Chapter 4: Fractions and Decimals

Ans: The addition of the numbers is False

$\Rightarrow 3.030 + 0.016 = 3.046$

$\Rightarrow 3.046 \ne 3.019$ 

Ans: The subtraction of the two numbers is True

Ans: The statement is True

Given fraction are like fraction. 

Comparing the numerator, we get $\dfrac{{16}}{{25}} > \dfrac{{13}}{{25}}$

Ans: The given fraction type is False

Since, convert the $19.25$and $19.053$ in like decimal. It's become $19.250$ and $19.053.$

Compare the place value $19.250 < 19.053$, we get hundred place of $19.250$ is $2$ and the hundred place of $19.053$ is $0$

Hence, the statement is $19.25 > 19.053$

Ans: The given number is True

Since, convert the $13.730$ and $13.73$in like decimal. It's become $13.730$ and $13.730$

So,$13.730 = 13.73$

In Each of the Questions 66 to 71, fill in the Blanks Using '>', '<' or '=':

Ans: The L.C.M. of $16$ and $15$ is $2 \times 2 \times 2 \times 2 \times 3 \times 5 = 240$

Make it as like a fraction, multiply in numerator and denominator with the same digit

$\dfrac{{11}}{{16}} \times \dfrac{{15}}{{15}} = \dfrac{{165}}{{240}}$

$\dfrac{{14}}{{15}} \times \dfrac{{16}}{{16}} = \dfrac{{224}}{{240}}$

$\dfrac{{224}}{{240}} > \dfrac{{165}}{{240}}{\text{ So, }}\dfrac{{11}}{{16}} < \dfrac{{14}}{{15}}$

Ans: The L.C.M of $15$ and $14$ is $2 \times 3 \times 5 \times 7 = 210$

Make it as like a fraction, multiply in numerator and denominator with the same digit

$\dfrac{8}{{15}} \times \dfrac{{14}}{{14}} = \dfrac{{112}}{{210}}$

$\dfrac{{95}}{{14}} \times \dfrac{{15}}{{15}} = \dfrac{{1425}}{{210}}$

$\dfrac{{1425}}{{210}} > \dfrac{{112}}{{210}}$

Therefore,  $\dfrac{8}{{15}} < \dfrac{{95}}{{14}}$

Ans: The L.C.M of $75$ and $200$is $2 \times 2 \times 2 \times 3 \times 5 \times 5 = 600$

Make it as like a fraction, multiply in numerator and denominator with the same digit

$\dfrac{{12}}{{75}} \times \dfrac{8}{8} = \dfrac{{96}}{{600}}$

$\dfrac{{32}}{{200}} \times \dfrac{3}{3} = \dfrac{{96}}{{600}}$

$\dfrac{{96}}{{600}} = \dfrac{{96}}{{600}}$ 

Hence, $\dfrac{{12}}{{75}} = \dfrac{{32}}{{200}}$

Ans: Since, convert the $3.25$and $3.4$in like decimal. It's become $3.25$ and $3.40$

Compare the place value of $3.25$and $3.40,$we get tenth place of $3.25$ is $2$ and the tenth place of $3.40$is $4$

Hence,$3.25 < 3.4$

Ans: Since, convert $1.3$ into fraction from, we get $\dfrac{{13}}{{10}}$

$\dfrac{{18}}{{15}} \ldots ..\dfrac{{13}}{{10}}$

The L.C.M. of $15$ and $10$ is $2 \times 3 \times 5 = 30$

Make it as like a fraction, multiply in numerator and denominator with the same digit

$\dfrac{{18}}{{15}} \times \dfrac{{10}}{{10}} = \dfrac{{180}}{{150}}{\text{ and }}\dfrac{{13}}{{10}} \times \dfrac{{15}}{{15}} = \dfrac{{195}}{{150}}$

$\dfrac{{180}}{{150}} < \dfrac{{195}}{{150}}{\text{ So, }}\dfrac{{18}}{{15}} < 1.3$