Find the HCF of 28m'n and 63mn

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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 greatest common factor of 28 and 63 is 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 both by 5: $15 : 21$
Divide both 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 $11 \text{cm}$ , breadth $9 \text{cm}$ and height $5 \text{cm}$ .
The question asks for "area" but the options are in $cm^3$ , which are units for volume. Given the options, it is highly probable that the question intended to ask for the volume of the cuboid.
Identify the dimensions.
Length $l = 11 \text{ cm}$
Breadth $b = 9 \text{ cm}$
Height $h = 5 \text{ cm}$
Calculate the volume of the cuboid.
$\text{Volume} = l \times b \times h$ $\text{Volume} = 11 \text{ cm} \times 9 \text{ cm} \times 5 \text{ cm}$ $\text{Volume} = 495 \text{ cm}^3$
The correct option is B.
The 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.
$\text{Number of notebooks} = 17$
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 the numerator and denominator.
Both 105 and 225 are divisible by 5.
$\frac{105 \div 5}{225 \div 5} = \frac{21}{45}$
Continue dividing by common factors.
Both 21 and 45 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 option C is $87\frac{1}{2}\%$ , it is highly probable that the question intended to ask for the percentage equivalent of $\frac{7}{8}$ .
Convert the fraction $\frac{7}{8}$ to a percentage.
$\text{Percentage} = \frac{7}{8} \times 100\%$
Calculate the percentage.
$\text{Percentage} = 0.875 \times 100\% = 87.5\%$ $\text{Percentage} = 87\frac{1}{2}\%$
The correct option is C.
The percentage is $\boxed{87\frac{1}{2}\%}$ .

29. The number 10,080,008 can be interpreted in words as:
Break down the number by place value.
$10,000,000 \implies \text{Ten Million}$
$80,000 \implies \text{Eighty Thousand}$
$8 \implies \text{Eight}$
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?
Recall the definition of an obtuse angle.
An obtuse angle is an angle that measures greater than $90^\circ$ but less than $180^\circ$ .
Evaluate each option.
A. $89^\circ$ is an acute angle (less than $90^\circ$ ).
B. $92^\circ$ is an obtuse angle (greater than $90^\circ$ and less than $180^\circ$ ).
C. $184^\circ$ is a reflex angle (greater than $180^\circ$ ).
D. $0.237^\circ$ is an acute angle.
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.
$117 \div 3 = 39$ $39 \div 3 = 13$ $13 \div 13 = 1$
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 a base of $8 \text{ cm}$ and a height of $6 \text{ cm}$ .
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 given equations results in $6a = 20$ , so $a = \frac{10}{3}$ , which is not an integer. Since all options are integers, there is likely a typo in equation (ii). If equation (ii) was $5a - 6b = -7$ , then the solution would match option C. Assuming this typo:

(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 the expression $y^2 + 10y - 24 = 0$ .
Find two numbers that multiply to -24 and add to 10.
The two numbers are 12 and -2, because $12 \times (-2) = -24$ and $12 + (-2) = 10$ .
Rewrite the middle term using these numbers 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 of the cuboid.

Divide the total money by the cost per notebook.

Perform the division.

Find the greatest common divisor (GCD) of the numerator and denominator.

Continue dividing by common factors.

Convert the fraction 78\frac{7}{8}87​ to a percentage.

Calculate the percentage.

Break down the number by place value.

Combine the parts.

Recall the definition of an obtuse angle.

Evaluate 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 using these numbers 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 $x$ .

Convert the fraction $\frac{7}{8}$ 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 $y$ .