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Replace square in each of the following ...

Replace `square` in each of the following by the correct number :
(i) `1/3=square/21" (ii) "45/60=3/square`

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The correct Answer is:
To solve the given problems, we will replace the `square` with the correct number by using cross multiplication. Let's break it down step by step. ### Question (i): **Find `square` in the equation:** \[ \frac{1}{3} = \frac{\text{square}}{21} \] **Step 1:** Let the `square` be represented by \( x \). So, we rewrite the equation as: \[ \frac{1}{3} = \frac{x}{21} \] **Step 2:** Cross multiply to eliminate the fractions: \[ 1 \times 21 = 3 \times x \] This simplifies to: \[ 21 = 3x \] **Step 3:** To solve for \( x \), divide both sides by 3: \[ x = \frac{21}{3} \] **Step 4:** Calculate \( \frac{21}{3} \): \[ x = 7 \] So, the value of `square` in the first equation is **7**. ### Question (ii): **Find `square` in the equation:** \[ \frac{45}{60} = \frac{3}{\text{square}} \] **Step 1:** Let the `square` be represented by \( y \). So, we rewrite the equation as: \[ \frac{45}{60} = \frac{3}{y} \] **Step 2:** Cross multiply to eliminate the fractions: \[ 45y = 3 \times 60 \] This simplifies to: \[ 45y = 180 \] **Step 3:** To solve for \( y \), divide both sides by 45: \[ y = \frac{180}{45} \] **Step 4:** Calculate \( \frac{180}{45} \): \[ y = 4 \] So, the value of `square` in the second equation is **4**. ### Final Answers: - For the first question, `square` = 7 - For the second question, `square` = 4
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