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Answer :
Sure! Let's find the irreducible fractions step-by-step for the given expressions.
### Part A
We start with the expression [tex]\(\frac{60}{4}\)[/tex] divided by [tex]\(\frac{62 + 2}{4}\)[/tex].
1. Calculate individual fractions:
- First, [tex]\(\frac{60}{4}\)[/tex] simplifies to 15 because [tex]\(60 \div 4 = 15\)[/tex].
- Next, [tex]\(\frac{62 + 2}{4}\)[/tex] simplifies as follows: [tex]\(62 + 2 = 64\)[/tex], and [tex]\(64 \div 4 = 16\)[/tex], so it becomes [tex]\(\frac{64}{4} = 16\)[/tex].
2. Perform the division:
- We are dividing [tex]\(\frac{60}{4}\)[/tex] by [tex]\(\frac{64}{4}\)[/tex], which is the same as multiplying [tex]\(\frac{60}{4}\)[/tex] by the reciprocal of [tex]\(\frac{64}{4}\)[/tex]. So, we get [tex]\(\frac{15}{16}\)[/tex].
3. Result:
- The fraction [tex]\(\frac{15}{16}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 15 and 16 is 1.
### Part B
Now, look at the fraction [tex]\(\frac{30}{12}\)[/tex].
1. Simplify the fraction:
- Find the greatest common divisor (GCD) of 30 and 12, which is 6.
- Divide both the numerator and denominator by their GCD:
[tex]\[
\frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2}
\][/tex]
2. Result:
- The fraction [tex]\(\frac{5}{2}\)[/tex] is in its simplest form.
Summary:
- For part A, the irreducible fraction is [tex]\(\frac{15}{16}\)[/tex].
- For part B, the irreducible fraction is [tex]\(\frac{5}{2}\)[/tex].
I hope this helps clarify how to reduce fractions to their simplest form!
### Part A
We start with the expression [tex]\(\frac{60}{4}\)[/tex] divided by [tex]\(\frac{62 + 2}{4}\)[/tex].
1. Calculate individual fractions:
- First, [tex]\(\frac{60}{4}\)[/tex] simplifies to 15 because [tex]\(60 \div 4 = 15\)[/tex].
- Next, [tex]\(\frac{62 + 2}{4}\)[/tex] simplifies as follows: [tex]\(62 + 2 = 64\)[/tex], and [tex]\(64 \div 4 = 16\)[/tex], so it becomes [tex]\(\frac{64}{4} = 16\)[/tex].
2. Perform the division:
- We are dividing [tex]\(\frac{60}{4}\)[/tex] by [tex]\(\frac{64}{4}\)[/tex], which is the same as multiplying [tex]\(\frac{60}{4}\)[/tex] by the reciprocal of [tex]\(\frac{64}{4}\)[/tex]. So, we get [tex]\(\frac{15}{16}\)[/tex].
3. Result:
- The fraction [tex]\(\frac{15}{16}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 15 and 16 is 1.
### Part B
Now, look at the fraction [tex]\(\frac{30}{12}\)[/tex].
1. Simplify the fraction:
- Find the greatest common divisor (GCD) of 30 and 12, which is 6.
- Divide both the numerator and denominator by their GCD:
[tex]\[
\frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2}
\][/tex]
2. Result:
- The fraction [tex]\(\frac{5}{2}\)[/tex] is in its simplest form.
Summary:
- For part A, the irreducible fraction is [tex]\(\frac{15}{16}\)[/tex].
- For part B, the irreducible fraction is [tex]\(\frac{5}{2}\)[/tex].
I hope this helps clarify how to reduce fractions to their simplest form!
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