3\)

\(= 83313.978 + 89575.183\)

\(= 172889.161\)

Пояснення:

Answer 2

Sure, I can help you with these math expressions. Let's solve each one:

1. $\frac{15}{20} + \frac{42}{30} - \frac{56}{40}$

First, simplify each fraction: $\frac{3}{4} + \frac{7}{5} - \frac{7}{5}$

Next, add and subtract the fractions: $\frac{3}{4}$

2. $\left(\frac{1}{2} - \frac{1}{3}\right) + \left(\frac{1}{3} - \frac{1}{4}\right)$

Simplify each set of parentheses: $\frac{1}{6} + \frac{1}{12}$

Find a common denominator (12 in this case) and add the fractions: $\frac{2}{12} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}$

3. $\frac{17}{51} + \frac{19}{57} - \frac{13}{39}$

Simplify each fraction: $\frac{1}{3} + \frac{1}{3} - \frac{1}{3}$

Add and subtract the fractions: $\frac{1}{3}$

4. $\frac{2}{3} + \frac{3}{2} - \frac{1}{4}$

Convert the mixed number to an improper fraction: $\frac{4}{6} + \frac{9}{6} - \frac{1}{4}$

Add and subtract the fractions: $\frac{13}{6} - \frac{1}{4}$

Find a common denominator (12 in this case) and perform the operations: $\frac{26}{12} - \frac{3}{12} = \frac{23}{12}$

5. $\left(\frac{3}{6} - \frac{1}{4}\right) + \left(\frac{1}{2} - \frac{1}{3}\right)$

Simplify each set of parentheses: $\frac{1}{12} + \frac{1}{6}$

Find a common denominator (12 in this case) and add the fractions: $\frac{1}{12} + \frac{2}{12} = \frac{3}{12} = \frac{1}{4}$

6. $\left(1\frac{5}{5} - \frac{3}{10}\right) + \left(\frac{1}{4} - \frac{1}{8}\right)$