Question

Rewrite the fractions with their LCD.
\[\frac{11}{6x^2y^2}, \frac{4}{5xy^3}\]

Answer 1

Find the LCD of both fractions. First, factor each denominator completely, breaking its factors down into simple parts.\[6x^2y^2=2 \times 3 \times x^2 \times y^2\]\[5xy^3=5\times x \times y^3\] Next, list all the factors in each denominator. Then identify the greatest power of each factor.

Answer 2

Multiply the greatest power of each factor to find the LCD.

\[2 \times 3 \times 5 \times x^2 \times y^3 = 30x^2y^3\]

Answer 3

Find equivalent fractions. Consider the first fraction. \[\frac{11}{6x^2y^2}\] Ask yourself this question: What do I need to multiply this denominator by to get the common denominator? \[30x^2y^3\]

Answer 4

5y?

Answer 5

Yes! Multiply both the numerator and denominator by 5y.\[\frac{11}{6x^2y^2} \times \frac{5y}{5y} = \frac{55y}{30x^2y^3}\]Now consider the second fraction. \[\frac{4}{5xy^3}\] Follow the same process. What do you need to multiply this denominator by to get the common denominator? \[30x^2y^3\]

Answer 6

6x?

Answer 7

Good. Multiplying the denominator by 6x will give you the common denominator 30x^2y^3.
\[\frac{4}{5xy^3} \times \frac{6x}{6x} = \frac{24x}{30x^2y^3}\]You've found your equivalent fractions.
\[\frac{55y}{30x^2y^3} = \frac{11}{6x^2y^2} and \frac{24x}{30x^2y^3} = \frac{4}{5xy^3}\]

Answer 8

Thank you! I understand now

Answer 9

:D