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patrick drank 3/4 liters of water on wednesday before going jogging and 4/5 liter of water after his jog . how much water did patrick drink altogether? write your answer as a mixed number

Respuesta :

To find the total of 3/4 and 4/5 is to add them together. However, in order to add them together you need to find the least common denominator (LCD). And the LCD of both denominators would be 20, because that is the smallest number both 4 and 5 can divide into. And here is the tricky part, now you have to change the numerators. So since 3/4th's now has a denominator of 20 you have to make the 3 match the 20. So 4 times what it 20? It is 5. So now multiply 5 by three and that will give you 15/20, which can reduce to 3/4 which means that you did this correctly! Now repeat the same steps with 4/5:

4/5=4/20
20÷5=4
4•4=16
16/20    (16/20 can reduce to 4/5 which means you did this correctly.

Now to add them keep the denominators the same and only add the numerators:

15/20 + 16/20 = 31/20

Now this as a mixed number would be 1 11/20. I hope this was helpful!
BladeRunner212

1 ¹¹/₂₀ liters of water.

Further explanation

Given:

  • Patrick drank ³/₄ liters of water on Wednesday before going jogging, and
  • ⁴/₅ liter of water after his jog.

Question:

How much water did Patrick drink altogether? Write your answer as a mixed number.

The Process:

We must add up the two fractions to find out how much water did Patrick drink altogether.

Previously, we must equate the denominator. We know that the least common multiple (LCM) of 4 and 5 is 20.

[tex]\boxed{ \ \frac{3}{4} + \frac{4}{5} = \ ? \ }[/tex]

[tex]\boxed{ \ = \frac{3 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} = \ }[/tex]

[tex]\boxed{ \ = \frac{15}{20} + \frac{16}{20} \ }[/tex]

[tex]\boxed{ \ = \frac{15 + 16}{20} \ }[/tex]

[tex]\boxed{\boxed{ \ \frac{31}{20} \ }}[/tex]

Let us change it into a mixed fraction.

[tex]\boxed{\boxed{ \ \frac{31}{20} = \frac{20}{20} + \frac{11}{30} \ }}[/tex]

[tex]\boxed{\boxed{ \ \frac{31}{20} = 1 + \frac{11}{30} \ }}[/tex]

Recall [tex]\boxed{\boxed{ \ a + \frac{b}{c} = a \ \frac{b}{c} \ }}[/tex]

[tex]\boxed{\boxed{ \ 1 \ \frac{11}{20} \ }}[/tex]

Thus, the amount of water that Patrick drank altogether is [tex]1 \ \frac{11}{20}[/tex] liters of water.

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