Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

c)
(2)/(3)×(5)/(7)
(2 Marks)
d)
(3)/(4)÷(21)/(16)
e)
((3)/(5))^(3)
(2 Marks)
f)
2(3)/(4)-7(1)/(2)

c) $\frac{2}{3} \times \frac{5}{7}$ $\newline$ ( $2$ Marks) $\newline$ d) $\frac{3}{4} \div \frac{21}{16}$ $\newline$ e) $\left(\frac{3}{5}\right)^{3}$ $\newline$ ( $2$ Marks) $\newline$ f) $2 \frac{3}{4}-7 \frac{1}{2}$

View step-by-step help

View step-by-step help

Sum of finite series starts from 1

Full solution

Q. c)

\frac{2}{3} \times \frac{5}{7}

\newline

(

2

Marks)

\newline

d)

\frac{3}{4} \div \frac{21}{16}

\newline

e)

\left(\frac{3}{5}\right)^{3}

\newline

(

2

Marks)

\newline

f)

2 \frac{3}{4}-7 \frac{1}{2}

Multiply fractions: c) Multiply the fractions $(\frac{2}{3})$ and $(\frac{5}{7})$ . $\frac{2}{3} \times \frac{5}{7} = \frac{2\times5}{3\times7} = \frac{10}{21}$ .
Divide fractions: d) Divide the fractions $(\frac{3}{4})$ by $(\frac{21}{16})$ . $\frac{3}{4} \div \frac{21}{16} = \frac{3}{4} \times \frac{16}{21} = \frac{3\times16}{4\times21} = \frac{48}{84}$ . Simplify $\frac{48}{84}$ by dividing both numerator and denominator by $12$ . $\frac{48}{84} \div \frac{12}{12} = \frac{4}{7}$ .
Raise to power: e) Raise the fraction $(\frac{3}{5})$ to the power of $3$ . $\left(\frac{3}{5}\right)^3 = \frac{3^3}{5^3} = \frac{27}{125}$ .
Subtract mixed numbers: f) Subtract the mixed numbers $2\left(\frac{3}{4}\right)$ and $7\left(\frac{1}{2}\right)$ . $\newline$ First, convert mixed numbers to improper fractions. $\newline$ $2\left(\frac{3}{4}\right) = \left(\frac{8}{4}\right) + \left(\frac{3}{4}\right) = \frac{11}{4}$ . $\newline$ $7\left(\frac{1}{2}\right) = \left(\frac{14}{2}\right) + \left(\frac{1}{2}\right) = \frac{15}{2}$ . $\newline$ Now subtract the improper fractions. $\newline$ $\left(\frac{11}{4}\right) - \left(\frac{15}{2}\right) = \left(\frac{11}{4}\right) - \left(\frac{30}{4}\right) = -\frac{19}{4}$ . $\newline$ Convert the improper fraction back to a mixed number. $\newline$ $-\frac{19}{4} = -4 \frac{3}{4}$ .

More problems from Sum of finite series starts from 1

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 2 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 1 month ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 2 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 2 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 1 month ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 1 month ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 2 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 1 month ago