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Math  /  Numbers & Operations

QuestionDate: Pager b. 57\frac{5}{7} parts of a pole are in the mud, 374\frac{3}{74} parts in the water and remaining parts above the surface of water. i) Find the total parts of the pole inside the mud and water. ii) Find the parts of the pole above the surfare of water.

Studdy Solution

STEP 1

1. The pole is divided into fractional parts.
2. 57\frac{5}{7} parts of the pole are in the mud.
3. 374\frac{3}{74} parts of the pole are in the water.
4. The remaining parts of the pole are above the surface of the water.
5. The total parts of the pole add up to 1.

STEP 2

1. Calculate the total parts of the pole inside the mud and water.
2. Calculate the parts of the pole above the surface of the water.

STEP 3

Add the fractions representing the parts of the pole in the mud and water.
Total parts in mud and water=57+374\text{Total parts in mud and water} = \frac{5}{7} + \frac{3}{74}

STEP 4

Find a common denominator to add the fractions.
The least common multiple of 77 and 7474 is 518518.
Convert each fraction to have the common denominator:
57=5×747×74=370518\frac{5}{7} = \frac{5 \times 74}{7 \times 74} = \frac{370}{518}
374=3×774×7=21518\frac{3}{74} = \frac{3 \times 7}{74 \times 7} = \frac{21}{518}

STEP 5

Add the fractions with the common denominator:
370518+21518=391518\frac{370}{518} + \frac{21}{518} = \frac{391}{518}

STEP 6

Subtract the total parts in mud and water from the whole pole to find the parts above the water.
1−391518=518518−391518=1275181 - \frac{391}{518} = \frac{518}{518} - \frac{391}{518} = \frac{127}{518}
The total parts of the pole inside the mud and water are:
391518\boxed{\frac{391}{518}}
The parts of the pole above the surface of the water are:
127518\boxed{\frac{127}{518}}

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