Question

Уровень 5-го класса 1) 8 1/8 + 1 2/3 - 3 1/4 = 2) 5 2/3 + 2 2/3 - 1 1/5 = 3) 12 7/15 - 9 3/7 + 5 11/12 =

Answer 1

1) 6 13/24
2) 6 2/24
3) 8 221/252

Answer 2

1. To add or subtract fractions, we need to have a common denominator. Let's first convert all the mixed numbers into improper fractions.

8 1/8 = (8 x 8 + 1)/8 = 65/8 1 2/3 = (1 x 3 + 2)/3 = 5/3 3 1/4 = (3 x 4 + 1)/4 = 13/4

Now, let's find a common denominator. The smallest number that all the denominators (8, 3, and 4) divide into is 24.

65/8 can be rewritten as 195/24 by multiplying the numerator and denominator by 3. 5/3 can be rewritten as 40/24 by multiplying the numerator and denominator by 8. 13/4 can be rewritten as 78/24 by multiplying the numerator and denominator by 6.

Now we can add and subtract the fractions:

195/24 + 40/24 - 78/24 = 157/24

We can convert this improper fraction back into a mixed number:

157 ÷ 24 = 6 with a remainder of 13 So the answer is 6 13/24.

2. Let's again convert all the mixed numbers into improper fractions.

5 2/3 = (5 x 3 + 2)/3 = 17/3 2 2/3 = (2 x 3 + 2)/3 = 8/3 1 1/5 = (1 x 5 + 1)/5 = 6/5

Now we can find a common denominator. The smallest number that all the denominators (3 and 5) divide into is 15.

17/3 can be rewritten as 85/15 by multiplying the numerator and denominator by 5. 8/3 can be rewritten as 40/15 by multiplying the numerator and denominator by 5. 6/5 can be left as is since it already has a denominator of 5.

Now we can add and subtract the fractions:

85/15 + 40/15 - 6/5 = 119/15 - 6/5

To subtract these fractions, we need a common denominator. The smallest number that both 15 and 5 divide into is 15, so we can rewrite 6/5 as 18/15.

119/15 - 18/15 = 101/15

We can simplify this fraction by finding a common factor of the numerator and denominator. Both 101 and 15 are prime, so the fraction is already in its simplest form.

So the answer is 6 5/15 or 6 1/3.

3. Let's again convert all the mixed numbers into improper fractions.

12 7/15 = (12 x 15 + 7)/15 = 187/15 9 3/7 = (9 x 7 + 3)/7 = 66/7 5 11/12 = (5 x 12 + 11)/12 = 71/12

Now we can find a common denominator. The smallest number that all the denominators (15, 7, and 12) divide into is 2520.

187/15 can be rewritten as 187 x 168/2520 by multiplying the numerator and denominator by 168. 66/7 can be rewritten as 66 x 360/2520 by multiplying the numerator and denominator by 360. 71/12 can be rewritten as 71 x 210/2520 by multiplying the numerator and denominator by 210.

Now we can add and subtract the fractions:

187 x