Question

4 2/3+1/4×(1 7/9-1/9)

Answer 1

Решение.

Вычислить.

$\bf \displaystyle 4\frac{2}{3}+\frac{1}{4}\cdot \Big(1\frac{7}{9}-\frac{1}{9}\Big)=\frac{14}{3}+\frac{1}{4}\cdot 1\frac{6}{9}=\frac{14}{3}+\frac{1}{4}\cdot 1\frac{2}{3}=\frac{14}{3}+\frac{1}{4}\cdot \frac{5}{3}=\\\\\\=\frac{14}{3}^{|4}+\frac{5}{12}^{|1}=\frac{14\cdot 4+5\cdot 1}{12}=\frac{61}{12}=5\frac{1}{12}$

Answer 2

Ответ:

$5\frac{1}{12}$

Объяснение:

$4\frac{2}{3}+\frac{1}{4} \cdot(1 \frac{7}{9}-\frac{1}{9})=4\frac{2}{3}+\frac{1}{4} \cdot1 \frac{6}{9}=4\frac{2}{3}+\frac{1}{4} \cdot\frac{15}{9}=4\frac{2}{3}+\frac{1 \cdot15}{4 \cdot9}=4\frac{2}{3}+\frac{15}{36}=4\frac{2\cdot12}{3\cdot12}+\frac{15}{36}=4\frac{24}{36}+\frac{15}{36}=4\frac{24+15}{36}=4\frac{39}{36}=5\frac{3}{36}=5\frac{1}{12}$

Answer 3

To solve the expression 4 2/3 + 1/4 × (1 7/9 - 1/9), we need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Let's break down the expression step by step:

1. Start with the parentheses: Inside the parentheses, we have 1 7/9 - 1/9. To subtract fractions, the denominators must be the same. We can find a common denominator of 9, so the expression becomes: 1 7/9 - 1/9 = 16/9 - 1/9 = 15/9

2. Next, we perform the multiplication: 1/4 × (15/9) To multiply fractions, we multiply the numerators and the denominators separately: (1 × 15) / (4 × 9) = 15/36 This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 3: (15 ÷ 3) / (36 ÷ 3) = 5/12

3. Finally, we perform the addition: 4 2/3 + 5/12 To add mixed numbers, we need to convert the mixed number to an improper fraction. We multiply the whole number by the denominator and add the numerator to get the new numerator. The denominator remains the same. 4 2/3 can be converted to (4 × 3 + 2) / 3 = 14/3

   Now we can add the fractions: 14/3 + 5/12 To add fractions, we need a common denominator. The least common multiple (LCM) of 3 and 12 is 12. We can convert both fractions to have a denominator of 12: (14/3) × (4/4) = 56/12 56/12 + 5/12 = 61/12

Therefore, the result of the expression 4 2/3 + 1/4 × (1 7/9 - 1/9) is 61/12.