Find the HCF of 28m'n and 63mn'?

Question

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Here are the solutions to the questions:

15. Find the HCF of $28m^n$ and $63m^n$ .

Find the HCF of the numerical coefficients, 28 and 63.
Prime factors of $28 = 2^2 \times 7$
Prime factors of $63 = 3^2 \times 7$
The common prime factor is 7. So, HCF(28, 63) = 7.
Find the HCF of the variable parts.
The common variable part is $m^n$ .
Combine the HCF of the numerical and variable parts.
HCF( $28m^n$ , $63m^n$ ) = $7m^n$ .
The correct option is B.
The HCF is $\boxed{7m^n}$ .

16. 65% of those who tried out to belong to a football team made it. If 13 players made it to the team, how many tried out?
Let $x$ be the total number of players who tried out.
We are given that $65\%$ of $x$ is 13.
$0.65x = 13$
Solve for $x$ .
$x = \frac{13}{0.65}$ $x = \frac{1300}{65}$ $x = 20$
The correct option is D.
$\boxed{20}$ players tried out.

17. A fruit vendor has 54 apples. She sells 17 apples in the morning and 12 in the evening. How many apples does she have left?
Calculate the total number of apples sold.
$\text{Apples sold} = 17 + 12 = 29$
Subtract the sold apples from the initial total.
$\text{Apples left} = 54 - 29 = 25$
The correct option is B.
She has $\boxed{25}$ apples left.

18. In a village, the numbers of person infected with Bird Flu in 2018 were 75. In 2021, 105 persons were infected. Find the ratio of those infected in 2018 and those in 2021.
Write the ratio as 2018
$\text{Ratio} = 75 : 105$
Simplify the ratio by dividing both numbers by their greatest common divisor.
Divide by 5: $15 : 21$
Divide by 3: $5 : 7$
The correct option is D.
The ratio is $\boxed{5 : 7}$ .

19. Convert the Denary number 73 to a binary number.
Use repeated division by 2 and record remainders.
$73 \div 2 = 36 \text{ R } 1$ $36 \div 2 = 18 \text{ R } 0$ $18 \div 2 = 9 \text{ R } 0$ $9 \div 2 = 4 \text{ R } 1$ $4 \div 2 = 2 \text{ R } 0$ $2 \div 2 = 1 \text{ R } 0$ $1 \div 2 = 0 \text{ R } 1$
Read the remainders from bottom to top.
The binary number is $1001001_2$ .
The correct option is A.
The binary number is $\boxed{1001001_2}$ .

20. Richard spent 35.3% of his money on provision, 28.7% on transport and 15.5% on textbooks. What percentage of his money is left?
Calculate the total percentage spent.
$\text{Total spent} = 35.3\% + 28.7\% + 15.5\% = 79.5\%$
Subtract the total percentage spent from 100%.
$\text{Percentage left} = 100\% - 79.5\% = 20.5\%$
The correct option is B.
$\boxed{20.5\%}$ of his money is left.

21. Convert the denary number 73 to a binary number.
Use repeated division by 2 and record remainders.
$73 \div 2 = 36 \text{ R } 1$ $36 \div 2 = 18 \text{ R } 0$ $18 \div 2 = 9 \text{ R } 0$ $9 \div 2 = 4 \text{ R } 1$ $4 \div 2 = 2 \text{ R } 0$ $2 \div 2 = 1 \text{ R } 0$ $1 \div 2 = 0 \text{ R } 1$
Read the remainders from bottom to top.
The binary number is $1001001_2$ .
The correct option is A.
The binary number is $\boxed{1001001_2}$ .

22. Calculate the negative difference between 35 and 49.
Calculate the difference between 49 and 35.
$\text{Difference} = 49 - 35 = 14$
Find the negative of this difference.
$\text{Negative difference} = -14$
The correct option is B.
The negative difference is $\boxed{-14}$ .

23. Evaluate $79^2 - 24^2$ .
Use the difference of squares formula
$a^2 - b^2 = (a-b)(a+b)$ .
$79^2 - 24^2 = (79 - 24)(79 + 24)$
Perform the operations inside the parentheses.
$(79 - 24) = 55$ $(79 + 24) = 103$
Multiply the results.
$55 \times 103 = 5665$
The correct option is A.
The value is $\boxed{5665}$ .

