Question

Выполните действия представив десятичные дроби в виде обыкновенных: а) 0,8 - 5/7 б) 0,5+ 1/3 в) 7/8-0.25 г) 0,4 + 0.67 д) 0.5 + 1/3 е) 1/3 - 0.25 ж) 0.125 + 5/12 з) 0.75 - 3/16+1/4

Answer 1

А) 0,8 - 5/7 = 8/10 - 5/7 = 8/10 * 7 - 5/7 * 10 = 56/70 - 50/70 = 6/70 : 2 = 3/35
б) 0,5 +1/3 = 5/10 + 1/3 = 5/10 * 3 + 1/3 * 10 = 15/30 + 10/30 = 25/30 : 5 = 5/6
в) 7/8 - 0,25 = 7/8 - 25/100 : 25 = 7/8 - 1/4 = 7/8 -1/4 * 2 = 7/8 - 2/8 = 5/8
г) 0,4 + 0,67 = 4/10 + 67/100 = 4/10 * 10 + 67/100 = 40/100 + 67/100 = 107/100 = 1 цел 7/100
д) 0,5 +1/3 = 5/10 + 1/3 = 5/10 * 3 + 1/3 * 10 = 15/30 + 10/30 = 25/30 : 5 = 5/6
е) 1/3 - 0,25 = 1/3 - 25/100 : 25 = 1/3 -  1/4 = 1/3 * 4 - 1/4 * 3 = 4/12 - 3/12 = 1/12
ж) 0,125 + 5/12 = 125/1000 + 5/12 = 125/1000 : 125 + 5/12 = 1/8 + 5/12 = 1/8 * 3 + 5/12 * 2 = 3/24 + 10/24 = 13/24
з) 3/16 + 1/4 = 3/16 + 1/4 * 4 = 3/16 + 4/16 = 7/16

Answer 2

a) 0,8 - 5/7

To convert a decimal fraction into a common fraction, we follow these steps:

1. Write down the decimal fraction as the numerator of the fraction. 2. Determine the denominator by considering the number of decimal places in the decimal fraction.

In this case, we have the decimal fraction 0.8. To convert it into a common fraction, we can follow these steps:

1. Write down the decimal fraction as the numerator: 0.8. 2. Determine the denominator by considering the number of decimal places, which is 1 in this case. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with one zero, which gives us 10.

Therefore, the common fraction equivalent of 0.8 is 8/10. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case. Dividing both 8 and 10 by 2, we get:

8/10 = 4/5.

So, the answer to a) is 4/5.

b) 0,5 + 1/3

Following the same steps as above:

1. Write down the decimal fraction as the numerator: 0.5. 2. Determine the denominator by considering the number of decimal places, which is 1 in this case. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with one zero, which gives us 10.

Therefore, the common fraction equivalent of 0.5 is 5/10. Simplifying this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 5 in this case. Dividing both 5 and 10 by 5, we get:

5/10 = 1/2.

So, the answer to b) is 1/2.

c) 7/8 - 0.25

To subtract fractions, we need to have a common denominator. In this case, we can convert the decimal fraction 0.25 into a fraction by following the steps mentioned above:

1. Write down the decimal fraction as the numerator: 0.25. 2. Determine the denominator by considering the number of decimal places, which is 2 in this case. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with two zeros, which gives us 100.

Therefore, the fraction equivalent of 0.25 is 25/100. Now, we can subtract the fractions:

7/8 - 25/100.

To subtract these fractions, we need to have a common denominator. The least common multiple (LCM) of 8 and 100 is 400. We can convert both fractions to have a denominator of 400:

(7/8) * (50/50) - (25/100) * (4/4)

Simplifying this expression:

350/400 - 100/400 = 250/400.

To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 50 in this case. Dividing both 250 and 400 by 50, we get:

250/400 = 5/8.

So, the answer to c) is 5/8.

d) 0.4 + 0.67

Following the same steps:

1. Write down the decimal fractions as the numerators: 0.4 and 0.67. 2. Determine the denominator by considering the number of decimal places, which is 1 for 0.4 and 2 for 0.67. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with one zero, which gives us 10 for 0.4, and 1 with two zeros, which gives us 100 for 0.67.

Therefore, the common fraction equivalents are 4/10 and 67/100. We can add these fractions:

4/10 + 67/100.

To add these fractions, we need to have a common denominator. The least common multiple (LCM) of 10 and 100 is 100. We can convert both fractions to have a denominator of 100:

(4/10) * (10/10) + (67/100) * (1/1)

Simplifying this expression:

40/100 + 67/100 = 107/100.

So, the answer to d) is 107/100.

e) 0.5 + 1/3

We have already solved this problem in part b). The answer is 1/2.

f) 1/3 - 0.25

To subtract a decimal fraction from a common fraction, we first need to convert the decimal fraction into a fraction. We have already done this in part c). The fraction equivalent of 0.25 is 25/100.

Now, we can subtract the fractions:

1/3 - 25/100.

To subtract these fractions, we need to have a common denominator. The least common multiple (LCM) of 3 and 100 is 300. We can convert both fractions to have a denominator of 300:

(1/3) * (100/100) - (25/100) * (3/3)

Simplifying this expression:

100/300 - 75/300 = 25/300.

To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 25 in this case. Dividing both 25 and 300 by 25, we get:

25/300 = 1/12.

So, the answer to e) is 1/12.

g) 0.125 + 5/12

Following the same steps:

1. Write down the decimal fraction as the numerator: 0.125. 2. Determine the denominator by considering the number of decimal places, which is 3 in this case. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with three zeros, which gives us 1000.

Therefore, the fraction equivalent of 0.125 is 125/1000. Now, we can add the fractions:

125/1000 + 5/12.

To add these fractions, we need to have a common denominator. The least common multiple (LCM) of 1000 and 12 is 6000. We can convert both fractions to have a denominator of 6000:

(125/1000) * (6/6) + (5/12) * (500/500)

Simplifying this expression:

750/6000 + 2500/6000 = 3250/6000.

To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 250 in this case. Dividing both 3250 and 6000 by 250, we get:

3250/6000 = 13/24.

So, the answer to g) is 13/24.

h) 0.75 - 3/16

Following the same steps:

1. Write down the decimal fraction as the numerator: 0.75. 2. Determine the denominator by considering the number of decimal places, which is 2 in this case. So, we put a 1 followed by as many zeros as the number of decimal places as the denominator: 1 with two zeros, which gives us 100.

Therefore, the fraction equivalent of 0.75 is 75/100. Now, we can subtract the fractions:

75/100 - 3/16.

To subtract these fractions, we need to have a common denominator. The least common multiple (LCM) of 100 and 16 is 800. We can convert both fractions to have a denominator of 800:

(75/100) * (8/8) - (3/16) * (50/50)

Simplifying this expression:

600/800 - 150/800 = 450/800.

To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 50 in this case. Dividing both 450 and 800 by 50, we get:

450/800 = 9/16.

So, the answer to h) is 9/16.

i) 1/4

The fraction 1/4 is already in the form of a common fraction, so no conversion is needed. The answer to i) is 1/4.