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### Comparing and Ordering Rational Numbers

• To compare fractions, first make the denominators the same by finding the least common multiple. Then compare the numerators. You can also change the fractions to decimals by dividing the numerator by the denominator.
• You can always find a common denominator for two fractions by multiplying the two denominators, but the result may not be the least common denominator.
• To compare a list of rational numbers, change all numbers to decimals or change all numbers to fractions with common denominators.

## Which number is larger, [5/6] or [3/4]?

• [(5 ×4)/(6 ×4)] = [20/24]
• [(3 ×6)/(4 ×6)] = [18/24]

## Which number is larger, [2/3] or [5/8]?

• [(2 ×8)/(3 ×8)] = [16/24]
• [(5 ×3)/(8 ×3)] = [15/24]

## Which number is larger, [4/13] or [6/15]?

• [(4 ×15)/(13 ×15)] = [60/195]
• [(6 ×13)/(15 ×13)] = [78/195]

## Which number is smaller, [8/3] or [9/5]?

• [(8 ×5)/(3 ×5)] = [40/15]
• [(9 ×3)/(5 ×3)] = [27/15]

## Which number is smaller, [4/6] or [7/10]?

• [(4 ×10)/(6 ×10)] = [40/60]
• [(7 ×6)/(10 ×6)] = [42/60]

## Which number is smaller, [5/12] or [3/5]?

• [(5 ×5)/(12 ×5)] = [25/60]
• [(3 ×12)/(5 ×12)] = [36/60]

## Order these numbers from least to greatest by writing them as decimals: 0.4, [1/4], 1.2, 0.7, 1[3/8]

• [1/4] = 4|  1.00   = 0.25
• 1[3/8] = 1 + 8|  3.000   = 1.375
• 0.25 < 0.4 < 0.7 < 1.2 < 1.375

## Order these numbers from greatest to least by writing them as fractions: 0.6, 1[3/5], 1.4, [5/6].

• 0.6 = [6/10]
• 1.4 = 1[4/10]
• Which is greater, 1[3/5] or 1[4/10]?
• 1[(3 ×2)/(5 ×2)] = 1[6/10], so 1[3/5] is greater than 1[4/10]
• Which is greater, [6/10] or [5/6]?
• [(6 ×6)/(10 ×6)] = [36/60]
• [(5 ×10)/(6 ×10)] = [50/60], so [5/6] is greater than [6/10]
• 1[3/5] > 1[4/10] > [5/6] > [6/10]

## Write the numbers from least to greatest: [1/3], [2/5], [4/15].

• Find the LCM of 3, 5, and 15.
• 3: 3, 6, 9, 12, 15, 18, 21
5: 5, 10, 15, 20, 25
15: 15, 30
LCM: 15
• [(1 ×5)/(3 ×5)] = [5/15]
• [2/5] = [6/15]

## Two boxes of cereal have the same price. Box A has 15[5/8] ounces of cereal, while Box B has 15[7/12] ounces of cereal. Which cereal is the better buy?

• Find the LCM of 8 and 12.
• 8: 8, 16, 32, 40, 48, 56
12: 12, 24, 36, 48, 60, 72
LCM: 48
• Box A: 15[(5 ×6)/(8 ×6)] = 15[30/48]
• Box B: 15[(7 ×4)/(12 ×4)] = 15[28/48]

### Box A is the better buy.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.