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MATHS 1 Marks Question

Integers · UP Board (UPMSP) STD 7 (UPMSP - English Medium). 82 questions.

Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
While multiplying a positive integer and a negative integer, we multiply them as _____ numbers and put a _____ sign before the product.
Answer
While multiplying a positive integer and a negative integer, we multiply them as whole numbers and put a negative sign before the product.

Solution:

When multiplying a positive integer and a negative integer, we multiply them as whole numbers and put a negative sign before the product.

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Question 521 Mark
$(-8) + (-8) + (-8) = \_\_\_\_\_ \times (-8)$
Answer
Let $x$ be the missing number.
Then, $-8 - 8 - 8 = x \times (-8)$
$\Rightarrow-24=\text{x}\times(-8)$
$\Rightarrow\frac{-24}{-8}=\text{x}$
$\Rightarrow\text{x}=3$
Hence, $(-8) + (-8) + (-8) = 3 \times (-8)$
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Question 531 Mark
$[(-8) + \_\_\_\_\_\_ ] + \_\_\_\_\_\_\_\_ = \_\_\_\_\_\_\_\_ + [(-3) + \_\_\_\_\_\_\_\_ ] = -3$
Answer
$[(-8) + (-3)] + 8 = (-8) + [(-3) + 8]$
$[\because$ addition is associative, i.e. $a + (to + c) = (a + b) + c] = -8 + 5 = -3$
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Question 541 Mark
$a \times b = b \times a.$
Answer
Multiplication is commutative for integers, i.e. $a \times b = b \times a$ where, $a$ and $b$ are integers.
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Question 551 Mark
$(-9) + (-11)$ is greater than $(-9) - (-11).$
Answer
$(-9) + (-11) = -9 - 11 = -20$ and $(-9) - (-11) = -9 + 11 = 2$ So, $(-9) - (-11)$ is greater than $(-9) + (-11).$
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Question 561 Mark
$[12 \times (-7)] \times 5 = $_____$ \times [(-7) \times $_____$ ]$
Answer
Multiplication is associative for integers, i.e. $(a \times b) \times c = a \times (b \times c)$
So, $[12 \times (-7)] \times 5 = 12 \times [(-7) \times 5]$
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Question 571 Mark
Integers are closed under subtraction.
Answer
True. Solution: Because, if we subtract two integers we get another integer.
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Question 581 Mark
$(-100) ÷ (-10) = $______.
Answer
$(-100)\div(-10)$ $=(-100)\times\frac{1}{(-10)}[\because$ division is inverse of multiplication$] = (-10)$
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Question 601 Mark
The sum of an integer and its additive inverse is zero $(0).$
Answer
Additive inverse is the number, that when added to a given number yields zero.
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Question 611 Mark
$23 \times (-99) =$_____$\times (-100 +$_____$ ) = 23 \times $_____$ + 23 \times $_____.
Answer
We can write the equation as, $23 \times (-99) = 23 \times (-100 + 1) = 23 \times (-100) + 23 \times 1$
$ [\because$ integers show distributive property of multiplication over addition,
i.e. $a \times (b + c) = a \times b + a \times c]$
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Question 631 Mark
What’s the Error? Reeta evaluated $-4\ + d$ for $d = -6$ and gave an answer of $2.$ What might Reeta have done wrong$?$
Answer
Reeta went wrong in solving $+\ (-6)$ and took it as $+ 6.$ Correct answer $= -4 + d = -4 + (-6) = -4 - 6 = -10$
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Question 641 Mark
$(-237) \times 0$ is same as $0 \times (-39)$
Answer
When we multiply a number with $0,$
we always get $0$
$\Rightarrow (-237) \times 0 = 0$
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Question 651 Mark
$(-5) \times (33) = 5 \times (-33)$
Answer
$\therefore LHS = (-5) \times 33 = (-165)$ and $RHS = 5 \times (-33) = (-165)$ Hence, $LHS = RHS$.
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Question 661 Mark
Product of a negative integer and a positive integer is a positive integer.
Answer
Product of a negative integer and a positive integer is a negative integer, i.e.
$a \times (-b)$
$= -ab$
where, $a$ and $b$ are two positive integers.
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Question 671 Mark
When we change the order of integers their difference remains the same.
Answer
Subtraction of two integers is not commutative,
i.e. $\text{a}-\text{b}\neq\text{b}-\text{a}$ for two integers $a$ and $b.$
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Question 681 Mark
Division is the inverse operation of _____.
Answer
Division is the inverse operation of multiplication.Solution:
Division is the inverse operation of multiplication.
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Question 691 Mark
$(-25) \times (-2) = $_____.
Answer
Two negative integers make the resultant integer,
positive. $(-25) \times (-2) = 50$
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Question 701 Mark
$(-43) +$_____$ = -43$
Answer
Zero $(0)$ is an additive identity for integers,
i.e. $a + 0 = 0 + a = a$ for any integer $a.$
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Question 711 Mark
Social Studies Application: Remembering that $1AD$ came immediately after $1BC$, while solving these problems take $1BC$ as $-1$ and $1AD$ as $+1$ Greek mathematician Archimedes lived between $287BC$ and $212BC$ and Aristotle lived between $380BC$ and $322BC.$ Who lived during an earlier period$?$
Answer
Aristotle lived in an earlier period, as $380BC$ and $322BC$ is earlier than $287BC$ and $212BC.$
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Question 721 Mark
If we multiply five positive integers and one negative integer, then the resulting integer is _____.
Answer
If we multiply $5$ positive integers and one negative integer, then the resulting integer is negative.
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Question 731 Mark
$a ÷ (-1) = -a.$
Answer
$a + (-1) = \frac{\text{a}}{(-1)} = -a$
$[$as division of a negative and positive integer is always negative$]$
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Question 741 Mark
Going $500\ m$ towards east first and then $200\ m$ back is same as going $200\ m$ towards west first and then going $500\ m$ back.
Answer
Case I Going $500\ m$ towards East first, i.e. point $A$ to $B$ and then $200\ m$ back, i.e. $B$ to $C.$

