Question

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 =

Answer 1

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