One-half divided by three-fourths = StartFraction 1 Over a EndFraction times StartFraction b Over c EndFraction = StartFraction d Over e EndFraction

Select the values that correctly complete the problem.

a =
b =
c =
d =
e =

1 answer

Let's solve the equation step-by-step:

  1. Calculate \( \frac{1}{2} \div \frac{3}{4} \):

    • Dividing by a fraction means multiplying by its reciprocal. So, \[ \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} \]
    • Now, multiply the fractions: \[ = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \quad \text{(after simplifying)} \]
  2. Write it in the required format: \[ \frac{1}{2} \div \frac{3}{4} = \frac{1}{a} \times \frac{b}{c} = \frac{d}{e} \]

    • From our computation, we have \( \frac{2}{3} \) as the result.
  3. Finding \( a, b, c, d, e \):

    • We can express \( \frac{2}{3} \) as \[ \frac{d}{e} = \frac{2}{3}. \] Therefore, we can set:
    • \( d = 2 \)
    • \( e = 3 \)
  4. Next, we need to find \( a, b, c \):

    • For \( \frac{1}{a} \times \frac{b}{c} = \frac{2}{3} \):
    • Choose \( a = 1 \) (as this will simplify our equation easily), then: \[ \frac{1}{a} = 1 \]
    • So we are left with: \[ 1 \times \frac{b}{c} = \frac{b}{c} = \frac{2}{3} \]
    • Hence, we can choose \( b = 2 \) and \( c = 3 \).

So we have:

  • \( a = 1 \)
  • \( b = 2 \)
  • \( c = 3 \)
  • \( d = 2 \)
  • \( e = 3 \)

The completed values are:

a = 1
b = 2
c = 3
d = 2
e = 3