AskSia

Plus

1a. Calculate the exact value of: 2 1/2 × 3 3/4 = …………………………………...

May 8, 2024

1a. Calculate the exact value of: 2 1/2 × 3 3/4 = ……………………………………………………………………………………….(1p) b. Calculate the value in standard form: 4^3× 5^2 = ……………………………………………………………………………………….(1p) 2a. Find the H.C.F. of: 12,18,42 ……………………………………………………………………………………….(1p) b. Find the L.C.M. of: 45,60,110 ……………………………………………………………………………………….(1p) 3a. Simplify this equation and leave it in index form: 1(a^2× a^5 ) + (c^2 ÷ c)= ……………………………………………………………………………………….(1p) b. (f^3×f^5)÷(f^6÷f2)= ……………………………………………………………………………………….(1p) 4a. Find the value of : √16 × 8 = ……………………………………………………………………………………….(1p) b. ∛125×5^(-2)= ……………………………………………………………………………………….(1p) 5. A.J. Singh’s electricity bill is

49.88.How many units does he use if the cost per units is 43 cent ? ……………………………………………………………………………………….(2p) 6. Jason bought his bicycle for

450. He sold it for

300 What was his percentage loss ? ……………………………………………………………………………………….(1p) 7.Andrew Prescot bought his car for

63 500 and sold it at a 20% loss. What did he sell the car for? ……………………………………………………………………………………….(2p) 8.Given that EC

2,71 = US

1,00 a. US

45,35 to EC

……………………………………………………………………………………….(2p) b. Given that US

3,71 = TT

1,00 Calculate EC

56,35 to TT

……………………………………………………………………………………….(2p)

Generated Graph

Solution by Steps

step 1

To calculate the exact value of

2 \frac{1}{2} \times 3 \frac{3}{4}

, first convert the mixed numbers to improper fractions

step 2

Convert

2 \frac{1}{2}

to an improper fraction:

2 \frac{1}{2} = \frac{5}{2}

step 3

Convert

3 \frac{3}{4}

to an improper fraction:

3 \frac{3}{4} = \frac{15}{4}

step 4

Multiply the improper fractions:

\frac{5}{2} \times \frac{15}{4} = \frac{75}{8}

step 5

Convert the improper fraction

\frac{75}{8}

to a mixed number:

\frac{75}{8} = 9 \frac{3}{8}

[1a] Answer

9 \frac{3}{8}

step 1

To calculate the value in standard form of

4^3 \times 5^2

, compute each exponentiation separately

step 2

Calculate

4^3 = 64

step 3

Calculate

5^2 = 25

step 4

Multiply the results:

64 \times 25 = 1600

[1b] Answer

1600

step 1

To find the H.C.F. (highest common factor) of 12, 18, and 42, list the prime factors of each number

step 2

Prime factors of 12:

2^2 \times 3

step 3

Prime factors of 18:

2 \times 3^2

step 4

Prime factors of 42:

2 \times 3 \times 7

step 5

The H.C.F. is the product of the lowest powers of common prime factors:

2 \times 3 = 6

[2a] Answer

6

step 1

To find the L.C.M. (least common multiple) of 45, 60, and 110, list the prime factors of each number

step 2

Prime factors of 45:

3^2 \times 5

step 3

Prime factors of 60:

2^2 \times 3 \times 5

step 4

Prime factors of 110:

2 \times 5 \times 11

step 5

The L.C.M. is the product of the highest powers of all prime factors:

2^2 \times 3^2 \times 5 \times 11 = 1980

[2b] Answer

1980

step 1

To simplify the equation

1(a^2 \times a^5) + (c^2 \div c)

, apply the laws of exponents and simplify

step 2

Multiply the powers of

a

a^2 \times a^5 = a^{2+5} = a^7

step 3

Divide the powers of

c

c^2 \div c = c^{2-1} = c

step 4

Combine the results:

a^7 + c

[3a] Answer

a^7 + c

step 1

To simplify the expression

(f^3 \times f^5) \div (f^6 \div f^2)

, apply the laws of exponents

step 2

Multiply the powers of

f

in the numerator:

f^3 \times f^5 = f^{3+5} = f^8

step 3

Divide the powers of

f

in the denominator:

f^6 \div f^2 = f^{6-2} = f^4

step 4

Divide the results:

f^8 \div f^4 = f^{8-4} = f^4

[3b] Answer

f^4

step 1

To find the value of

\sqrt{16} \times 8

, first calculate the square root of 16

step 2

Calculate

\sqrt{16} = 4

step 3

Multiply the result by 8:

4 \times 8 = 32

[4a] Answer

32

step 1

To find the value of

\sqrt[3]{125} \times 5^{-2}

, first calculate the cube root of 125

step 2

Calculate

\sqrt[3]{125} = 5

step 3

Calculate

5^{-2} = \frac{1}{5^2} = \frac{1}{25}

step 4

Multiply the results:

5 \times \frac{1}{25} = \frac{1}{5}

[4b] Answer

\frac{1}{5}

0.2

step 1

To find how many units A.J. Singh uses if his electricity bill is $49.88 and the cost per unit is 43 cents, divide the total cost by the cost per unit

step 2

Convert the total cost to cents:

49.88 = 4988

cents

step 3

Divide the total cost in cents by the cost per unit:

4988 \div 43

step 4

Calculate the number of units:

4988 \div 43 = 116

[5] Answer

116

units

step 1

To calculate the percentage loss when Jason sold his bicycle for

300 after buying it for

450, first find the loss amount

step 2

Calculate the loss:

450 - 300 =

150

step 3

Calculate the percentage loss:

\frac{150}{450} \times 100\%

step 4

Simplify the percentage:

\frac{1}{3} \times 100\% = 33.\overline{3}\%

[6] Answer

33.\overline{3}\%

step 1

To find the selling price of Andrew Prescot's car after a 20% loss on the purchase price of $63,500, calculate the loss amount

step 2

Calculate 20% of

63,500: 0.20 \times 63,500 =

12,700

step 3

Subtract the loss from the purchase price:

63,500 - 12,700 =

50,800

[7] Answer

$50,800

step 1

To convert US

45.35 to EC

, use the given exchange rate EC

2.71 = US

1.00

step 2

Calculate the conversion:

45.35 \times \frac{2.71}{1.00}

step 3

Perform the multiplication:

45.35 \times 2.71 = 122.8985

[8a] Answer

122.8985

step 1

To convert EC

56.35 to TT

, first convert EC

to US

using the given exchange rate EC

2.71 = US

1.00

step 2

Calculate the conversion to US

:

56.35 \div 2.71$

step 3

Perform the division:

56.35 \div 2.71 = 20.7952

US $

step 4

Now convert US

to TT

using the given exchange rate US

3.71 = TT

1.00

step 5

Calculate the conversion to TT

:

20.7952 \times 3.71$

step 6

Perform the multiplication:

20.7952 \times 3.71 = 77.1501

TT $

[8b] Answer

77.1501

Key Concept

Conversion of mixed numbers to improper fractions, application of exponent rules, and understanding of percentage calculations.

Explanation

The solutions involve converting mixed numbers to improper fractions for multiplication, using exponent rules for simplification, and applying percentage formulas for financial calculations.