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Sagot :
To solve for [tex]\(c\)[/tex] given the proportion [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], follow these steps:
1. Start with the given proportion:
[tex]\[ \frac{a}{b} = \frac{c}{d} \][/tex]
2. Cross-multiply to eliminate the fractions. This involves multiplying the numerator of each fraction by the denominator of the other fraction:
[tex]\[ a \cdot d = b \cdot c \][/tex]
3. Solve for [tex]\(c\)[/tex] by isolating [tex]\(c\)[/tex] on one side of the equation. You can do this by dividing both sides of the equation by [tex]\(b\)[/tex]:
[tex]\[ c = \frac{a \cdot d}{b} \][/tex]
Let's demonstrate this using example values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(d\)[/tex]:
- Assume [tex]\(a = 6\)[/tex]
- Assume [tex]\(b = 4\)[/tex]
- Assume [tex]\(d = 3\)[/tex]
4. Substitute these values into the equation:
[tex]\[ c = \frac{6 \cdot 3}{4} \][/tex]
5. Perform the multiplication in the numerator:
[tex]\[ c = \frac{18}{4} \][/tex]
6. Divide the numerator by the denominator:
[tex]\[ c = 4.5 \][/tex]
Thus, the value of [tex]\(c\)[/tex] is [tex]\(4.5\)[/tex].
1. Start with the given proportion:
[tex]\[ \frac{a}{b} = \frac{c}{d} \][/tex]
2. Cross-multiply to eliminate the fractions. This involves multiplying the numerator of each fraction by the denominator of the other fraction:
[tex]\[ a \cdot d = b \cdot c \][/tex]
3. Solve for [tex]\(c\)[/tex] by isolating [tex]\(c\)[/tex] on one side of the equation. You can do this by dividing both sides of the equation by [tex]\(b\)[/tex]:
[tex]\[ c = \frac{a \cdot d}{b} \][/tex]
Let's demonstrate this using example values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(d\)[/tex]:
- Assume [tex]\(a = 6\)[/tex]
- Assume [tex]\(b = 4\)[/tex]
- Assume [tex]\(d = 3\)[/tex]
4. Substitute these values into the equation:
[tex]\[ c = \frac{6 \cdot 3}{4} \][/tex]
5. Perform the multiplication in the numerator:
[tex]\[ c = \frac{18}{4} \][/tex]
6. Divide the numerator by the denominator:
[tex]\[ c = 4.5 \][/tex]
Thus, the value of [tex]\(c\)[/tex] is [tex]\(4.5\)[/tex].
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