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forsale [732]
3 years ago
11

Four friends are training for long races. Eduardo ran 5.123 miles, Kandis ran 6.34 miles, Khaliyah ran 7.1 miles, and Moises ran

8 miles. b: Khaliyah ran how much further than Eduardo?​
Mathematics
1 answer:
Inessa [10]3 years ago
8 0

Answer:

1.977 miles

Step-by-step explanation:

Focus on how many miles Khaliyah and Eduardo are training.

Khaliyah = 7.100 miles

Eduardo = 5.123 miles

Difference = 7.100 - 5.123 = 1.977

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To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

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Step 2: Simplify the denominator

$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}

Step 3: Using step 1 and step 2

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}

Step 4: Using fraction rule:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}

$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}

Cancel the common factor r and t², we get

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Cancel the common factors 16 and 3 on both numerator and denominator.

           $=\frac{4 r^{2} \cdot 3 }{  5 t^2 }

           $=\frac{12 r^{2}  }{  5 t^2 }

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2}  }{  5 t^2 }

The simplified fraction is \frac{12 r^{2}  }{  5 t^2 }.

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