Question

`-(21)/(5) / (7)/(8)`

Answer 1

-24/5 or -4.8

Explanation:

You want the quotient from dividing -21/5 by 7/8.

Division

Division by a number is the same as multiplication by its multiplicative inverse. The multiplicative inverse of a fraction is formed by swapping the numerator and denominator.

Application

`-(21)/(5)/(7)/(8)=-(21)/(5)*(8)/(7)\qquad\text{multiplication by the inverse}\\\\=-(21\cdot8)/(5\cdot7)=-(7\cdot3\cdot8)/(7\cdot5)=-(3\cdot8)/(5)\qquad\text{factors of 7 cancel}\\\\=\boxed{-(24)/(5)}`

Common denominator

The ratio of fractions with the same denominator is the ratio of their numerators.

`-(21)/(5)/(7)/(8)=-(168)/(40)/(35)/(40)=-(168)/(35)\\\\=-(7\cdot24)/(7\cdot5)=\boxed{-(24)/(5)}`

Common numerator

The ratio of fractions with the same numerator is the inverse of the ratio of their denominators.

`-(21)/(5)/(7)/(8)=-(21)/(5)/(21)/(24)=\boxed{-(24)/(5)}`

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Additional comment

Many calculators and spreadsheets can work directly with fractions.

Answer 2

We can solve this with the Skip, Flip, Multiply method:

1. Skip

We can keep the fraction -21/5.

2. Flip

We now need to flip the fraction 7/8, which turns into 8/7.

3. Multiply

We can now multiply these numbers.

-21/5 • 8/7 = -168/35

This reduces to -4 4/5, or -4.8.

Answer Recap: -21/5 / 7/8 = -4.8 OR -4 4/5