Question

51/25:(8/25+9/20)-64/35•5/4

Answer 1

$\frac{51}{25}$:($\frac{8}{25}$ + $\frac{9}{20}$) - $\frac{64}{35}$*$\frac{5}{4}$ = $\frac{4}{11}$

1) $\frac{8}{25}$+$\frac{9}{20}$ = $\frac{4*8}{4*25}$+$\frac{5*9}{5*20}$ = $\frac{32}{100}$+$\frac{45}{100}$ = $\frac{77}{100}$

2) $\frac{51}{25}$:$\frac{77}{100}$ = $\frac{51*100}{25*77}$ = $\frac{51*4}{1*77}$ = $\frac{204}{77}$

3) $\frac{64}{35}$*$\frac{5}{4}$ = $\frac{64*5}{35*4}$ = $\frac{16*1}{7*1}$ = $\frac{16}{7}$

4) $\frac{204}{77}$ - $\frac{16}{7}$ = $\frac{204}{77}$ - $\frac{11*16}{11*7}$ = $\frac{204}{77}$ - $\frac{176}{77}$ = $\frac{28}{77}$ = $\frac{4}{11}$

Answer 2

To solve the expression, let's break it down step by step:

Step 1: Simplify the division in the numerator and denominator separately.

8/25 + 9/20 = (8 * 20)/(25 * 20) + (9 * 25)/(20 * 25) = 160/500 + 225/500 = (160 + 225)/500 = 385/500

Step 2: Simplify the multiplication in the expression.

64/35 * 5/4 = (64 * 5)/(35 * 4) = 320/140 = (32 * 10)/(14 * 10) = 32/14

Step 3: Substitute the simplified values back into the expression.

51/25 : (385/500) - 32/14

Step 4: Convert the division to multiplication by taking the reciprocal of the divisor.

51/25 * (500/385) - 32/14

Step 5: Perform the multiplications.

(51 * 500)/(25 * 385) - 32/14

Step 6: Simplify the fractions.

(25500)/(9625) - 32/14

Step 7: Find a common denominator for the fractions.

(25500)/(9625) - (32 * 625)/(14 * 625)

Step 8: Perform the subtraction.

(25500 - 20000)/(9625)

Step 9: Simplify the fraction.

5500/9625

Step 10: Reduce the fraction, if possible.

110/193

Therefore, the simplified value of the expression 51/25:(8/25+9/20)-64/35•5/4 is 110/193.