how will we get to know by which number we have to multiply both numerator and denominator with and we have different denominator fractions

Answer: To find the number to multiply both numerator and denominator by: first find the LCM of the denominators, then divide this LCM by the original denominator of each fraction. The resulting quotient is the exact number to multiply with both the numerator and denominator.

Step-by-step solution

Step 1: Find the Common Target Denominator (LCM)

To compare, add, or subtract fractions with unlike denominators, we first need to make their denominators equal. We do this by finding the Least Common Multiple (LCM) of the given denominators, which serves as our common denominator. For example, if our fractions are $\frac{2}{3}$ and $\frac{1}{4}$ , the LCM of $3$ and $4$ is $12$ .

Step 2: Divide the LCM by Each Fraction's Denominator

To determine the exact number needed to multiply both the numerator and the denominator, we divide the LCM by the fraction's original denominator. For the fraction $\frac{2}{3}$ , dividing the LCM $12$ by the denominator $3$ gives $12 \div 3 = 4$ . For the fraction $\frac{1}{4}$ , dividing $12$ by the denominator $4$ gives $12 \div 4 = 3$ .

Step 3: Multiply Both Numerator and Denominator

Multiply both the top and bottom of each fraction by its corresponding multiplier found in the previous step. Multiplying both terms by the same non-zero number produces an equivalent fraction without changing its actual value. Now, both fractions have the identical denominator of $12$ , making them like fractions ready for comparison or addition.

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