26 practice questions on adding-and-subtracting-integers from the The Other Side of Zero section of the UPSC Prelims syllabus. 26 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.
Starting at $-2$ on the number line, which move lands on $-9$?
Correct answer: D - $7$ steps to the left
Going from $-2$ to $-9$ means decreasing by $7$, which is $7$ steps left. Moving right would increase the value, and $9$ steps left would reach $-11$.
What is $(-12) + 12$?
Correct answer: B - $0$
An integer and its opposite cancel exactly, so the sum is $0$. Answering $24$ ignores the minus sign and adds the sizes.
Subtracting an integer is the same as
Correct answer: D - adding its opposite
The rule $a - b = a + (-b)$ turns every subtraction into an addition. Adding the same integer would give a different answer, and signs may never simply be ignored.
What is $13 + (-13)$?
Correct answer: C - $0$
An integer and its opposite are the same distance from zero on opposite sides, so they cancel exactly to give $0$. Answering $26$ ignores the minus sign.
What is $(-4) + 9$?
Correct answer: C - $5$
Starting at $-4$ and moving $9$ steps right passes zero after $4$ steps and continues $5$ more, landing on $5$. Answering $-5$ reverses the sign, and $13$ ignores the minus.
The temperature falls from $3^\circ$C by $5$ degrees. What is the new temperature?
Correct answer: D - $-2^\circ$C
A fall means subtracting, so $3 - 5 = -2^\circ$C. The first $3$ degrees bring it to zero and the remaining $2$ take it below.
What is $0 - (-7)$?
Correct answer: C - $7$
Subtracting $-7$ means adding $7$, so $0 - (-7) = 7$. Answering $-7$ treats the double minus as a single one.
On a number line, start at $1$ and move $4$ steps to the left. Where do you land?
Correct answer: C - $-3$
Moving left means subtracting, so $1 - 4 = -3$. The move passes zero and continues three steps beyond it.
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