What is the missing number 7/8 = ?/48
The Correct Answer and Explanation is:
To find the missing number in the equation ( \frac{7}{8} = \frac{?}{48} ), we can use the concept of cross-multiplication. This method helps us find equivalent fractions by cross-multiplying the terms in the fractions.
Step-by-Step Solution:
- Set Up the Equation: We start with the equation:
[
\frac{7}{8} = \frac{x}{48}
]
where ( x ) is the missing number we need to find. - Cross-Multiply: Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction. Thus, we perform the following multiplication:
[
7 \times 48 = 8 \times x
] - Calculate the Left Side: Now calculate ( 7 \times 48 ):
[
7 \times 48 = 336
] - Set Up the Equation: We can now rewrite our equation as:
[
336 = 8x
] - Solve for ( x ): To isolate ( x ), divide both sides of the equation by 8:
[
x = \frac{336}{8}
] - Calculate ( x ): Now perform the division:
[
x = 42
]
Conclusion:
The missing number is ( 42 ). Thus, the equation ( \frac{7}{8} = \frac{42}{48} ) holds true.
Verification:
To confirm that ( \frac{42}{48} ) is equivalent to ( \frac{7}{8} ), we can simplify ( \frac{42}{48} ):
- Find the GCD: The greatest common divisor (GCD) of 42 and 48 is 6.
- Divide Numerator and Denominator by GCD:
[
\frac{42 \div 6}{48 \div 6} = \frac{7}{8}
]
This verifies that both fractions are indeed equivalent, confirming that our solution is correct. Understanding how to manipulate fractions through cross-multiplication and simplification is a crucial skill in mathematics, allowing us to solve various proportion problems effectively.