Question

4 3\8:2 1\2 ; 2 9\28:1 1\4 ; -4 1\8+81\8 ; (1\2-41\12):35\36 ; 2 7\10:3\20

Answer 1

4  3/8:2  1/2=1 3/4
2 9/28:11/4=59/77
4 1/8+81/8=14 1/4
(1/2+41/12):35=47/420
2 7/10:3/20=18

Answer 2

It looks like you've provided a series of mathematical expressions, and I'll help you simplify them:

1. $4 \frac{3}{8} : 2 \frac{1}{2}$

To simplify this, convert the mixed numbers to improper fractions and then divide:

$(4 \cdot 8 + 3) : (2 \cdot 2 + 1) = (32 + 3) : (4 + 1) = 35 : 5 = 7$

2. $2 \frac{9}{28} : 1 \frac{1}{4}$

Convert the mixed numbers to improper fractions and then divide:

$(2 \cdot 28 + 9) : (1 \cdot 4 + 1) = (56 + 9) : (4 + 1) = 65 : 5 = 13$

3. $-4 \frac{1}{8} + 8 \frac{1}{8}$

To simplify this, convert the mixed numbers to improper fractions and then add:

$(-4 \cdot 8 - 1) + (8 \cdot 8 + 1) = (-32 - 1) + (64 + 1) = -33 + 65 = 32$

4. $\frac{1}{2} - \frac{41}{12} : \frac{35}{36}$

To simplify this, first divide the fractions on the right side and then subtract from $\frac{1}{2}$:

$\frac{1}{2} - \frac{41}{12} \div \frac{35}{36} = \frac{1}{2} - \left(\frac{41}{12} \cdot \frac{36}{35}\right) = \frac{1}{2} - \frac{41}{35} = \frac{18}{35}$

5. $2 \frac{7}{10} : \frac{3}{20}$

To simplify this, convert the mixed number to an improper fraction and then divide:

$(2 \cdot 10 + 7) : \frac{3}{20} = \frac{27}{10} \div \frac{3}{20}$

When you divide by a fraction, you multiply by its reciprocal:

$\frac{27}{10} \cdot \frac{20}{3} = \frac{27 \cdot 20}{10 \cdot 3} = \frac{540}{30} = 18$

So, the simplified results are:

1. $4 \frac{3}{8} : 2 \frac{1}{2} = 7$
2. $2 \frac{9}{28} : 1 \frac{1}{4} = 13$
3. $-4 \frac{1}{8} + 8 \frac{1}{8} = 32$
4. $\frac{1}{2} - \frac{41}{12} : \frac{35}{36} = \frac{18}{35}$