Solve the following equation:
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Solve the following equation:
We must first identify the lowest common denominator between 3 and 9.
In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 9.
In this case, the common denominator is 9.
We will then proceed to multiply each fraction by the appropriate number to reach the denominator 9.
We'll multiply the first fraction by 3
We'll multiply the second fraction by 1
Finally we'll combine and obtain the following:
Without calculating, determine whether the quotient in the division exercise is less than 1 or not:
\( 5:6= \)
Fractions represent parts of a whole, and you can only add parts when they're the same size! Think of it like adding 1 slice of a 3-piece pizza to 4 slices of a 9-piece pizza - you need equal-sized pieces first.
The LCD is the smallest number that both denominators divide into evenly. Since 9 ÷ 3 = 3 and 9 ÷ 9 = 1, and there's no smaller number that works, 9 is the LCD.
Sometimes both fractions need converting! For example, with , the LCD is 12, so you'd convert both: .
Always check if you can simplify! In this problem, is already in lowest terms since 7 and 9 share no common factors besides 1.
You could use any common multiple, but the LCD makes the math easiest. Using 18 instead of 9 would work but create unnecessarily large numbers to work with.
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