Question

4 1/2×5 2/3-5 1/4; 11 1/3÷4/21+8 1/2;

Answer 1

Ответ:

1) 4 1/2×5 2/3-5 1/4 =

$4\frac{1}{2}*5\frac{2}{3}-5\frac{1}{4} =\frac{9}{2} *\frac{17}{3} -\frac{21}{4}=\frac{3}{2}*\frac{17}{1}-\frac{21}{4}=\frac{51}{2}-\frac{21}{4}=\frac{102-21}{4} =\frac{81}{4} =20\frac{1}{4}=20,25$

2) 11 1/3÷4/21+8 1/2 =

$11\frac{1}{3}:\frac{4}{21}+8\frac{1}{2}= \frac{34}{3}*\frac{21}{4} + \frac{17}{2} = \frac{34}{1} *\frac{7}{4} + \frac{17}{2} = 17 *\frac{7}{2}+ \frac{17}{2}=\frac{119}{2} + \frac{17}{2}= \frac{119+17}{2} \\\\= \frac{136}{2}=68$

Answer 2

Let's solve each of these arithmetic expressions step by step:

1. 4 1/2 × 5 2/3 - 5 1/4:

First, convert the mixed numbers to improper fractions. 4 1/2 = 9/2 5 2/3 = 17/3 5 1/4 = 21/4

Now, perform the calculations:

(9/2) × (17/3) - (21/4)

To multiply fractions, multiply the numerators and denominators separately:

(9/2) × (17/3) = (9 * 17) / (2 * 3) = 153/6

Now, subtract (21/4) from (153/6):

(153/6) - (21/4)

To subtract fractions, you need a common denominator, which is 12 in this case. So, let's convert both fractions to have a denominator of 12:

(153/6) = (153/6) * (2/2) = 306/12 (21/4) = (21/4) * (3/3) = 63/12

Now, subtract:

(306/12) - (63/12) = (306 - 63) / 12 = 243/12

Finally, simplify the fraction:

243/12 = 20 3/12

2. 11 1/3 ÷ (4/21) + 8 1/2:

First, convert the mixed numbers to improper fractions. 11 1/3 = 34/3 8 1/2 = 17/2

Now, perform the calculations:

(34/3) ÷ (4/21) + (17/2)

To divide by a fraction, multiply by its reciprocal:

(34/3) × (21/4) + (17/2)

Now, perform the multiplications:

(34 * 21) / (3 * 4) + (17/2) = 714/12 + 17/2

To add these fractions, find a common denominator, which is 12:

(714/12) + (17/2) = (714/12) + (102/12)

Now, add the fractions:

(714/12) + (102/12) = (714 + 102) / 12 = 816/12

Finally, simplify the fraction:

816/12 = 68

So, the result is 68.