How much should be added to each term of 4:7 so that it becomes 2:3

Let's denote the number that should be added to each term of the ratio \( 4:7 \) by \( x \). The goal is to transform the ratio \( 4:7 \) into \( 2:3 \) by adding \( x \) to both terms.

So, the new ratio will be:

\[
\frac{4 + x}{7 + x} = \frac{2}{3}
\]

Now, let's solve this equation step by step:

### Step 1: Cross-multiply
\[
3(4 + x) = 2(7 + x)
\]

### Step 2: Expand both sides
\[
12 + 3x = 14 + 2x
\]

### Step 3: Bring all terms involving \( x \) to one side and constants to the other side
\[
3x - 2x = 14 - 12
\]

### Step 4: Simplify
\[
x = 2
\]

Thus, \( x = 2 \).

### Final Answer:
We need to add 2 to both terms of the ratio \( 4:7 \) to get the ratio \( 2:3 \).

Would you like more details or have any questions?

Here are some related questions to practice:
1. What should be added to the ratio \( 5:9 \) to make it \( 3:4 \)?
2. What should be subtracted from the ratio \( 6:11 \) to make it \( 1:2 \)?
3. How do you solve ratios where both terms are multiplied by a variable?
4. What is the effect of adding the same value to both terms of a ratio?
5. How can we adjust a ratio by multiplying or dividing both terms?

**Tip:** When solving ratio problems, cross-multiplication is a powerful method to simplify and solve the equations easily.

Find out how to adjust the ratio 4:7 to become 2:3 by adding the same value to both terms. This step-by-step guide involves cross-multiplication and algebraic equations. Suitable for students in Grades 6-8.

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