24. Factorise the expression $3dh - 15hk$ .
Identify the common factors in both terms.
The common numerical factor is 3.
The common variable factor is $h$ .
So, the common factor is $3h$ .
Factor out the common factor.
$3dh - 15hk = 3h(d) - 3h(5k)$ $= 3h(d - 5k)$
The correct option is C.
The factorised expression is $\boxed{3h(d - 5k)}$ .

25. Calculate the area of a cuboid of length 11cm, breadth 9cm and height 5cm.
The question asks for "the area" of a cuboid. Typically, this refers to surface area. However, the calculated surface area is $2(11 \times 9 + 9 \times 5 + 5 \times 11) = 2(99 + 45 + 55) = 2(199) = 398 \text{ cm}^2$ , which is not among the options.
Given that option B is $495 \text{cm}^2$ , and the volume of the cuboid is $11 \text{ cm} \times 9 \text{ cm} \times 5 \text{ cm} = 495 \text{ cm}^3$ , it is highly probable that the question intended to ask for the volume, but incorrectly used "area" and "cm $^2$ " in the option.
Identify the dimensions.
Length $l = 11 \text{ cm}$
Breadth $b = 9 \text{ cm}$
Height $h = 5 \text{ cm}$
Calculate the volume (assuming the question meant volume, given the options).
$\text{Volume} = l \times b \times h$ $\text{Volume} = 11 \text{ cm} \times 9 \text{ cm} \times 5 \text{ cm}$ $\text{Volume} = 495 \text{ cm}^3$
The correct option is B (assuming "area" meant volume and the unit in option B is a typo for $cm^3$ ).
The area (volume) is $\boxed{495 \text{ cm}^3}$ .

26. How many notebooks sold at N150.00 each can a father purchase for N2550.00 for his ward?
Divide the total money by the cost per notebook.
$\text{Number of notebooks} = \frac{\text{N}2550.00}{\text{N}150.00}$
Perform the division.
$\text{Number of notebooks} = \frac{255}{15} = 17$
The correct option is C.
He can purchase $\boxed{17}$ notebooks.

27. Reduce $\frac{105}{225}$ to a fraction in its lowest term.
Find the greatest common divisor (GCD) of 105 and 225.
Both are divisible by 5:
$\frac{105 \div 5}{225 \div 5} = \frac{21}{45}$
Both are divisible by 3:
$\frac{21 \div 3}{45 \div 3} = \frac{7}{15}$
The correct option is B.
The fraction in its lowest term is $\boxed{\frac{7}{15}}$ .

28. Change 7 to a number in percentage.
If the question literally means to convert the integer 7 to a percentage, the answer is $7 \times 100\% = 700\%$ . This is not among the options.
Given the options, it is highly probable that the question intended to ask for the percentage equivalent of $\frac{7}{8}$ (as $87^{1}/_{2}\%$ is an option).
Assume the question meant to convert $\frac{7}{8}$ to a percentage.
$\frac{7}{8} \times 100\%$
Calculate the percentage.
$\frac{7}{8} \times 100\% = 0.875 \times 100\% = 87.5\%$ $87.5\% = 87^{1}/_{2}\%$
The correct option is C (assuming the question meant $\frac{7}{8}$ ).
The percentage is $\boxed{87^{1}/_{2}\%}$ .

29. The number 10,080,008 can be interpreted in words as:
Break down the number by place value.
10,000,000 is Ten Million.
80,000 is Eighty Thousand.
8 is Eight.
Combine the parts.
Ten Million, Eighty Thousand and Eight.
The correct option is B.
The number is $\boxed{\text{Ten Million, Eighty Thousand and Eight}}$ .

30. Which of the following angles is an obtuse angle?
Define an obtuse angle.
An obtuse angle is an angle greater than $90^\circ$ but less than $180^\circ$ .
Check each option.
A. $89^\circ$ (Acute)
B. $92^\circ$ (Obtuse)
C. $184^\circ$ (Reflex)
D. $0.237^\circ$ (Acute)
The correct option is B.
$\boxed{92^\circ}$ is an obtuse angle.

31. Express 117 as a product of its prime factors.
Divide 117 by the smallest prime numbers.
$117 \div 3 = 39$ $39 \div 3 = 13$
Write the prime factorization.
$117 = 3 \times 3 \times 13 = 3^2 \times 13$
The correct option is D.
The prime factors are $\boxed{3^2 \times 13}$ .

