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Write the numbers 3, 9, and 25 into the three empty boxes below to make the mathematical statement true - Junior Cycle Mathematics - Question 1 - 2021
Question 1
Write the numbers 3, 9, and 25 into the three empty boxes below to make the mathematical statement true. Use each number only once. 5 + _____ = 24/25 Write the num... show full transcript
Worked Solution & Example Answer:Write the numbers 3, 9, and 25 into the three empty boxes below to make the mathematical statement true - Junior Cycle Mathematics - Question 1 - 2021
Step 1
Write the numbers 3, 9, and 25 into the three empty boxes below to make the mathematical statement true.
Answer
To satisfy the equation, we need the left side to equal the right side:
5 + x = 24/25.
Calculating gives us:
yielding x = 24/25 - 5 = -119/25.
Since this is not possible using the numbers 3, 9, and 25, let's look for another possibility. The correct placement is:
5 + 25 = 30, which simplifies to be false, so we try:
5 + 9 = 14, which indicates that the formulation is incorrect or we need to rethink.
Realizing that 3 + 9 = 12 gives us no closure, we might have to look elsewhere, but upon fitting, it should be:
5 + 25 = 30 also invalidates jousts meaning seek out of correctness.
Step 2
Write the numbers 3, 5, 9, and 25 into the empty boxes below so that the difference between the two fractions is as large as possible.
Answer
To maximize the difference, we want to maximize the first fraction and minimize the second. Thus, using the biggest numerator and smallest denominator is key:
Using 25 and 3 gives:
[ \frac{25}{5} - \frac{3}{9} ]
Calculating: [ \frac{25}{5} - \frac{3}{9} = 5 - \frac{3}{9} = 5 - 0.3333 = 4.6667 ]
This gives the largest possible difference.
Step 3
A positive whole number has exactly 4 factors. One of the factors is 9.
Answer
A number with exactly 4 factors can be expressed as p^3 (where p is prime) or as p * q (where p and q are distinct primes). Since 9 is not prime, we explore: 9 can be factorized as 3^2, meaning the structure is: Thus, the number can be derived through the product: [ 9 = 3^2 ] This implies: [ 9 \to {1, 3, 9 t{, other factors to realize }} Observably, this leads us to explore based on primative heuristics to right understanding.