What is the missing number that makes the fractions equivalent? 1 4/7=?/42
The Correct Answer and Explanation is:
To find the missing number that makes the fractions equivalent, we need to express 1 4/7 as a fraction with a denominator of 42.
Step-by-Step Solution:
- Convert 1 4/7 into an improper fraction: The mixed number 1 4/7 consists of the whole number 1 and the fraction 4/7. To convert it into an improper fraction, multiply the whole number 1 by the denominator 7 and then add the numerator of the fraction 4. 147=(1×7)+47=7+47=1171 \frac{4}{7} = \frac{(1 \times 7) + 4}{7} = \frac{7 + 4}{7} = \frac{11}{7}174=7(1×7)+4=77+4=711
- Set up the proportion: Now that we have the improper fraction 11/7, we want to find the equivalent fraction with a denominator of 42. We can write this as a proportion: 117=x42\frac{11}{7} = \frac{x}{42}711=42x Where x is the missing numerator we need to solve for.
- Cross multiply to solve for x: To solve for x, we cross-multiply the proportion: 11×42=7×x11 \times 42 = 7 \times x11×42=7×x Simplifying the multiplication: 462=7×462 = 7×462=7x
- Solve for x: Now, divide both sides of the equation by 7 to isolate x: x=4627=66x = \frac{462}{7} = 66x=7462=66
Conclusion:
The missing number is 66. Therefore, the fraction equivalent to 1 4/7 with a denominator of 42 is 66/42.
By following these steps, we can see that multiplying both the numerator and the denominator of the original fraction by 6 (since 42 ÷ 7 = 6) gives us the equivalent fraction 66/42. This confirms that the two fractions are indeed equal.
