Final answer:
The student is asked to rewrite pairs of fractions using common denominators, a mathematics concept taught in middle school. It involves finding the least common multiple (LCM) of the denominators and adjusting the numerators to achieve the common denominator, which is critical for comparing and operating with fractions.
Step-by-step explanation:
The question is asking to rewrite the pairs of fractions using common denominators. This is a mathematics concept typically taught in middle school. To find a common denominator for each pair of fractions, we can look for the least common multiple (LCM) of the denominators. If the denominators are already the same, we only need to simplify the fractions. When the denominators are different, we have to adjust the numerators accordingly after finding the LCM. This process helps us to compare, add, or subtract fractions correctly.
- For the pair 30/42 and 56/42, the denominators are already common, so no changes are necessary.
- For the pair 35/49 and 16/12, we can rewrite them using the LCM of 49 and 12, which is 588, to get new fractions with this common denominator.
- For the pair 10/14 and 24/18, we can rewrite them using the LCM of 14 and 18, which is 126, to get fractions with a common denominator.
- For the pair 40/56 and 16/12, we can rewrite them with the LCM of 56 and 12, which is 168, to obtain fractions with a common denominator.
Simplifying fractions and finding common denominators is essential for working with fractions as it allows for direct comparison and mathematical operations such as addition and subtraction.