Question

1) 4 7/12 * (-1 3/11) - (-1 1/15) * (-45/64) 2) -81/88 * (-6 + (-1 13/15) * (-1 19/21))

Answer 1

Ответ:

Пошаговое объяснение:

1) 4 7/12 * (-1 3/11)=55/12*(-14/11)=-35/6=-5 5/6

(-1 1/15) * (-45/64)=-16/15*(-45/64)=3/4

-5 5/6-3/4=-5 10/12-9/12=-6 7/12

2) (-1 13/15) * (-1 19/21)=-28/15*(-40/21)=32/9=3 5/9

-6+3 5/9=-2 4/9

-81/88*(-2 4/9)=-81/88*(-22/9)=9/4=2 1/4

Answer 2

Let's solve the expressions step by step:

1. $4 \frac{7}{12} \times (-1 \frac{3}{11}) - (-1 \frac{1}{15}) \times (-\frac{45}{64})$

To begin, let's convert the mixed numbers into improper fractions:

$4 \frac{7}{12} = \frac{(4 \times 12) + 7}{12} = \frac{48 + 7}{12} = \frac{55}{12}$

$-1 \frac{3}{11} = \frac{-(1 \times 11) + 3}{11} = \frac{-11 + 3}{11} = \frac{-8}{11}$

$-1 \frac{1}{15} = \frac{-(1 \times 15) + 1}{15} = \frac{-15 + 1}{15} = \frac{-14}{15}$

Now we can rewrite the expression:

$\frac{55}{12} \times \frac{-8}{11} - \frac{-14}{15} \times \frac{-45}{64}$

To multiply fractions, we multiply the numerators and multiply the denominators:

$\frac{55 \times -8}{12 \times 11} - \frac{-14 \times -45}{15 \times 64}$

Simplifying further:

$\frac{-440}{132} - \frac{630}{960}$

We need to find a common denominator for the fractions:

The least common multiple of 132 and 960 is 2,640.

$\frac{-440 \times 20}{132 \times 20} - \frac{630 \times 4}{960 \times 4}$

Simplifying the numerators:

$\frac{-8,800}{2,640} - \frac{2,520}{2,640}$

Combining the fractions:

$\frac{-8,800 - 2,520}{2,640}$

Calculating the numerator:

$-11,320$

Final result:

$\frac{-11,320}{2,640}$

The fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 40:

$\frac{-283}{66}$

2. $-\frac{81}{88} \times \left(-6 + \left(-1 \frac{13}{15}\right) \times \left(-1 \frac{19}{21}\right)\right)$

Let's convert the mixed numbers into improper fractions:

$-1 \frac{13}{15} = \frac{-(1 \times 15) + 13}{15} = \frac{-15 + 13}{15} = \frac{-2}{15}$

$-1 \frac{19}{21} = \frac{-(1 \times 21) + 19}{21} = \frac{-21 + 19}{21} = \frac{-2}{21}$

Now we can rewrite the expression:

$-\frac{81}{88} \times (-6 + \left(-\frac{2}{15}\right) \times \left(-\frac{2}{21}\right))$