Question

Simplify the following:

$\frac{0.0406 \times 5.84}{0.0146 \times 14.5 \times 1.4}$

• A. 0.6
• B. 0.4
• C. 0.8
• D. 1.2

Answer 1

Answer:

C. 0.8

The simplified value of the expression is 0.8 (or $\frac{4}{5}$).

Given expression:

$\frac{0.0406 \times 5.84}{0.0146 \times 14.5 \times 1.4}$

Step 1: Count and remove the decimal places

* Numerator: 4 places (0.0406) + 2 places (5.84) = 6 decimal places

* Denominator: 4 places (0.0146) + 1 place (14.5) + 1 place (1.4) = 6 decimal places

Since both sides have an equal number of decimal places, you can remove the decimals entirely:

$\frac{406 \times 584}{146 \times 145 \times 14}$

Step 2: Simplify by cancellation

* Divide $406$ by $14$:

$\frac{406}{14} = 29 \implies \frac{29 \times 584}{146 \times 145}$

* Simplify $29$ and $145$ (since $29 \times 5 = 145$):

$\frac{29}{145} = \frac{1}{5} \implies \frac{584}{146 \times 5}$

* Divide $584$ by $146$ (since $146 \times 4 = 584$):

$\frac{584}{146} = 4 \implies \frac{4}{5}$

Step 3: Convert the final fraction to a decimal

$\frac{4}{5} = 0.8$