Question

Find the rational numbers that should be added and substracted so that they will make sum
$3 \times \frac{1}{2} + 1 \times \frac{3}{4} + 2 \times \frac{3}{8}$
to the nearest whole number.

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Answer 1

$\sf {\underline {\underline{Solution:-}}}$

$3\times \frac{1}{2} + 1 \times \frac{3}{4} + 2 \times \frac{3}{8}$

$\sf = \frac{7}{2} + \frac{7}{4} + \frac{19}{8} =\frac{7 \times 4 + 7 \times 2 + 19 \times 1}{8} = \frac{28 + 14 + 19}{8}$___________________________________________________________ $\sf = \frac{61}{8} = 7 \times \frac{5}{8}, \\ \sf \: it \: lies \: btw \: the \: whole \: numbers \: 7 \: and \: 8$$\sf \: If \: we \: substract \: \frac{5}{8} from \: 7\frac{5}{8} \\ \sf,it \: becomes \: 7. If \: we \: add \: \frac{3}{8} \: to \: 7 \times \frac{5}{8} , \\ \sf it \: becomes \: 7 + \frac{5}{8} + \frac{3}{8} = 7 + 1 = 8.$___________________________________________________________

I hope this helps you ✌

Answer 2

Answer:-

$3 \frac{1}{2} + 1 \frac{3}{4} + 2 \frac{3}{8}$

$⇒ \frac{7}{2} + \frac{7}{4} + \frac{19}{8}$

$⇒ \frac{7 \times 4 +7 \times 2 + 19 \times 1 }{8} = \frac{28 + 14 + 19}{8}$

$= \frac{61}{8} = 7 \frac{5}{8}$

★which lies between the whole numbers 7 and 8.

Now,

$⇒ \frac{64}{8} = 8 \textbf{ \: and} \: \frac{56}{8} = 7$

Therefore,

The Rational number to be added to

$\frac{61}{8} \: \textbf{to \: get \: } \frac{64}{8} \: \textbf{is \: } \frac{64}{8} - \frac{61}{8} = \frac{3}{8}$

and the rational number to be subtracted from

$\frac{61}{8} \: \textbf{to \: get \: } \frac{56}{8} \textbf{ \: is \: } \frac{61}{8} - \frac{56}{8} = \frac{5}{8}$

$\\ \\ \\ \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙ⌨}$