Question

1)9-2/3+6 7/24-2 1/62)8 13/30 +13 4/5-5 5/6 +7/103)17 3/4 9 1/32 + 4 3/8 -5 3/164)21 4/15 +1 5/6-9 7/30+16 7/24​

Answer 1

Ответ:

Пошаговое объяснение:

Третье дорешай самостоятельно, там нет знака действия. Четвёртое сделала в двух вариантах.

Answer 2

1) To simplify the expression 9 - 2/3 + 6 + 7/24 - 2 + 1/6, we can follow the order of operations, which is often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, let's simplify the addition and subtraction of whole numbers: 9 + 6 - 2 = 13

Next, let's simplify the addition and subtraction of fractions: -2/3 + 7/24 + 1/6

To add fractions with different denominators, we need to find a common denominator. The common denominator for 3, 24, and 6 is 24. We can convert -2/3, 7/24, and 1/6 to fractions with a denominator of 24:

-2/3 = -16/24 7/24 = 7/24 1/6 = 4/24

Now, we can add the fractions: -16/24 + 7/24 + 4/24 = -5/24

So, the expression simplifies to: 13 + (-5/24)

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction: 13 = 13/1

Now, we can add the fractions: 13/1 + (-5/24)

To add fractions, we need a common denominator, which in this case is 24. We can convert 13/1 to a fraction with a denominator of 24:

13/1 = 312/24

Now, we can add the fractions: 312/24 + (-5/24) = 307/24

Therefore, the expression 9 - 2/3 + 6 + 7/24 - 2 + 1/6 simplifies to 307/24.

2) To simplify the expression 8 + 13/30 + 13 + 4/5 - 5 + 5/6 + 7/103, we can again follow the order of operations.

First, let's simplify the addition and subtraction of whole numbers: 8 + 13 + 5 - 5 = 21

Next, let's simplify the addition and subtraction of fractions: 13/30 + 4/5 + 5/6 + 7/103

To add fractions with different denominators, we need to find a common denominator. The common denominator for 30, 5, 6, and 103 is 3090. We can convert 13/30, 4/5, 5/6, and 7/103 to fractions with a denominator of 3090:

13/30 = 427/3090 4/5 = 793/3090 5/6 = 515/3090 7/103 = 210/3090

Now, we can add the fractions: 427/3090 + 793/3090 + 515/3090 + 210/3090

When adding fractions, we can simply add the numerators while keeping the denominator the same: (427 + 793 + 515 + 210)/3090 = 1945/3090

So, the expression simplifies to: 21 + 1945/3090

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction: 21 = 6510/3090

Now, we can add the fractions: 6510/3090 + 1945/3090 = 8455/3090

Therefore, the expression 8 + 13/30 + 13 + 4/5 - 5 + 5/6 + 7/103 simplifies to 8455/3090.

3) To simplify the expression 17 + 3/4 + 9 + 1/32 + 4 + 3/8 - 5 + 3/16, we can once again follow the order of operations.

First, let's simplify the addition and subtraction of whole numbers: 17 + 9 + 4 - 5 = 25

Next, let's simplify the addition and subtraction of fractions: 3/4 + 1/32 + 3/8 + 3/16

To add fractions with different denominators, we need to find a common denominator. The common denominator for 4, 32, 8, and 16 is 32. We can convert 3/4, 1/32, 3/8, and 3/16 to fractions with a denominator of 32:

3/4 = 24/32 1/32 = 1/32 3/8 = 12/32 3/16 = 6/32

Now, we can add the fractions: 24/32 + 1/32 + 12/32 + 6/32 = 43/32

So, the expression simplifies to: 25 + 43/32

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction: 25 = 800/32

Now, we can add the fractions: 800/32 + 43/32 = 843/32

Therefore, the expression 17 + 3/4 + 9 + 1/32 + 4 + 3/8 - 5 + 3/16 simplifies to 843/32.

4) To simplify the expression 21 + 4/15 + 1 + 5/6 - 9 + 7/30 + 16 + 7/24, we can once again follow the order of operations.

First, let's simplify the addition and subtraction of whole numbers: 21 + 1 - 9 + 16 = 29

Next, let's simplify the addition and subtraction of fractions: 4/15 + 5/6 + 7/30 + 7/24

To add fractions with different denominators, we need to find a common denominator. The common denominator for 15, 6, 30, and 24 is 360. We can convert 4/15, 5/6, 7/30, and 7/24 to fractions with a denominator of 360:

4/15 = 96/360 5/6 = 300/360 7/30 = 28/360 7/24 = 35/360

Now, we can add the fractions: 96/360 + 300/360 + 28/360 + 35/360 = 459/360

So, the expression simplifies to: 29 + 459/360

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction: 29 = 10440/360

Now, we can add the fractions: 10440/360 + 459/360 = 10999/360

Therefore, the expression 21 + 4/15 + 1 + 5/6 - 9 + 7/30 + 16 + 7/24 simplifies to 10999/360.