Tree A grew by 15 rac12 centimetres in 2012. Tree B grew 17 rac34 centimetres more than Tree A in the same…

Question

Tree A grew by 15 rac12 centimetres in 2012. Tree B grew 17 rac34 centimetres more than Tree A in the same year. What was the increase in the height of Tree B?

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4. Tree A grew by $15\frac{1}{2}$ centimetres in 2012. Tree B grew $17\frac{3}{4}$ centimetres more than Tree A in the same year. What was the increase in the height of Tree B?

Identify the growth of Tree A and the additional growth of Tree B.
Tree A's growth: $15\frac{1}{2}$ cm
Tree B's additional growth: $17\frac{3}{4}$ cm
Add Tree A's growth to the additional growth to find the total increase in height for Tree B.
$15\frac{1}{2} + 17\frac{3}{4}$
Add the whole numbers.
$15 + 17 = 32$
Find a common denominator for the fractions $\frac{1}{2}$ and $\frac{3}{4}$ .
The least common denominator is 4.
$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
Add the fractions.
$\frac{2}{4} + \frac{3}{4} = \frac{2+3}{4} = \frac{5}{4}$
Convert the improper fraction to a mixed number.
$\frac{5}{4} = 1\frac{1}{4}$
Add this to the sum of the whole numbers from Step 3.
$32 + 1\frac{1}{4} = 33\frac{1}{4}$
The increase in the height of Tree B was \boxed{\text{33\frac{1}{4} cm}}.

5. At a $12\frac{1}{2}$ kilometres running competition, Jamie ran for $3\frac{7}{10}$ kilometres before he stopped for a rest. After the rest, he completed the running competition. How far did Jamie run after the rest?
Identify the total distance and the distance run before the rest.
Total distance: $12\frac{1}{2}$ km
Distance before rest: $3\frac{7}{10}$ km
Subtract the distance run before the rest from the total distance to find the distance run after the rest.
$12\frac{1}{2} - 3\frac{7}{10}$
Convert the mixed numbers to improper fractions.
$12\frac{1}{2} = \frac{(12 \times 2) + 1}{2} = \frac{25}{2}$ $3\frac{7}{10} = \frac{(3 \times 10) + 7}{10} = \frac{37}{10}$
Find a common denominator for the fractions $\frac{25}{2}$ and $\frac{37}{10}$ .
The least common denominator is 10.
$\frac{25}{2} = \frac{25 \times 5}{2 \times 5} = \frac{125}{10}$
Perform the subtraction.
$\frac{125}{10} - \frac{37}{10} = \frac{125 - 37}{10} = \frac{88}{10}$
Convert the improper fraction to a mixed number and simplify.
$\frac{88}{10} = 8\frac{8}{10} = 8\frac{8 \div 2}{10 \div 2} = 8\frac{4}{5}$
Jamie ran \boxed{\text{8\frac{4}{5} km}} after the rest.

6. The total mass of two bags was $28\frac{1}{4}$ kilograms. One of the bags was $14\frac{1}{10}$ kilograms. What was the mass of the other bag?
Identify the total mass and the mass of one bag.
Total mass: $28\frac{1}{4}$ kg
Mass of one bag: $14\frac{1}{10}$ kg
Subtract the mass of one bag from the total mass to find the mass of the other bag.
$28\frac{1}{4} - 14\frac{1}{10}$
Subtract the whole numbers.
$28 - 14 = 14$
Find a common denominator for the fractions $\frac{1}{4}$ and $\frac{1}{10}$ .
The least common multiple of 4 and 10 is 20.
$\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$ $\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}$
Subtract the fractions.
$\frac{5}{20} - \frac{2}{20} = \frac{5-2}{20} = \frac{3}{20}$
Combine the whole number from Step 3 and the fraction from Step 5.
$14 + \frac{3}{20} = 14\frac{3}{20}$
The mass of the other bag was \boxed{\text{14\frac{3}{20} kg}}.

Tree A grew by 15 rac12 centimetres in 2012. Tree B grew 17 rac34 centimetres more than Tree A in the same year. What was the increase in the height of Tree B?

Step-by-step solution

Identify the growth of Tree A and the additional growth of Tree B.

Add Tree A's growth to the additional growth to find the total increase in height for Tree B.

Add the whole numbers.

Find a common denominator for the fractions $\frac{1}{2}$ and $\frac{3}{4}$ .

Add the fractions.

Convert the improper fraction to a mixed number.

Add this to the sum of the whole numbers from Step 3.

Identify the total distance and the distance run before the rest.

Subtract the distance run before the rest from the total distance to find the distance run after the rest.

Convert the mixed numbers to improper fractions.

Find a common denominator for the fractions $\frac{25}{2}$ and $\frac{37}{10}$ .

Perform the subtraction.

Convert the improper fraction to a mixed number and simplify.

Identify the total mass and the mass of one bag.

Subtract the mass of one bag from the total mass to find the mass of the other bag.

Subtract the whole numbers.

Find a common denominator for the fractions $\frac{1}{4}$ and $\frac{1}{10}$ .

Subtract the fractions.

Combine the whole number from Step 3 and the fraction from Step 5.

Still stuck on this one?

More Mathematics Questions

Tree A grew by 15 rac12 centimetres in 2012. Tree B grew 17 rac34 centimetres more than Tree A in the same year. What was the increase in the height of Tree B?

Step-by-step solution

Identify the growth of Tree A and the additional growth of Tree B.

Add Tree A's growth to the additional growth to find the total increase in height for Tree B.

Add the whole numbers.

Find a common denominator for the fractions 12\frac{1}{2}21​ and 34\frac{3}{4}43​.

Add the fractions.

Convert the improper fraction to a mixed number.

Add this to the sum of the whole numbers from Step 3.

Identify the total distance and the distance run before the rest.

Subtract the distance run before the rest from the total distance to find the distance run after the rest.

Convert the mixed numbers to improper fractions.

Find a common denominator for the fractions 252\frac{25}{2}225​ and 3710\frac{37}{10}1037​.

Perform the subtraction.

Convert the improper fraction to a mixed number and simplify.

Identify the total mass and the mass of one bag.

Subtract the mass of one bag from the total mass to find the mass of the other bag.

Subtract the whole numbers.

Find a common denominator for the fractions 14\frac{1}{4}41​ and 110\frac{1}{10}101​.

Subtract the fractions.

Combine the whole number from Step 3 and the fraction from Step 5.

Still stuck on this one?

More Mathematics Questions

Find a common denominator for the fractions $\frac{1}{2}$ and $\frac{3}{4}$ .

Find a common denominator for the fractions $\frac{25}{2}$ and $\frac{37}{10}$ .

Find a common denominator for the fractions $\frac{1}{4}$ and $\frac{1}{10}$ .