5 Marks Questions

Question 15 Marks

Simplify:
$7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\Big)\Big\}\Big]$

Answer

Given expression:

$=7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{3}{2}-\frac{1}{6}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{9-1}{6}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\times\frac{4}{3}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{2}{3}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{15-8}{12}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\frac{7}{12}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\times\frac{12}{7}\Big]$

$=\frac{15}{2}-\frac{27}{7}$

$\frac{105-54}{14}=\frac{51}{14}=3\frac{9}{14}$

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Question 25 Marks

Match the following:

$1.$	$625 \times 436 = 625 \times 400 + 625 \times 30 + 625 \times 6$	$a$	Commutativity under addition.
$2.$	$25 \times 69 \times 8 = 25 \times 8 \times 69$	$b$	Commutativity under multiplication.
$3.$	$60 + 19758 + 840 = 60 + 940 + 19758$	$c$	Distributivity of multiplication over addition.

Answer

$1.$	$625 \times 436 = 625 \times 400 + 625 \times 30 + 625 \times 6$	$a$	Distributive of multiplication over addition.
$2.$	$25 \times 69 \times 8 = 25 \times 8 \times 69$	$b$	Commutative under multiplication.
$3.$	$60 + 19758 + 840 = 60 + 940 + 19758$	$c$	Commutative under addition.

$i.\ 625 \times 436 = 625 \times (400 + 30 + 6)$
$= 625 \times 400 + 625 \times 30 + 625 \times 6$
This is the distributive law of multiplication over addition.
$ii.\ 25 \times 69 \times 8$
$= 25 \times 8 \times 69$
This is the commutative law of multiplication.
$iii.\ 60 + 19758 + 840$
$= 60 + 940 + 19758$
This is the commutative law of addition.

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Question 35 Marks

Simplify: $4\frac{4}{5}\div\Big\{2\frac{1}{5}-\frac{1}{2}\Big(1\frac{1}{4}-\overline{\frac{1}{4}-\frac{1}{5}}\Big)\Big\}$

Answer

Given expression: $=4\frac{4}{5}\div\Big\{2\frac{1}{5}-\frac{1}{2}\Big(1\frac{1}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{5}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{5}{4}-\frac{1}{20}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{25-1}{20}\Big)\Big\}$
$=\frac{24}{5}\Big\{\frac{11}{5}-\frac{1}{2}\times\frac{24}{20}\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{12}{20}\Big\}$
$=\frac{24}{5}\div\Big\{\frac{44-12}{20}\Big\}$
$=\frac{24}{5}\div\frac{32}{20}$
$=\frac{24}{5}\times\frac{20}{32}$
$=\frac{3}{4}\times4=3$

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Question 45 Marks

What least number must be subtracted from $13801$ to get a number exactly divisible by $87?$

Answer

We have to find the least number that must be subtracted from $13801$ to get a number exactly divisible by $87.$
So, first we will divide $13801$ by $87.$

Remainder $= 55$
The number $55 $should be subtracted from $13801$ to get a number divisible by $87.$
i.e., $13801 - 55 = 13746$

$\therefore$ $13746$ is divisible by $87.$

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Question 55 Marks

Match the following columns on whole numbers:

S.No.	Column A	S.No.	Column B
$(a)$	$137 + 63 = 63 + 137$	$(i)$	Associativity of multiplication
$(b)$	$(16 \times 25)$ is a number	$(ii)$	Commutativity of multiplication
$(c)$	$365 \times 18 = 18 \times 365$	$(iii)$	Distributive law of multiplication over addition.
$(d)$	$(d) (86 \times 14) \times 25 = 86 \times (14 \times 25)$	$(iv)$	Commutativity of addition
$(e)$	$23 \times (80 + 5) = (23 \times 80) + (23 \times 5)$	$(v)$	Closure property for multiplication

Answer

S.No.	Column A	S.No.	Column B
$(a)$	$137 + 63 = 63 + 137$	$(iv)$	Commutativity of addition
$(b)$	$(16 \times 25)$ is a number	$(v)$	Closure property for multiplication
$(c)$	$365 \times 18 = 18 \times 365$	$(ii)$	Commutativity of multiplication
$(d)$	$(86 \times 14) \times 25 = 86 \times (14 \times 25)$	$(i)$	Associativity of multiplication
$(e)$	$23 \times (80 + 5) = (23 \times 80) + (23 \times 5)$	$(iii)$	Distributive law of multiplication over addition

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