MYP 3 Mathematics · Number

Finding rational numbers between two given numbers

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Question 1
What is the lowest common denominator (LCD) of $f r a c 56$ and $f r a c 38$ ?
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B24
Step-by-step walkthrough
Choose a solution method
Method #1Direct Approach
Step 1: Identify the denominators
The denominators are 6 and 8. The LCD is the lowest common multiple (LCM) of 6 and 8.
Step 2: List multiples of each denominator
Multiples of 6: 6, 12, 24, 30 … Multiples of 8: 8, 16, 24, 32 … The first number appearing in both lists is 24.
Step 3: State the LCD
The LCD of 6 and 8 is 24.
Method #2Process of Elimination
Step 1: What LCD means
The LCD must be divisible by both 6 and 8, and should be the smallest such number.
Step 2: Eliminate 14
$14 \div 6 = 2.33 \dots$ and $14 \div 8 = 1.75$ — 14 is not divisible by either 6 or 8.
Step 3: Eliminate 48
48 is divisible by both 6 and 8, but $48 = 2 \times 24$ , so it is not the lowest common denominator.
Step 4: Eliminate 16
$16 \div 6 = 2.67 \dots$ — 16 is not divisible by 6, so it cannot be the LCD.
Step 5: Select the correct answer
24 is divisible by both 6 ( $24 \div 6 = 4$ ) and 8 ( $24 \div 8 = 3$ ), and it is the smallest such number.

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