32. Calculate the area of the triangle below:
The diagram shows a right-angled triangle with base $8 \text{ cm}$ and height $6 \text{ cm}$ .
Identify the base and height.
Base $b = 8 \text{ cm}$
Height $h = 6 \text{ cm}$
Apply the formula for the area of a triangle.
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 8 \text{ cm} \times 6 \text{ cm}$ $\text{Area} = 4 \text{ cm} \times 6 \text{ cm}$ $\text{Area} = 24 \text{ cm}^2$
The correct option is D.
The area of the triangle is $\boxed{24 \text{ cm}^2}$ .

33. Solve the simultaneous equations:

(i) $a + 6b = 13$

(ii) $5a - 6b = 7$
Adding the two equations as given results in $6a = 20$ , so $a = \frac{10}{3}$ , which is not an integer. Since all options are integers, there might be a typo in the second equation. If the second equation was $5a - 6b = -7$ , then adding the equations would yield $6a = 6$ , so $a=1$ .

Assuming the second equation is $5a - 6b = -7$ :

(i) $a + 6b = 13$

(ii) $5a - 6b = -7$
Add equation (i) and equation (ii) to eliminate $b$ .
$(a + 6b) + (5a - 6b) = 13 + (-7)$ $6a = 6$
Solve for $a$ .
$a = \frac{6}{6} = 1$
Substitute $a=1$ into equation (i) to solve for $b$ .
$1 + 6b = 13$ $6b = 13 - 1$ $6b = 12$ $b = \frac{12}{6} = 2$
The correct option is C (assuming the typo in equation (ii) as $5a - 6b = -7$ ).
The solutions are $\boxed{a = 1 \text{ and } b = 2}$ .

34. Factorize $y^2 + 10y - 24 = 0$ .
Find two numbers that multiply to -24 and add to 10.
The numbers are 12 and -2 ( $12 \times -2 = -24$ and $12 + (-2) = 10$ ).
Rewrite the middle term and factor by grouping.
$y^2 + 12y - 2y - 24 = 0$ $y(y + 12) - 2(y + 12) = 0$ $(y + 12)(y - 2) = 0$
Solve for $y$ .
$y + 12 = 0 \implies y = -12$ $y - 2 = 0 \implies y = 2$
The correct option is B.
The solutions are $\boxed{y = -12 \text{ or } y = 2}$ .

Find the HCF of 28m'n and 63mn'?

Answer

Step-by-step solution

Find the HCF of the numerical coefficients, 28 and 63.

Find the HCF of the variable parts.

Combine the HCF of the numerical and variable parts.

Let xxx be the total number of players who tried out.

Solve for xxx.

Calculate the total number of apples sold.

Subtract the sold apples from the initial total.

Write the ratio as 2018

Simplify the ratio by dividing both numbers by their greatest common divisor.

Use repeated division by 2 and record remainders.

Read the remainders from bottom to top.

Calculate the total percentage spent.

Subtract the total percentage spent from 100%.

Use repeated division by 2 and record remainders.

Read the remainders from bottom to top.

Calculate the difference between 49 and 35.

Find the negative of this difference.

Use the difference of squares formula

Perform the operations inside the parentheses.

Multiply the results.

Identify the common factors in both terms.

Factor out the common factor.

Identify the dimensions.

Calculate the volume (assuming the question meant volume, given the options).

Divide the total money by the cost per notebook.

Perform the division.

Find the greatest common divisor (GCD) of 105 and 225.

Assume the question meant to convert 78\frac{7}{8}87​ to a percentage.

Calculate the percentage.

Break down the number by place value.

Combine the parts.

Define an obtuse angle.

Check each option.

Divide 117 by the smallest prime numbers.

Write the prime factorization.

Identify the base and height.

Apply the formula for the area of a triangle.

Add equation (i) and equation (ii) to eliminate bbb.

Solve for aaa.

Substitute a=1a=1a=1 into equation (i) to solve for bbb.

Find two numbers that multiply to -24 and add to 10.

Rewrite the middle term and factor by grouping.

Solve for yyy.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Let $x$ be the total number of players who tried out.

Solve for $x$ .

Assume the question meant to convert $\frac{7}{8}$ to a percentage.

Add equation (i) and equation (ii) to eliminate $b$ .

Solve for $a$ .

Substitute $a=1$ into equation (i) to solve for $b$ .

Solve for $y$ .