15. $$ \frac{40 \mathrm{~kg}}{1 \mathrm{~m}}=\frac{x \mathrm{~g}}{1 \mathrm{~cm}} $$

Question

UpStudy AI · Accepted Answer

Given the equation

$$
\frac{40\,\mathrm{kg}}{1\,\mathrm{m}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}},
$$

we need to find $$ x $$.

---

**Step 1: Convert kilograms to grams**

Recall that

$$
1\,\text{kg} = 1000\,\text{g}.
$$

Thus,

$$
40\,\text{kg} = 40 \times 1000\,\text{g} = 40000\,\text{g}.
$$

---

**Step 2: Convert meters to centimeters**

Recall that

$$
1\,\text{m} = 100\,\text{cm}.
$$

Thus,

$$
1\,\text{m} = 100\,\text{cm}.
$$

---

**Step 3: Substitute the converted values into the equation**

Substituting, we have

$$
\frac{40000\,\mathrm{g}}{100\,\mathrm{cm}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}}.
$$

---

**Step 4: Simplify the left side**

Dividing $$ 40000\,\text{g} $$ by $$ 100\,\text{cm} $$ gives

$$
\frac{40000}{100} = 400.
$$

Thus, the equation becomes

$$
\frac{400\,\mathrm{g}}{1\,\mathrm{cm}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}}.
$$

---

**Step 5: Solve for $$ x $$**

Since the denominators are the same, the numerators must be equal:

$$
x = 400.
$$

---

**Final Answer:**

$$
x = 400\,\mathrm{g}.
$$
$$ x = 400\,\mathrm{g} $$

15. \( \frac{40 \mathrm{~kg}}{1 \mathrm{~m}}=\frac{x \mathrm{~g}}{1 \mathrm{~cm}} \)