If a - b - c - d- thenwhich of the following statement is true-A- a-b-a-n c-b-n dB- a-b a - nc - b - ndD- ac - bd -1

The correct option is A a/b = a + nc/b + nd We have If a/b = c/d then we know ad = bc a( b + nd) = ab + nad b(a + nc) = ab + nbc We have ad = bc ∴ ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Patterns in Equivalent Fractions

If a / b = c ...

Question

If $\frac{a}{b}$ = $\frac{c}{d}$ , then

which of the following statement is true?

$\frac{a}{b}$ = $\frac{a + n c}{b + n d}$

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$\frac{a}{b}$ < $\frac{a + n c}{b + n d}$

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$\frac{a}{b}$ > $\frac{a + n c}{b + n d}$

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$\frac{a c}{b d}$ =1

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Solution

The correct option is A
$\frac{a}{b}$ = $\frac{a + n c}{b + n d}$

We have

If $\frac{a}{b}$ = $\frac{c}{d}$

then we know ad = bc

a( b + nd) = ab + nad

b(a + nc) = ab + nbc

We have ad = bc

$∴$ nad = nbc

Hence $a (b + n d$ = $b (a + n c)$

$∴$ $\frac{a}{b}$ = $\frac{b + n d}{a + n c}$

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If ab = cd, then which of the following statement is true?

The correct option is A ab = a+ncb+nd We have If ab = cd then we know ad = bc a( b + nd) = ab + nad b(a + nc) = ab + nbc We have ad = bc ∴ nad = nbc Hence a(b+nd = b(a+nc) ∴ ab = b+nda+nc

If $\frac{a}{b}$ = $\frac{c}{d}$ , then

which of the following statement is true?

The correct option is A
$\frac{a}{b}$ = $\frac{a + n c}{b + n d}$

We have

If $\frac{a}{b}$ = $\frac{c}{d}$

then we know ad = bc

a( b + nd) = ab + nad

b(a + nc) = ab + nbc

We have ad = bc

$∴$ nad = nbc

Hence $a (b + n d$ = $b (a + n c)$

$∴$ $\frac{a}{b}$ = $\frac{b + n d}{a + n c}$