As per the above figure shown, final position is $C,$ i.e. $300\ m$ in East.
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Question 751 Mark
Product of three negative integers is a negative integer.
Answer
Product of three negative integers is a negative integer, i.e. $(-a) × (-0) × (-c) = (-abc)$ where, $a,b$ and $c$ are three positive integers.
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Question 771 Mark
$(-1) \times (-2) \times (-3) = 1 \times 2 \times 3$
Answer
$\because LHS = (-1) \times (-2) \times (-3) = (-6)$
$RHS = 1 \times 2 \times 3 = 6$
Hence, $LHS = RHS.$
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Question 781 Mark
Multiplication fact $(-8) \times (-10) = 80$ is same as division fact $80 ÷ (-8) = (-10)$
Answer
Multiplication fact Division fact
$(-8) × (-10) = 80$ $80 + (-8) = (-10)$
$LHS = (-1) × 8 × (-1) × 10 = (-1) (-1) × 8 × 10$ $LHS = 80 + (-8) = \frac{80}{-8}$
$= 1 × 80 = 20 = RHS.$ $= (-10) = RHS.$
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Question 791 Mark
$(-19) \times (-11) = 19 \times 11$
Answer
Product of two negative integers is a positive integer,
i.e. $(-a) \times (-b) = a \times b$ where, $a$ and $b$ are positive integers.
$\Rightarrow LHS = (-19) \times (-11) = 209 $
$RHS = 19 \times 11 = 209$
Hence, $LHS = RHS.$
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Question 801 Mark
If we multiply _____ number of negative integers, then the resulting integer is positive.
Answer
If we multiply even number of negative integers, then the resulting integer is positive.Solution:
If we multiply even numbers of negative integers, then the resulting integer is positive.
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Question 821 Mark
Sum of two negative integers always gives a number smaller than both the integers
Answer
e.g. Taking two negative integers, i.e. $(-5)$ and $(-3) + (-5) + (-3) = -5 - 3 = -8 = -8 < -5$ and $-8 < -3$
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